Compensation and Performance

Suppose you are an employer and thinking about how to compensate your workers. If you pay them a fixed salary, you have a good idea of what your costs are going to be. However, there is uncertainty about revenue. If you pay your workers a fixed salary and the company has a very good year, all the extra revenue is a windfall. However, if you have a bad year, you might have to let those workers go, or you might have to completely shut down your business.

Alternatively, you could write a different employment contract. You could make your workers’ salaries a function of revenue. When times are good, workers get more compensation. When times are bad, workers get less compensation. This eliminates the windfalls you will get during good times, but it reduces your costs during bad times.

The pay structure also affects the workers’ incentives. Imagine you own a roofing company. You could pay your workers hourly or you could pay them by the job. If you pay them by the job, they will have an incentive to finish each job quickly so they can move on to the next one. More jobs mean more revenue for you and more compensation for your employees. However, by paying them by the job, you are incentivizing speed. In doing so, you might also incentivize carelessness, which might lead to roofing shingles blowing off the roof during a storm. This creates unhappy customers and reduces the present discounted value of future demand.

By contrast, paying the workers by the hour disincentivizes speed. Workers will not necessarily be in a rush to complete a job because they get paid the same amount for a given number of hours, independent of how many jobs they complete. That could result in higher-quality work. The workers are more likely to take their time and do the job correctly since they don’t have a financial incentive to get to the next job. However, fixed hourly pay might lead them to shirk.

Which option you choose is likely to be determined by my ability to monitor the workers. Armen Alchian and Harold Demsetz presented a theory of the firm based on monitoring and information costs. According to their theory, when workers are engaged in team production but their individual productivity is difficult to monitor, you are likely to get shirking. The solution to this problem is to hire a manager who can monitor the workers and whose compensation is tied to the success of the firm.

However, it is important to ask what the manager can monitor and how costly it is to do the monitoring. My roofing example illustrates a point made by Yoram Barzel that wage contracts require monitoring effort whereas per-job contracts require monitoring the quality of output. The option you choose will depend on the relative costs of each type of monitoring.

Many contracts are not either/or compensation schemes. Many contracts are fixed compensation plus incentives. This works when the output in question is easy to identify. For example, suppose that you want to hire someone to build a new factory. It is important that the factory be built by a particular time. You might offer to pay the builder a fixed dollar amount for construction with a bonus if it is finished by a particular date.

We also see this in sports. Professional athletes are often compensated for achieving easily measured outputs. The same is true of coaches, who are often given a base salary with additional earning opportunities tied to performance.

It is obvious why this would apply to sports. Inputs are hard to measure. Think about coaching. Every coach has their own philosophy on how the team should practice. Some coaches like to coach hard. Other coaches like to practice light to keep their players healthy. Some coaches like to yell at their players. Others prefer positive reinforcement and prefer not to yell. If I hire a coach and I try to monitor the coach’s performance based on the inputs, like observing how many hours he spends in his office or at practice and how he runs practices, it is probably going to be difficult to do. Successful coaches don’t have one observable style. What works for one coach might not work for another.

Outputs, however, are easy to measure. The coach’s team is either going to win or lose. I can easily observe which outcome occurs. Thus, it is much better to use incentive-based compensation for the output than the coach’s input.

Financial Markets

Now let’s return to how I began the previous section and discuss uncertainty. There are various sources of uncertainty in production. Let’s think about a specific example. Imagine that you are a farmer. Some amount of your production is determined by your inputs, the amount of seed you plant, the type of seed you plant, the amount of irrigation you provide, etc. However, some things are beyond your control. Bad weather can lead to a bad harvest in terms of a reduction in yields, lower quality crops, or even the loss of particular types of crops. The same can be said for infestations by insects or pests that trample, eat, or destroy some of the crops. You also face uncertainty about the price of the crops that you are selling. You plant your crops with some expectation of what the price will be. However, a lot of things can happen between when you plant and when you take the crops to market.

Let’s focus specifically on this price uncertainty. Farming is a time-to-build production process, by definition. You have to expend the resources to plant, fertilize, and irrigate. The output comes later, when the crops grow. Fluctuations in prices therefore create a risk. What you are willing to invest ahead of time depends on what you expect prices to be when you bring your harvest to market. If you come to market when prices are higher than you expected, you get a windfall. If you come to market when prices are lower than expected, you might not have enough to cover the wages that you have paid. The equity you have in your farm is the amount of assets less liabilities. Should you not have the revenue to cover the costs, your equity will decline as you cover those costs. If the revenue is sufficiently low, you might not have enough equity to cover the costs and will become insolvent.

The really bad outcome here is the downside risk. If your goal is income and survival, then you might be willing to forgo the chance at a windfall for greater certainty about the price.

This is where financial markets come into play. Suppose that you are worried about the price of your crops. What if you could sign a contract today to sell those crops at a fixed price in the future? That would solve your uncertainty problems. But who would accept that risk?

It turns out that there are people who might be willing to bear the risk. For example, someone who uses your crops as an input in production. Whereas high prices produce a windfall for you, they increase the costs of production for others and make it harder for them to compete. They want to eliminate upside risk in the price. You want to eliminate downside risk. Thus, you sign a contract with a fixed price ahead of time and neither of you has to worry what happens to the price in the interim.

Another person who might be willing to agree to this contract is a speculator. Suppose that this contract is tradable. The speculator might buy the contract in the hopes of selling it for a profit at a future date if the price rises. The cost to the speculator is that there is a chance that when the contract expires, the price has fallen. The speculator will then need to sell the contract to someone willing to take delivery of your crop and doing so will result in a financial loss for the speculator.

This type of trading occurs in futures markets. However, with prediction markets, there are all sorts of opportunities to do something similar.

Prediction Markets, Universities, and Hedging

All of that brings me back to the subject of the introductory paragraph. Some trades have been made on prediction markets with payouts equal to bonuses built into college football coaches’ contracts. To be clear, the schools themselves did not make these trades.

College football coaches tend to have fairly standard contracts. There is a base salary and then there are incentives built into the contract. Making the playoffs and advancing to each of the next rounds of the playoffs and winning the championship tend to produce bonuses for coaches.

When we discuss these contracts, these clauses are often referred to as “contract incentives.” However, as I just discussed, there are a couple of reasons why you might include bonuses in a contract. The first is that you are paying for performance. The second reason is that you are sharing some of the risk associated with random things that could go wrong. The revenue generated by the school will be tied to the success that the team has on the field. Players get hurt. Games are played in bad weather, which mitigates raw athletic differences. Star players have bad games. Mediocre opponents play the greatest game of their lives. Bad luck might limit ticket sales or playoff appearances, which reduce revenue. Including bonuses tied to performance means the school and the coach share that risk.

What is remarkable about the recent story is that it seems that schools like LSU and South Carolina (those included in the story) seem to be betting on their own successful performance using prediction markets. By doing so, they are able to insure themselves against their own success, which would result in significant bonuses for their coaches.

Although the schools are not directly involved in these trades, there are insurers that have underwritten policies to cover bonus payouts in the past. It is possible that the trades are a coincidence. However, it would be quite the coincidence for the payouts from five trades to almost exactly equal to the bonus amounts in Lane Kiffin’s contract at LSU. What seems more likely is that insurers or other third parties representing the schools are using prediction markets to manage their budgets and protect themselves against large bonus payments in the event of on-field success.

Why use insurers or third parties to interact with prediction markets? This seems like regulatory arbitrage. College athletics has strict rules about gambling on sports. One recent scandal involved quarterback Brandon Sorsby, who was deemed ineligible to play when it was revealed that he had placed thousands of sports bets using online betting apps. Players and staff are prohibited from gambling. Although prediction markets are not operated by sportsbooks, NCAA rules do not seem to care about the distinction. One way to get around this would be to pay an insurance premium to an established insurer. In exchange, the insurer takes some of that premium and uses it to purchase event contracts with prediction markets and keeps what is left of the premium as its profit for serving as middleman.

There is reason to believe that this might happen more frequently in the future. College sports are now permitted to share revenue with their student-athletes. Some sports have significant costs but very little revenue. Salaries for coaches remain quite high. To compete, schools are facing tighter financial constraints. As a result, schools might be willing to effectively pay a higher base salary by using prediction markets to price the risk of their success. As prediction markets become more liquid, they might price risk more accurately. Insurers and other third parties might find it profitable to serve as a middleman between the schools and the prediction markets.

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Without solving the full optimal pricing problem, we know for sure that the seller won’t sell to everyone who values the good more than they do. This is the first thing we learn about. “Monopolies” restrict output. Nothing weird about this.

Now, let’s think of a slightly different situation. Instead of selling the good in a normal fixed-price setup, we’re in an auction room, and the seller has one object. Let’s assume they don’t care for it and it is worth nothing to them. There are two bidders who both value the good more than zero. Suppose A values it at $4 and B values it at $12. There is $12 of value in the room, the object is worth nothing to the seller, and if the seller wants the most money, the right move is to sell to neither of them. Refuse both bids.

How is that possible? I’m not pulling any tricks. I’m not assuming there is a second round. The auction ends, and everyone goes home, and the object stays unsold.

What I want to convince you of today is that this monopoly output restriction, which is week 3 stuff in Econ 101, is the same thing as the seemingly more complicated problem of the auctioneer.

More than that, sometimes the seller does sell, and sells to the bidder who values the object less. The high bidder goes home with nothing, and the low bidder walks out with the object. So we can’t summarize that as restricting output.

So what’s going on? That’s what this newsletter is about.

In a 1989 paper, Jeremy Bulow and John Roberts gave us the tools, which we will go through today. (Bulow has so many bangers.) There will be a little bit of notation and graphs along the way but no real math to worry about.

From values to demand curves

Let’s start with one buyer (not bidder yet). I’ll follow Bulow and Roberts’s numbers. A’s value is somewhere between 0 and 10. If we want to be precise, it’s drawn from a uniform distribution (each value is equally likely) between 0 and 10.

If the seller posts a price of $8, A will buy whenever his value exceeds $8, which happens 20% of the time. The seller has an expected revenue of $1.60. On the margin, lowering the price will attract bidder A when he values it below $8, but the seller will collect less when he values it above $8.

This generates the usual marginal revenue trade-off. How much do you get by trying to sell the product a little bit more? We’re used to thinking about selling one more unit of the good. Here since we have one good, we can think of the probability of sale and selling a bit more often.

This is easier to visualize if we don’t have a uniform which is a straight line. More generally, if the bidder has a value from some cumulative distribution function (CDF of v), given by F(v), we can plot that on the left. If we imagine a posted price, this just flips to become the demand function (but with quantity on the y-axis). We can flip again to get our more standard inverse demand function.

If we think of a uniform distribution of values, this becomes the usual linear demand curve that we teach in Econ 101.

Bulow and Roberts show how that MR curve is what auction theory calls the virtual value.

Hard floors

Assume that you want to set some floor, a “hard floor.” You will not sell it to any bids below some price. Where do we find that? If you’d ask most people, maybe one idea would be to set it at the seller’s own value. That’d be the efficient thing to do, and you’d make sure that you always give it to somebody who values it more than the seller.

Let’s think about two bidders from the same distribution, uniform on (0,10). Let’s suppose we have a second-price auction with no reserve. That means people announce their bids, and the high bidder wins and pays the low bidder’s bid.

You can do better by setting a hard floor and refusing to sell below it. Suppose you set the floor at $5, which is where the MR curve hits zero, then traced up to the demand curve. It is the optimal floor to set, where the marginal revenue curve is zero.

Notice that my argument did not depend on how many bidders show up. The floor only matters in two different situations:

1. Nobody clears the floor, so there is no sale.

2. Exactly one bidder does, and they pay the floor.

In both of those cases, everyone else is below the floor and basically out of the picture. Whatever the number of bidders is, the seller in those situations is a one-bidder monopolist facing one demand curve, and sets the floor where that curve’s marginal revenue hits zero, $5. More bidders make those situations less common but they don’t change where the floor is.

Price discrimination

Now let’s let the two bidders differ. Again, I’m gonna follow Bulow and Roberts’ example, so you can check the numbers. Suppose bidder B’s value is uniform between 10 and 30, so B always values the object more than A possibly could. We can do the same thing and draw their marginal revenue curve.

From here, we are able to calculate the reserve price for each market if they were separate: $5 for A and $15 for B, where each marginal revenue curve hits zero.

In the price theory, monopoly translation, we can think of each bidder as a separate market. Adding B doesn’t change A’s demand, does not make it more elastic, or change the marginal revenue curve. This competition doesn’t enter through that margin.

Competition instead operates through a capacity constraint. The seller only has one unit. Since we have one unit, the marginal cost is zero up to one and then infinite above that. This jump didn’t matter with one buyer but it does show up with two.

Suppose both bidders bid above their reserves, so the seller cannot serve both, and the marginal cost of the unit in A’s market is no longer zero. The marginal cost (opportunity cost) is what the seller gives up by not selling to B. What she would have collected from B is, on average, B’s marginal revenue. So the marginal cost of the unit in A’s market is B’s marginal revenue at B’s bid.

Selling to the low bidder

So who gets the good? Suppose A truthfully reports a value of $8 and B reports $17.

We can go back to their marginal revenue curves and see that the MR for A is 6 and for B is 4. So “on the margin” giving the good to A is more valuable than it is to give to B. We should have a rule that gives the good to the low value in this case. We can keep going and find the boundary at which these MR curves are the same to find the rule.

Set the two marginal revenues equal. A’s is 2a − 10 and B’s is 2b − 30, so they match when a = b − 10.

This turns into the following auction. To determine who wins, subtract $10 from every bid B makes, then run an ordinary second-price auction with a $5 floor. A pays the larger of $5 and b-10, B pays the larger of $15 and a+10.

At $4 and $12, neither bidder is above each’s floor, and the object stays with the seller. At $8 and $17, A clears his floor, beats B’s adjusted bid of $7, and pays $7

Real auctioneers already use both instruments, floors and handicaps, usually for other reasons. Bidding credits for small firms in the FCC’s spectrum auctions are a handicap, and Ian Ayres and Peter Cramton argued they raised the government’s revenue.

As Bulow and Roberts point out, this is just standard optimization, so we can apply this to much more complicated problems. The general rule is “allocate units to the buyers with the highest marginal revenues, by choosing prices to equate the marginal revenues of the lowest-valued buyers actually supplied in each market.”

That’s really all any of this is, whether a fixed price or an auction. People optimize, and adjust. Everything is price theory, if you hadn’t figured that out from this newsletter.

With that in mind, I would like to address a topic that has received a lot of attention recently. That topic is central bank independence. We try not to write much about politics here, except to give context or explain what policymakers are doing or whether a policy will accomplish its stated goals. However, it is hard to avoid mentioning the politics of this topic. The discourse about central bank independence is largely a response to what many perceive as political pressure being put on the Federal Reserve by the Trump administration to lower interest rates.

In my view, the political aspect of the issue has been to the detriment of the discourse. Much of the recent discourse consists of people saying “we all know that central bank independence is good.” Some of the better discourse will at least cite an old paper by Alberto Alesina and Larry Summers showing a negative relationship between inflation and their index of central bank independence.

However, the literature on central bank independence is more nuanced than this popular discussion would make you think. We need to think carefully about how we are defining independence. We also need to keep in mind that decisions have tradeoffs. Sure, independence has benefits, but what are the costs? How do we assess the benefits and the costs, and what are the implications for independence?

Tradeoffs

A simple lesson from price theory is that we rarely end up in corner solutions. The opportunity cost of consuming more apples is that I have to consume fewer bananas, but generally I’m not going to consume only apples or only bananas.

When it comes to central bank independence, it is easy to see the potential benefits. If politicians can tell central bankers what to do, then they might direct the central bank toward actions that create short-term benefits for themselves, but impose costs on the general public. For example, increasing the money supply prior to the election might cause a short-term boost to economic activity and improve the politician’s election prospects. However, in the longer-term, this doesn’t make the public better off because the increase in the money supply will simply lead to a higher price level.

Similarly, if politicians know that they can force the central bank to monetize the debt, this effectively relaxes the government’s budget constraint. Politicians will spend more and tax less, resulting in higher inflation for the general public.

The benefit of central bank independence is that it removes politicians from the decision-making process. In doing so, it helps to reduce or eliminate government spending financed by money creation and the type of political business cycle I just described.

It is important to remember, however, that central bank independence also has costs. Consider a central bank that is completely independent of the political process. If that is the case, how could anyone hold the central bank accountable for bad policy decisions or mistakes? No one wants to experience the consequences of bad monetary policy. Even policymakers with the best of intentions might produce bad outcomes.

Thus, although the benefits of central bank independence are pretty obvious, there are costs as well. There is a tradeoff between independence and accountability. The design of a central bank must take this tradeoff into account. In fact, I would argue that the design of many modern central banks does demonstrate a recognition of this tradeoff. However, to see it, you have to understand the nuances of what is meant by central bank independence. The common, broad definition is too imprecise.

What is meant by independence?

People seem to get the basic idea behind central bank independence. It means that the central bank is independent of the political process. But is it? In what way? Certainly, if we think about the Board of Governors of the Federal Reserve, its members are appointed by the president and approved by the Senate. To what extent is that independent of the political process?

Shortly after Alesina and Summers published their paper, Guy Debelle and Stanley Fischer wrote their own paper that addressed the tension between independence and accountability. They separated out three types of independence. There is goal independence (the ability of the central bank to set its own objective), political independence (the role of government in appointing policymakers at the central bank), and instrument independence (the ability of the central bank to conduct policy as it sees fit). They find that the only type of independence that matters for inflation is instrument independence. In fact, they find weak evidence that goal dependence actually lowers inflation. This suggests that what matters for low inflation is having the government set the goal while giving the central bank controls over the day-to-day operations.

More recently, Ed Balls, James Howat, and Anna Stansbury wrote a paper that starts with a puzzling result. If you look at the data during the 1980s on central bank independence and inflation, you see the clear negative relationship that Alesina and Summers highlighted. However, if you look at the data from the early 2000s, you see that many central banks in developed countries converged on low inflation rates despite there being substantial variation in the index measuring central bank independence. This is puzzling if you think central bank independence is important.

They dig a little deeper and differentiate between what they call political independence (the inability of politicians to influence goals and personnel) and operational independence. What they find is that operational independence has a negative and statistically significant relationship with inflation. They find no evidence that political independence matters.

Examination of central banks throughout the developed world suggests that this tradeoff between independence and accountability is recognized. Central banks tend to have limited, if any, control over their goals. These goals typically come from the government. Most central banks in the developed world have instrument independence, and all of them have some degree of accountability to the government in the form of reports and testimony to legislative bodies.

Concluding Thoughts

Some might read this and think that I am being a bit persnickety in my discussion of central bank independence. Perhaps what people have in mind is operational or instrument independence when they refer to central bank independence.

Nonetheless, I do not think this is trivial. I think that we need to be precise about how we discuss central bank independence. Holding up independence as a particular ideal without properly defining what we mean necessarily pushes accountability to the background. Accountability is important. Throughout their short history, central banks have been known to make mistakes because they have become wedded to a particular ideology or a particular macroeconomic theory. These have typically been costly mistakes. However, even when central banks didn’t suffer from these problems, they have still made mistakes. Good intentions do not rule out bad outcomes. For these reasons, it is important not to dismiss issues related to central bank accountability.

Those who shout about the virtues of central bank independence from the rooftops would be wise to specify what they mean by independence and to communicate in ways that reflect the modern evidence. Absolute independence is neither desirable in theory nor supported by the evidence. Particular types of independence are important. Accountability matters too. We economists spend most of our time discussing tradeoffs. This issue should be no different.

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The U.S. dollar is the global reserve currency and the U.S. Treasury security is the global reserve asset. I will refer to this as the "Treasury Standard.” What I try to do in my paper is explain how that system emerged as part of an evolutionary process related to the state’s desire for emergency finance. That sounds like a lot (it is, it’s a long paper!), but hopefully I can summarize the main arguments and interested readers can read the complete paper for more details.

The basic theme that runs throughout the paper is that a monopoly over money provides a unique ability for the state. If we understand this role and the commitments required of the state, we can better understand the evolution of the monetary system over time.

A basic place to start is to consider the fact that the sale of monopoly privileges was once a source of revenue for the state and various state monopolies have come and gone. Yet, the monopoly over money has been quite durable. So what is unique about money?

In the paper, I argue that the state’s desire for a monopoly over money is driven by the need to raise large sums of revenue in a short period of time during national emergencies, like war. Debasement, devaluation, and inflation provide the state with the ability to satisfy this demand for revenue. However, this is only possible if the state maintains a credible commitment to stabilize the purchasing power of money over the long run. In the absence of this commitment, continued use of debasement, devaluation, and inflation will reduce the demand for money and thus the “tax base” for seigniorage.

If this idea is correct, then one would expect to see the state monopoly over money driven the needs to finance war. Successful exploitation of the monopoly should correspond with a commitment to price stability (and one should be able to predict who can commit to price stability based on the expected durability of rule). Furthermore, changes in political, economic, and military constraints faced by the state should change the nature of the monetary system.

This seems to be generally true. A.R. Burns argues that ancient monopolies over the mint were motivated by war finance. George Selgin and Larry White point at the prerogative over coinage fluctuated with the borders of the realm in the Middle Ages. And even back then, there is evidence from Ancient Greece and the Middle Ages in England that rulers understood that exploiting the monopoly required periodic recoinage to restore the metallic content (and thus the purchasing power) of the currency.

In thinking about the modern world, I argue that a significant change in military constraints occurred in conjunction with the "Military Revolution." This was the shift to gunpowder, cannons, trained infantry, and complex fortifications that made warfare vastly more expensive.

I illustrate the importance of this shift by contrasting the fiscal approaches of England and Sweden during this period. England used the Bank of England to borrow heavily during warfare. They combined their wartime money printing with a commitment to revert to the original gold parity once peace was restored. This anchored long-term money demand and enabled large-scale deficit spending that ultimately bankrolled English military triumphs.

Sweden, on the other hand, lost its Baltic empire. The Riksbank wasn’t legally permitted to issue notes. Thus, it lacked institutional capacity to suspend convertibility while credibly recommitting to a future peg, causing funding woes that ultimately led to defeat in the Great Northern War.

This tool used by the Bank of England spread across Europe. States could monetize wartime budget deficits through convertibility suspensions. Despite short-run inflation, credible resumption commitments preserved long-run money demand could facilitate a large amount of borrowing.

By World War I, it was commonplace to suspend gold convertibility and commit to restoration. However, in the aftermath of World War I, countries sought to avoid the postwar deflation, but lacked a credible commitment for cooperation. The result was an international scramble for gold, which resulted in deflation and depression. Those chaotic interwar years convinced policymakers that there was a new monetary paradigm.

Enter Bretton Woods. The dollar was formally made the global reserve currency at a fixed gold parity. This meant that other states could settle imbalances in U.S. currency rather than draining American gold coffers. The logic was that since dollars were redeemable for gold, the Fed could create more dollars. A scramble for gold would be unnecessary in that system since the dollar and gold were perfect substitutes. And since the Federal Reserve could create more dollars, the world could avoid deflation.

The flaw in that system is that perfect substitutability cannot be determined by edict. It is a market outcome.

The expansionary fiscal policy and expansionary monetary policy of the 1960s put pressure on that substitutability. American policymakers responded with agreements to redeem dollars for U.S. Treasury securities rather than gold and what might politely be described as diplomatic arm-twisting. When the final collapse proved inevitable, Nixon closed the gold window. Nixon’s advisers had advocated this as a tool to motivate U.S. allies to come to an agreement about revaluations of their currencies. But the gold window was never re-opened. This paved the way for the Treasury Standard.

In the aftermath of the Nixon shock, U.S. policymakers took deliberate steps to keep the U.S. dollar as the global reserve currency. In the wake of oil shocks, the U.S. used it veto power to sideline efforts by the IMF to deal with the corresponding payment imbalances. The U.S. also made a secret agreement with the Saudi Arabian government for the Saudis to use their surplus dollars to purchase U.S. Treasury securities.

The subsequent reduction in inflation and commitment to low, stable rates of inflation by the Federal Reserve, combined with the Fed’s independence created the commitment mechanism required for emergency finance. Furthermore, given that the reserve asset is a debt instrument of the U.S. government, emergency financing temporarily increase those reserves. But the expectation that emergencies are temporary implies that the effect on the cost of borrowing is minimal. In addition, the Treasury Standard creates a tool of foreign policy of the U.S., since the U.S. can use dollar-based sanctions against foreign adversaries. In each sense, the current international monetary system resembles monetary systems of the past.

But this system is potentially fragile. As the world economy grows, the demand for reserves grows along with it. All else equal, this tends to drive down yields and incentivize policymakers to increase debt in conjunction with the increase in the demand. As long as debt remains sufficiently low, this is fine. However, if debt reaches a critically high level, people might expect that the U.S. is incapable of repaying the debt and will resort to inflation. These expectations can be self-fulfilling. In addition, the increased weaponization of the dollar as a tool of foreign policy is also a threat to the system. Excessive sanctions may drive targeted states towards establishing dollar alternatives.

This theory, history, and discussion should hopefully give one a better idea of how we got here, why we got here, and what the threats to the future of the system are. Despite the potential fragility of the system, I will stop short of forecasting the future of the dollar. Nonetheless, hopefully this post does a good job of explaining why the dollar is a source of U.S. hegemony and the inherent trade-offs associated with that. It should also hopefully give the reader a sense of how the U.S. is likely to respond if it sees this hegemony threatened. And if you’d like to read more, there’s always the paper.

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“Why do all SUVs look the same?” Hotelling.

“Why are all social media video reels the same?” Hotelling.

“Why does every restaurant have a chicken sandwich?” Hotelling.

The Hotelling model is one of the core models of competition in economics. In the world of imperfect competition, it’s Bertrand, Cournot, and Hotelling as the big three. That is the usual takeaway from Hotelling: sellers converge. It is certainly what I emphasized when teaching Econ 101. In the original Hotelling model, differentiation is often described as “location.” Where should I locate my shop when people have to come to buy stuff? But you could generalize that to be something like product type or quality in a more abstract space.

That’s fair for Econ 101. We can go a bit deeper at Economic Forces. I’ve been thinking a lot about Hotelling while updating my paper on the waterbed effect, so let’s talk.

In general, there are really two forces going on in the Hotelling model. You can pick a location, but you can also pick a price, and the interaction between those two pushes against each other. Moving further away allows you to increase price through differentiation. Moving closer allows you to capture more consumers, but you have to lower your price to win those consumers. Let’s call that the differentiation force, which is a reason for the sellers to differentiate from each other. That force allows them to raise the price and is a reason for the sellers to move away from the middle.

Let’s work through when each force dominates.

The classroom model

As is usual, the textbook version strips a few things down. Take, for example, McCloskey’s Applied Theory of Price. In that book, she teaches, like other textbooks do, that you have two sellers picking spots on a road. That’s it.

Imagine a beach with consumers spread out from one end to the other. There are two ice cream carts that charge the same price for their ice cream. They sell the same ice cream, and they have the same sort of cost for their ice cream. Consumers simply walk to whichever cart is closer in this situation.

Suppose one cart stands a quarter of the way down the beach, and the other stands 3/4 of the way down the beach. The consumer at the midpoint is indifferent, and each cart serves half the beach.

Now move the left cart towards the center a little bit. It keeps all of the consumers it was already winning on the left, but it wins some of the consumers on the right, so it wants to. Same thing with the ice cream cart on the right: if it moves a little toward the center, it wins more customers and doesn’t lose any. That logic keeps pulling the carts together until they both reach the midpoint. This is the convergence of Hotelling’s Law, or the “principle of minimal differentiation.”

This is also why you get the median voter result. There are no explicit prices, and so you move to the middle, to the median voter, under similar assumptions of one dimension etc. You break that result in a variety of ways, but one way is for the candidates themselves to have a preference, and that then becomes like a cost, pulling them the other direction, the other force pushing them away from the median. We need to have some opposing force, which is absense in the first past Econ 101 model.

Instead of pure location, you may have seen alternative “Hotelling model” which fixes the location and asks how firms are going to price. This is the type I’ve been working on recently, starting with the waterbed paper I wrote about in this newsletter.

In that model, as far as you’re concerned as a seller, you just face some demand curve that you back out from the locations and pricing of the other seller. There, by assumption, there is no convergence, but firms do think about the trade-off of pricing.

Hotelling had both

But neither of those is “Hotelling” in the original sense. Hotelling’s 1929 paper didn’t have this fixed-price location game. He allowed the sellers to choose prices and then used the resulting profits to study where they would locate. He had a fuller model of pricing and location, this two-dimensional competition.

Unlike the classroom example, Hotelling wasn’t tipping the scale towards convergence. He had this interaction between these two forces pulling in opposite directions, where moving further away from the center would allow you to increase prices through differentiation.

Hotelling worked backwards to solve his model. He took the sellers’ locations as given and calculated the prices that they would charge. He then fixed the location of one seller, say A, asked the other seller, B, where it would locate, and vice versa. Kind of a crude way of trying to construct an equilibrium but it was 1929.

As B moved closer to A, Hotelling’s calculation said that B would attract more customers and charge a higher price. Moving closer intensified competition with A but also placed B between A and the larger body of consumers. That stiffer competition created by proximity was always outweighed by the larger consumer base.

Hotelling assumed that travel costs were linear, with additional miles equally painful, regardless of where the consumer starts. That creates a constant force, whether you move from the far left a little bit or from roughly the center all the way to the center. That travel cost that the consumer is giving up is the same. linear costs limit the benefit from differentiation. In Hotelling’s model, the convergent force with that constant fixed level of linear travel cost always dominates.

So we get convergence.

Fixing Hotelling

First, it’s important to note there was an issue in Hotelling, as with many mathematical papers from that time period. To make the problem tractable, Hotelling assumed that a small change in price would produce a small change in demand. That may not be true in general. You can have discontinuities, like in a Bertrand model. It took 50 years but this was ultimately made explicit by Claude d’Aspremont, Jean Jaskold Gabszewicz, and Jacques-François Thisse, although Hotelling noticed it in a footnote but dismissed it.

They also clarified the forces further. Instead of linear cost, they replace that with quadratic costs before allowing the firms to choose prices. This means the marginal tradeoff from moving from 1 mile to 1.1 miles is different from 2 to 2.1. Now, with this growing mismatched location travel cost, the balance between reaching more customers and insulating yourself from competition can change depending on where you’re going. They show that if you have quadratic costs, the equilibrium is for the sellers to move as far away as possible to the edge of the model.

They have a Hotelling location model that produces the exact opposite outcome of what we teach in the classroom. You get maximum differentiation. It’s Hotelling. People are choosing location. It’s also Hotelling in that they’re choosing prices.

You can see this logic by thinking of moving the left firm a little inward from the endpoint. In the fixed price model, that seller wins customers, as we said, and they don’t lose anyone else. In the price-setting model with quadratic cost, it will still win customers, but in order to do that, it’s going to lower its margins to win those customers. At the endpoint, under their normalization, the loss from the lower margin is twice as large as the gain from new customers, and the inward move is going to lose any money. The exact magnitude is arbitrary, but it shows that at the edge, you don’t have an incentive to move in.

Is it really Hotelling?

Have I ever said that there are tradeoffs? Well, there are tradeoffs here. In general, you are going to want to move closer to your competitors sometimes and move away at other times, and the equilibrium will sort out what happens overall.

In updating that waterbed paper to expand to the big 3 models (spoiler: waterbed doesn’t cause harm in any of them), I realize these models are all just instantiations of the same trade off. The Economic Forces are really close to the traditional Bertrand forces: lowering your price wins consumers but reduces the margin of every unit you sell. Similarly, in a Cournot model, producing more wins sales but pushes down the market price. The fundamental competitive force in all of these is this trade-off between quantity and margin when maximizing profit.

I think we need to be careful about what we mean by location competition/Hotelling competition. It’s not enough to see two things that are similar and conclude that it’s Hotelling, because the exact same model under different specifications shows that that would predict complete differentiation. There’s an analog to how we think about similar prices. If we see two firms with the same price, some people will want to say that that’s collusion, but that’s also what you’d predict out of competition. It’s underspecified.

Go back to the chicken-sandwich example, which came from Byrne Hobart. Is that Hotelling, or is that a general shift towards chicken consumption in the model overall? What if there is more chicken now? That could be a combination of supply and demand reasons. Maybe chickens became cheaper to raise. Chicken availability (neither supply nor demand, but it’s what is measured) per person has been rising since the 1940s, passed pork in 1996, and passed beef in 2010. That seems relevant to things and not clearly about Hotelling competition.

To tease out the more Hotelling-like story, I’d want more detail on how one restaurant’s decision affects how the other will respond. Once Popeyes has a chicken sandwich, McDonald’s will lose customers who want chicken unless it adds one too. Sure, the relevant evidence wouldn’t necessarily be that McDonald’s added a chicken sandwich, but we should expect places that are facing more competition from Popeyes to respond more quickly. For example, did places closer to Popeyes, or business franchises with more stores near Popeyes, respond more quickly? That might be some evidence. But it’s speculative.

The important thing is that there’s always a trade-off between trying to attract more customers (in this case, by moving closer to them) or, in other cases, by lowering the price to attract them, versus making money on the customers you kind of already have. That shows up across all big three models of imperfect competition.

The key insight of Hotelling is that the force to conform, to be more like the median consumer, is there. That force alone is going to pull products toward each other, and we should take that force seriously. The takeaway is not that this is the only force, so they’re actually in practice pulled all the way to minimal differentiation. Multiple margins of adjustment.

I thought that I would take a moment today to try to explain what is happening and why it happened. I’m going to start with an abstract discussion of exchange rate intervention and then get into the specific issues at hand.

Thinking About Exchange Rate Intervention

Japan does not have a fixed exchange rate with the dollar. Nonetheless, let’s start by considering the world of fixed exchange rates to understand the role of intervention in foreign exchange markets.

Suppose that I run a country, Freedomland, and I have my own currency, freedom bucks. I decide that I want to peg my currency to the dollar at 100 freedom bucks per dollar. Naturally, my country is going to have to acquire dollars over time in order to maintain dollar-denominated reserves.

The problem I face by pegging my currency to the dollar is that there is an asymmetry in terms of the control of this exchange rate. For example, consider what happens when my currency appreciates. In that case the exchange rate might go to 95 freedom bucks per dollar (it takes fewer freedom bucks to buy a dollar and thus my currency is more valuable, all else equal). When this happens, I can print more freedom bucks and use them to buy dollars. The increase in the relative supply of freedom bucks will tend to push the exchange rate back to 100 freedom bucks per dollar. Furthermore, since I am able to print as many freedom bucks as I like, I can always print enough freedom bucks to depreciate the exchange rate back to the fixed exchange rate.

The asymmetry arises when things move in the other direction. Suppose that the currency depreciates to 105 freedom bucks per dollar. I need to intervene to strengthen the currency. I do this by using the dollar reserves that I have accumulated to buy freedom bucks and remove them from circulation. The asymmetry arises because I do not have the ability to print dollars. As a result, I only have a finite supply of dollars. Whether I’m able to get the exchange rate back to 100 freedom bucks per dollar depends on my credibility in using dollars to buy back my own currency.

Suppose that people do not believe that I’m committed to doing this. They can make a bet that freedom bucks will continue to depreciate. They can do this by borrowing freedom bucks, selling them for dollars, and investing those dollars in low-risk dollar accounts to earn some interest.

To see how this works, consider the following example. Suppose that you don’t think I have enough reserves to defend the peg, or that I am not committed to draining my reserves to defend it. The current exchange rate is 105 freedom bucks per dollar. You borrow 1050 freedom bucks and sell them for 10 dollars. Assuming that the interest rates in both countries are the same (more on this below), this is just a bet that the currency will continue to depreciate. To make things really simple, suppose that interest rates are 0 percent in each country. If the exchange rate moves to 110 freedom bucks per dollar, 10 dollars will buy 1100 freedom bucks. You can pay back your loan of 1050 freedom bucks and have 50 freedom bucks left over.

If a lot of people believe that my currency will continue to depreciate, they will all make this bet. All else equal, this creates a lot of selling of freedom bucks, which tends to cause depreciation. In order to correct this, I have to sell a bunch of dollars to buy back the freedom bucks and remove them from circulation. The weaker the selling pressure from speculators, the easier this is to do. However, suppose that I start draining my dollar reserves. As that happens, speculators will recognize that I cannot continue this forever. Once I run out of dollars, I will be helpless to support the value of freedom bucks. Thus, as my dollar reserves drain and the exchange rate fails to correct, this will tend to pull more and more speculators into the market. Eventually, I will be forced to give up. Once I do, there is no buying to offset all of the selling and freedom bucks will depreciate very rapidly with no hope of returning to the fixed exchange rate.

The asymmetry means that I might not be able to fix my exchange rate alone. The postwar experience of fixed exchange rates is littered with examples like this. The standard story goes like this. A country with high inflation wants to restore credibility to policy and bring inflation down. They impose a fixed exchange rate. When they do so credibly, in the short-run the exchange rate stabilizes, inflation comes down, and things improve. However, they face the problem of asymmetry at some point in the future. Knowing this, they need to transition away from the fixed exchange rate. Nonetheless, it is never clear when they should do this. If they do it too early, they might immediately lose credibility. If they wait too long, they might be subject to a speculative attack.

The way that one can avoid a speculative attack is if Freedomland could partner with the United States on this fixed exchange rate. For example, if freedom bucks depreciate to 105 freedom bucks per dollar, I can start using dollars to buy back freedom bucks, the U.S. could use dollars to buy freedom bucks, or some combination of both. Since the U.S. can print unlimited quantities of dollars, they will always be able to print dollars to buy freedom bucks. Of course, this raises an important question. Why would the U.S. care about Freedomland’s exchange rate?

Japan

As I said at the beginning of the previous section, Japan does not have a fixed exchange rate. However, to give the reader an idea of the importance of international trade, total trade (imports and exports) as a percentage of GDP in Japan is around 45%. As a result, although Japan doesn’t have a fixed exchange, it might still have a desire to intervene in foreign exchange markets to prevent significant moves in its exchange rate with the dollar (because of the dollar-based international trade system). The same principles of intervention apply.

Currently, Japan finds itself in a difficult position. Following Japan’s rapid growth in the postwar period, the Japanese economy has experienced slower growth since the early 1990s. Over the last 40 years, the Japanese economy has grown only around 1.3 percent per year on average. The average annual inflation rate from 1986 to 2021 was around 0.5 percent per year, experiencing deflation in nearly a third of those years. At the same time, Japan’s debt-to-GDP ratio has risen to over 200 percent. For years, people have been debating what happened to Japan. I’m not going to discuss those debates here. Instead, I present this as background information.

Back around 2012, Shinzo Abe introduced what was deemed “Abenomics.” This policy was designed to stimulate the Japanese economy and boost growth. The idea was to create an inflation target of 2 percent through aggressive bond buying by the Bank of Japan, to use fiscal policy to boost aggregate demand, and then also do various supply-side reforms related to tax policy and labor market regulation. Aggressive expanstionary monetary policy included implementing negative interest rates. In fact, the Bank of Japan’s policy rate was negative from 2016 through 2024.

In the aftermath of the pandemic, when a number of countries including the United States experienced high rates of inflation, central banks around the world started aggressively raising interest rates. As I just alluded to, this did not occur in Japan. The Bank of Japan continued to have a negative policy rate until 2024 when the policy rate was raised to 0.25 percent. This was in response to inflation finally rising above the Bank of Japan’s 2 percent target.

The important thing to realize here is that this dramatic interest rate discrepancy between Japan and other developed countries has fueled what is called the yen carry trade. This is equivalent to the abstract example that I gave above. What people are doing is they are borrowing the yen, selling it for some other currency (like the dollar) and then investing those dollars in low-risk, interest-bearing assets. This trade enables people to profit from the interest rate differential. But remember from our abstract example, as this type of trade expands in volume, it tends to depreciate the currency. This is exactly what has been observed in the post-pandemic period with the yen, which has experienced a pretty dramatic depreciation. (See the chart below, courtesy of CNBC.)

This has created a problem for Japan for several reasons. The first is that inflation is now above the Bank of Japan’s 2 percent target. The BoJ has been raising its policy rate to try to push inflation back down toward its target.

A higher policy rate creates another problem. Since Japan’s debt-to-GDP ratio is already over 200 percent, raising interest rates starts to increase debt servicing costs. As debt servicing costs rise, this might cause bondholders to become convinced that they won’t be repaid (at least in real terms). Expectations that they will have to continue to raise rates, which increases debt servicing costs, which increases the likelihood of default will tend to lead to increased speculation of further depreciation in the yen. Yet, abandoning the interest rate hikes might signal to the market that the BoJ has given up, which creates the expectation that inflation will remain higher for longer and thus lead speculators to expect a further depreciation of the currency.

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Two Predominant Criteria

There are two main criteria that economists tend to use to evaluate welfare. A Pareto improvement occurs when someone or some people can be made better off without any becoming worse off. The is the Pareto criterion. Pareto efficiency occurs when no such improvements remain.

A separate approach to welfare evaluation is what is known as the Kaldor-Hicks criterion. This criterion states that something is welfare-improving if the total gains exceed the total losses.

These concepts are not unrelated. Consider any sort of policy change. It is likely to create both winners and losers. The winners are the people are who better off. The losers are the people who are worse off. If these new benefits exceed the new costs, then this is considered a Kaldor-Hicks improvement. If the winners use some of their benefits to compensate the losers, then the outcome could also be a Pareto improvement. Why? Well, if the benefits exceed the costs, then some fraction of the benefits could be transferred to the losers with some benefit still left over. Some people are better off and no one is worse off.

For this reason, many people think that Kaldor-Hicks is sufficient. After all, if something is a Kaldor-Hicks improvement, a transfer is sufficient to generate a Pareto improvement. However, I don’t think that things are this simple. There are a couple of issues that need to be addressed.

First, a Kaldor-Hicks improvement might be sufficient for thinking about this on the chalkboard, but we need to think about things in practice. Just because a transfer could produce a Pareto improvement doesn’t mean that we will see such a transfer in reality. There might be important political constraints or transactions costs that prevent such transfers from taking place. If a transfer is feasible and likely, then economists have an objective standard upon which to argue in favor of the policy. If a policy makes some people better off without harming others, it doesn’t require any ethical judgement to say that the policy should be implemented.

On the other hand, if the transfer isn’t feasible, arguing that the policy should or should not be implemented requires an ethical judgement. One can appeal to Kaldor-Hicks to argue in favor of the policy, but in doing so one is implicitly making a utilitarian argument. That’s fine, if one is a utilitarian, but one should be explicit about that ethical judgement.

This isn’t a minor point about ethics and economics. Instead, I think that this distinction is often at the heart of political economy.

The second major point here is about which criterion leads to more empirically relevant predictions about what we actually see in the world. For example, how do people handle issues related to common pool resources? How do people deal with externalities? If you use the Pareto criterion for thinking through these issues, you might get different implications and predictions than if you use the Kaldor-Hicks criterion.

Winners, Losers, and Political Economy

Price discrimination (charging different prices to different consumers for the same good) tends to be unpopular. However, this isn’t universally true. There are many types of price discrimination that people do not complain about. People who show up at the store with coupons pay a different price than people who do not. Perhaps it happens, but I’ve never seen a person complain that the person with the coupon paid a lower price.

My own casual empiricism suggests that people tend to dislike price discrimination the closer it gets to first-degree price discrimination, in which every consumer gets charged their exact willingness to pay. For example, Brian previously wrote about accusations that Instacart was varying prices across consumers to try to get a sense of each individual customer’s willingness to pay for particular goods. That turned out to be incorrect, but a lot of people seemed really concerned about what Instacart was doing. They didn’t like it.

In a Kaldor-Hicks sense, price discrimination is always welfare-improving. However, this is not always true when it comes to the Pareto criterion. Let’s consider the logic and then a couple of scenarios.

A profit-maximizing firm will set marginal revenue equal to marginal cost. The marginal revenue of a price-setting firm that faces a downward-sloping demand curve will always be below its price. Thus, a profit-maximizing, price-setting firm will always set its price above the marginal cost of production. But think about the marginal consumer. Suppose the firm sets a price of $10 and the marginal cost is $7.50. The marginal consumer might be willing to pay $9.50 for the good. This is lower than the price that the firm is charging, but higher than the firm’s marginal cost. There is a potential gain from trade here that is going unrealized. Selling the good to this one consumer for $9.50 would allow the consumer to actually obtain the good, while also increasing the profit of the firm.

Nonetheless, the firm cannot lower the price to $9.50 for everyone. By doing so, the firm would gain $2 from that one consumer, but would lose $0.50 from every other consumer who would have been willing to pay $10.

Price discrimination can improve welfare using either criteria. Suppose the firm charged $10 to everyone and $9.50 to this one particular consumer. None of the previous consumers are made worse off. The new consumer by definition is indifferent between having $9.50 and having the good. The firm earns additional profits. The firm is better off and everyone else is no worse off.

Now consider moving from the $10 price to first-degree price discrimination. The total surplus from trade is maximized. By the Kaldor-Hicks criterion, this is a welfare improvement. Nonetheless, this is not a Pareto improvement. None of the consumers are better off. Many are worse off (all of those with a willingness to pay above $10). The firm is better off.

It therefore shouldn’t a surprise that consumers tend to dislike first-degree price discrimination.

A similar type of reasoning can help us to understand arguments over international trade. In a lot of standard trade models, you get the following type of result. Removing barriers to trade allows consumption beyond the production possibilities frontier. In other words, people are able to consume more than the productive capacity of their own economy because they exploit the new gains from trade. However, at the same time, the changing nature of production following the removal of the trade restriction will tend to lead to the convergence of factor prices. This means, for example, that workers in the high-wage country will tend to see downward-pressure on their wages. Overall, the benefits exceed the costs. Nonetheless, there are winners and losers. To turn the Kaldor-Hicks improvement into a Pareto improvement requires transfers to these workers. When there are no such transfers, it shouldn’t be surprising that some workers are opposed to the policy.

In short, what the distinction between Pareto improvements and Kaldor-Hicks improvements reveals is that a lot of issues in political economy revolve around distributional effects. When there are distributional effects that produce winners and losers, it is not surprising that the losers are not persuaded by the Kaldor-Hicks argument that the overall benefits exceed the overall costs. Furthermore, distributional effects make it difficult for economists to make normative arguments about the policy because it necessarily requires using some ethical standard.

Empirical Relevance

I view the main job of an economist as an attempt to understand and explain the world as it is. Prior to making any recommendations to improve the world, one should have some understanding of how things work.

Which criterion we use can matter for thinking about how people solve problems. For example, when we are thinking about markets as I described in my example above, property rights are well-defined and we have a sense of how people would behave. However, there are a lot of interesting questions that we think about where property rights are undefined or ill-defined. (As a testament to how interesting these types of issues are, just search this Substack for the posts that Brian and I have written on externalities.)

In a previous post, I discussed the example of externalities using the Pareto criterion. I tend to prefer this approach because it points to a Coaseian discussion. What that post was meant to point out is that even in the presence of externalities, we can think in terms of the Pareto criterion. Once we introduce all parties involved (consumers, firms, and those who suffer from the external cost), it should be clear that there are gains from trade to be had between the groups. In other words, it is possible to move in the direction of the optimal allocation even in the Paretian sense. This is a Chicago-style price theoretic approach to Coase.

What that example revealed is that the Pareto criterion can actually help us to understand how and why society tends to move in the direction of the optimal quantity. However, this approach requires a solution that is “off the demand curve.” If consumers are able to choose whatever quantity of consumption they like, such a solution is infeasible. To prevent that from taking place, you need some type of non-linear pricing scheme or you need some type of explicit agreement between the parties involved.

In that previous post, I focused on the non-linear pricing scheme, but here I want to focus on the alternative. When we think of issues related to incomplete, ill-defined, or undefined property rights, we actually see a lot of voluntary activity to mitigate the adverse effects thereof. Humans tend to form a variety of groups to solve these types of problems. These groups include families and homeowners associations and churches.

As a result, externalities don’t always require Pigouvian taxation. Common pool resources do not always lead to the Tragedy of the Commons. As the work of Nobel laureate Elinor Ostrom shows, societies turn out to be remarkably good at forming groups to sustain and manage common resources.

The Pareto criterion approach to these issues pushes one in a Coaseian direction and pushes one towards a better understanding of the institutions that make up a civil society. As a result, it seems (at least to me) to be much more empirically relevant for understanding how the world actually functions.

Some Final Thoughts

It might seem like a minor thing, but the distinction between the Kaldor-Hicks criterion and the Pareto criterion is important. Narrowing in on the differences between these criteria can help one to avoid making implicit ethical judgements and to understand the importance and significance of distributional issues for political economy.

But it is also useful to understand these distinctions for thinking about existing policies and solutions. The Pareto criterion leads one in the direction of Coase and Ostrom when it comes to externalities and property rights issues. That is an advantage, in my view, because it points to the development of the institutions that make up civil society, which seem much more empirically relevant than a lot of textbook conversation and textbook solutions to these issues.

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Today, I am proud to announce a collection of essential staples that will be predictably 30% cheaper at all five of our city-run grocery stores. This core set of goods will include all fresh produce, meat, and seafood, along with 20 other essential items like cheese, milk, and bread.

Here’s how it will work. Once a month, our five city-run grocery stores will set prices for this core set of goods at 30% below typical retail prices. No exceptions, no gimmicks. The savings will last for the entire month.

I could spend this post cataloging all the ways a municipal grocery store is a dumb idea. That’s boring.

So let’s take New York’s plan seriously and think through what we always think through. Who pays for the discount? What are the equilibrium responses? Where does adjustment occur when it cannot occur in the prices of those 20 items? Let’s think through the usual stuff: competition, transactions costs, fixed vs. marginal decisions.

Let’s start with a few of the details. The 30% covers a subset of items, not every item. So it’s not right to compare the 30% to the overall grocery margins, which are in the single digits. Also, this is not a price control. Nothing binds private stores; they can set their own prices. The price-control analogy will become useful later, but a low checkout price by itself does not tell us whether the store receives enough in total to keep the shelf stocked.

The city will provide the locations. That means low- or no-cost real estate, initial building support, and relief from rent and property taxes. So there will be a huge subsidy on that portion, and bids to run the stores will be judged on what subsidies are requested, but we don’t know the formula. This matters because many of these subsidies are about the fixed costs of the store, while pricing (and the rules around the 30%) are related to marginal costs. So we will need to be careful here. Lots of moving parts.

Competition for the bundle

Let’s start by assuming that the supported operator, which I’ll just call the government store, and the ordinary private grocer use the same resources to build their basket that consumers care about. I’m not going to assume that the government store is inherently inefficient at the start, but we’ll come back to that later.

It’s maybe an okay starting point. We don’t need to assume the city is learning how to price groceries. It’s going to hire private contractors to do that and give them some residual-claimant rights, so they have an incentive to learn. They’ll also likely have a scale advantage that other stores do not, so let’s start by assuming they are equally efficient.

As always, start with the simple model. Imagine two stores. One private store becomes the government store, and the other remains private. Assume every household consumes a fixed grocery basket, so we’re not going to think about substitution across goods. Consumers are going to go to whoever supplies the cheaper basket relative to their transportation cost.

We have core items whose prices are “forced” low and the rest of the items. Suppose half of the $100 on a normal trip is on those core items, and the city is going to tell the store to cut that by 30%. The dollar value of that portion falls to $35. If nothing else changes, the $100 trip now costs $85. Yay, everything is cheaper! The advertised 30% discount has produced a 15% discount overall.

But the operator doesn’t sell a single product. It sells lots of products together. Half are regulated, but the other half are flexible. This operator is still competing with the private store. What is it going to do? It’s going to raise prices on the non-core half until the total basket is back to $100.

In that world, nothing has changed. Every basket is the same price. Shopping behavior is the same. Even if some staples look like they’ve changed, consumers are no better off in this world because what they actually care about is the bundle.

Also notice that nothing on the subsidy side is really coming in here in terms of pricing. I’m not assuming that the government store made a loss and therefore is getting a subsidy to cover that loss. It’s just a direct transfer in the form of cheaper rent from the taxpayer to the store operator.

But none of that gets passed through to consumers.

Competitors respond

Now let’s relax the fixed-basket assumption. Suppose consumers are a little more responsive and non-core pricing isn’t going to undo the full discount, so the supported store’s total basket really does get cheaper. We can think of a variety of ways in which that happens. One possibility is that people shift toward the discounted core products, so the average bundle contains more goods with lower margins. The government store then has lower prices on average.

Again, let’s think of a simple model. Imagine it’s a spatial competition model. One store sits at each end of the neighborhood. Consumers differ in which store is more convenient. The supported store has cut its basket by 10%. The rival is going to respond. It can either keep its price unchanged and lose customers, or cut its own price and keep more of them. Suppose the government store cut its basket by $10, and then the other store is going to respond by $5.

Sounds great! Everyone gets cheaper groceries! People going to the government store get the larger reduction, while people who stay at the private store still benefit from the competition that has driven down its prices.

But we already know that these private stores have thin margins. With recurring fixed costs, it’s possible some are eventually driven out of business. In that case, this competitive pressure is weakened because the government store no longer has to compete with the private store. It can’t exercise its market power by raising prices on the core items, but it could still exercise its market power on all of those other goods.

The subsidy is real

So far, we basically ignored the subsidy. Think of it as just a transfer. Let’s dig into that a little bit more.

We have a supported operator that we’ve assumed has the same costs as the other firms involved. In the market, it’s just been told to charge less, and maybe it can’t make it all up on those other goods. Fixed contributions toward the site buildout and tax subsidies can help keep it operating, but they do not necessarily change the incentive to sell another basket.

This really turns the pricing into something like a two-part tariff, where you have kind of a fixed cost part of the pricing, and then you have your marginal cost pricing on the goods. Think of Costco as one example. Costco collects a membership fee and then charges very low prices inside the store. Maybe this is essentially what New York will do, but instead of membership fees, that fixed cost is coming from the government. After all, there’s a five-year plan that provides $70 million to go towards these sites.

We can see fixed vs. marginal in the profit function:

π = (P + s − c)q + G − F.

The store charges P, sells q baskets at marginal cost c, receives a fixed payment G and a per-basket payment s, and they themselves pay fixed cost F. They key is that the fixed payment doesn’t enter the pricing decision. It’s a sunk cost. Sure, it determines whether the operator opens (I’m fine assume it will be sufficient for the stores to open for a little bit), but it does not make the next basket, the next q, more profitable.

The way to change that is through s. So far, we don’t know what that subsidy looks like. But then that changes behavior as well. That changes the full equilibrium. In a model like Hotelling, another dollar of s lowers the government store’s price by say 67 cents and its rival’s by about 33 cents. That exact split is an artifact of symmetric Hotelling but the general point is that the fixed cost type support changes participation, or the extensive margin. Marginal support changes the incentive to expand/maintain quantity, which is the intensive margin. Always gotta think about extensive/intensive.

If that’s all we have, then again, we’re in the world where it’s just a transfer from the taxpayer to the store operators. Competition may make it optimal for the government store to pass some of the subsidy through to consumers rather than keep all of it.

Overall, we have a combination of fixed and per-basket or per-unit payments from taxpayers. That produces three distinct outcomes that often get collapsed in political discussions of subsidies:

• The amount transferred to the operator

• The amount that store shoppers receive—the pass-through rate

• The price cut at competing stores

The details will determine who captures each of these.

Will the stores be as efficient?

The elephant in the room is: why would these supported operators be more or less efficient? They could be more efficient because they’ve been given a scale or a chance to reach a scale that’s generally not permitted in New York City. After all, New York City has kept out stores like Walmart, and these will presumably be five bigger stores. We also have all of the usual reasons for thinking that the stores would be less efficient.

To what extent is there an inherent contradiction here? If you provide only a fixed-cost subsidy and let the operator maximize profits, then it has an incentive to be efficient. In that world, we go back to the case above, where most of the fixed subsidy is captured by the operator. Competition may pass some of it through to shoppers, but the operator will try to retain the savings.

Otherwise, if the operator can’t maximize profit, or if the government claws back profits that it considers too high, then the incentive to minimize costs is weaker. You’ve created a tension: letting the operator claim the gains from lower costs encourages efficiency, but it also lets the operator retain some of those gains rather than pass them through to consumers.

This will really depend on the details, so we will see.

What about shortages?

Notice I haven’t said anything about shortages or waiting in line, the usual things that people think about when they think about government-run stores. Let’s imagine that consumers go to the government store to get milk. Maybe they make one big trip there a week to stock up on the lower-priced, core items.

What incentive does the government store have to keep the shelves full? After all, the operator likely will lose money on the core items, and needs to make it back on the rest of the basket. But maybe it needs to have the core items to attract the shoppers for the rest of the basket. No one will show up to a grocery store with no milk and bread. So there is some incentive to keep shelves stocked.

Again, think about margins of adjustment. You know we love to bring up Barzel, but his ideas are key here. Measurement costs are real. He starts from the idea that what is sold is not one thing with one price. A carton of milk is a bundle. Yes, we all think about the (posted) price. That’s what all the emphasis is on. But we’re talking produce here. It doesn’t take a lot of thinking to recognize that quality matters too. But it’s also things like selection, checkout time, and even the probability it will still be on the shelf when you arrive. It’s just not possible to force the operator to do all of these correctly. That’s an aspect of all contracts, not just government ones. Writing and enforcing a contract over every attribute is costly, so contracts tend to be precise about the attributes that are easy to measure and looser about the rest.

The contract can be precise about the posted price. That’s what Mamdani is promising on. What about the other margins?

Suppose the contract requires the operator to “fix” the posted price. That’s the price control analogy, but it’s quite loose. That’s forced low, so another sale does not cover its cost. The operator then has an incentive to adjust on those less-measured attributes.

Let’s not assume shortages. It could be that other margins adjust. Less reliable availability or worse service may reduce demand enough, so we don’t actually have shortages. YAY! NO SHORTAGES! (Ignore for the moment that there are no shortages only because quality has fallen enough to offset the lower price.)

But if there are still more shoppers than groceries, Barzel’s earlier work on rationing by waiting tells us what comes next. Shoppers will then have to bid through another mechanism, in this case, bid with time. The line grows until the full price (price + waiting for simplicity), on the margin, is high enough to ration the available groceries. The market clears one way or another.

This is the standard deadweight loss of rationing. The time cost is wasted rather than being transferred to the store or anyone else.

So that brings us back to the opening. I still think this will end up displaying all the normal reasons to think a municipal grocery store is a dumb idea: bad pricing incentives, inefficient transfers, and all that stuff. At the end of the day, we can’t eliminate trade-offs and scarcity. This is a competitive industry. The discount is unlikely to come purely out of profits.

So the cost of the discount will show up in other grocery prices, taxpayer subsidies, product quality, or time. There’s no way around that.

A lot of the favorite casual criticisms of economics relate to GDP. They typically go something like this. GDP does a bad job of measuring X and X is a thing that really matters, therefore GDP is a bad measure. Often times, these criticisms aren’t necessarily wrong. GDP doesn’t measure X because that is not what it is designed to measure. GDP is designed to measure the total value of newly produced final goods and services in the economy (meaning within the borders of that economy) over a given period of time. Unless that is your definition of X, GDP isn’t going to measure it.

Ironically, however, GDP often tends to be a good proxy for X. For example, some people say that GDP isn’t good because what we really care about is happiness or life expectancy or consumption. It turns out that GDP is actually strongly correlated with all of these things.

Nevertheless, I don’t think that these correlations are something that we as economists should hang our hats on. It is fun to point out that “GDP is fine, actually,” but I also think that sometimes we risk taking this too far. After all, GDP is designed to measure a particular thing. Let’s keep it to that thing. When we want to measure something else, we should try to measure it precisely using the tools that we have.

One thing that we frequently use GDP for is to measure living standards. This seems to make sense. We calculate economic growth by finding the growth rate of the trend in real GDP per capita. As a matter of measuring how much more stuff the economy is producing over time, this seems like a good measure. However, while the phenomenon of economic growth is associated with a corresponding rise in living standards, it isn’t obvious that we can measure improvements in living standards using the growth of real GDP per capita. A recent paper by Philip Trammell and Chad Jones makes this point in an easy to understand way. Allow me to explain.

Preferences, GDP, and Living Standards

Back in the 1970s, Paul Samuelson and Subramanian Swamy wrote a paper that showed that real GDP provides a consistent measure of living standards if preferences are homothetic (a frequent assumption made by economists). I don’t really want to spend any time explaining what homothetic preferences are because I value you, the reader, too much to make you read through that. However, it suffices to say that with homothetic preferences, the income elasticity of all goods is unit elastic and the expenditure shares on each good is constant over time.

To see why that might be important, consider how we measure economic growth when we use a chain-weighted measure. The growth rate of real GDP is just the weighted average of the growth rate of the production of each good. With homothetic preferences, the weights are fixed. Thus, if there are two goods and the production of one good is growing at 4% and the other good is growing at 2% and each make up half of the expenditures, then the growth rate will be 3%.

However, consider the case of non-homothetic preferences. One example of this would be to consider a utility function in which the utility of consuming each good is bounded from above. In other words, consider a world in which there is (at least eventually) diminishing marginal utility for each of the two hypothetical goods already mentioned such that total utility from consuming that good reaches some maximum. Given that the production (and consumption; markets clear) of the first good is growing at 4%, consumers will hit the point of diminishing marginal utility earlier than for the other good. As a result, consumers will start to substitute away from this good and consume more of the other good because the marginal utility of the latter is higher. In fact, in the extreme case in which the consumer ultimately hits the upper bound for utility associated with the first good, all of consumption will be of the second good and thus the growth rate converges to 2%.

Note that the only thing that differs in each of these examples is consumer preferences. The measured growth rate is different just because the expenditure shares are changing over time under one set of preferences, but not the other.

Why does this matter?

As Trammell and Jones note in their paper, when we think about the way in which economic growth improves living standards, we tend not to think about it in terms of just more stuff. Instead, we think about economic growth improving living standards because of a wider variety of goods that are available. We don’t just get more of the same stuff. We get new stuff that is better than the old stuff. An example that they give in their paper is of Nathan Rothschild. Back in the 1830s, this was the richest man in the world. However, he died from something that would have been cured today by cheap antibiotics. The availability of antibiotics would have greatly improved his living standards.

With that in mind, let’s return to our previous example, but instead let’s imagine that the second good doesn’t initially exist. The introduction of the second good makes people better off. It raises total lifetime utility. However, with different assumptions about preferences, we get two different growth trajectories. More importantly, for non-homothetic preferences, the growth trajectory gives us a really perverse result if we think about living standards in terms of real GDP.

The reason for this perverse result is as follows. If only the first good exists, the economy will grow at 4% per year. If the second good is introduced, lifetime utility (and thus living standards) rise for everyone in the economy. However, the growth rate converges to 2%. In other words, projecting this out, real GDP will be lower in the world with the second good even though living standards are higher.

How to Measure Changes in Living Standards

Trammell and Jones suggest that to properly measure living standards, what we really need is lifetime utility. This is a problem since we cannot measure utility. Nonetheless, price theory can help here. Remember that I had a previous post on the statistical value of human life (or the value of a statistical life, VSL, for people who want to butcher the English language). We can estimate the VSL using data from labor markets. People are compensated for taking on risks in particular jobs. The VSL can be measured as the compensation for this risk per change in probability. This gives us a dollar value for human life. Conceivably, this could tell us something about living standards. As living standards improve, life is worth more to people and so they are less likely to take on risk without additional compensation. VSL will capture this change in living standards.

Of course, this is a measure in terms of dollars. To properly measure things, we need to have things in terms of total utility. Fortunately, if one solves an infinite horizon, representative agent problem, it follows that

Or

Where U is total utility from aggregate consumption and MU is the marginal utility of aggregate consumption. In other words, there is a way to convert lifetime utility to dollars to get VSL and correspondingly a way to convert VSL to lifetime utility. Unfortunately, doing so requires having some ability to measure the marginal utility of total consumption. We don’t have a way to do that. Thus, we are back to square one.

Or are we?

Trammell and Jones point out that although we cannot get the level of living standards, we can estimate the growth rate. For example, it follows from our equilibrium condition for VSL that:

where g_u measures the growth rate of lifetime utility, g_VSL measures the growth rate of VSL, and g_mu measures the growth rate of the marginal utility of consumption.

But we know from standard models of consumption that

In words, this means that the growth rate of the marginal utility of consumption is equal to the rate of time preference minus the risk-free interest rate. It therefore follows that

The right-hand side of this expression is all stuff we can measure. Thus, if we can measure the growth rate, we are always able to measure the magnitude of the difference in living standards over different periods of time.

Does This Matter Empirically?

One might wonder whether this matters empirically. Well, using Trammell and Jones’s baseline calculation, they find that the average annual growth rate of total utility from 1940 to 2024 was about 2.3%. This implies that living standards were 6.9 times higher in 2024 than in 1940. As a method of comparison, the average annual growth rate in real GDP per capita from 1940 to 2024 is about 2%. That doesn’t seem like much of a difference, but compound growth makes a difference here. Real GDP per capita would suggest that living standards were 5.4 times higher in 2024 than in 1940.

It is important to note that the estimates depend critically on how we measure VSL. We lack good time series data on VSL. Trammell and Jones splice together estimates from Costa and Khan (which I discussed in my post on VSL) and from the U.S. Bureau of Labor Statistics.

An alternative would be to start with estimates of VSL and then project them forward based on the income elasticity of VSL. Trammell and Jones also do this. They find that if you use the standard BLS assumption that the income elasticity is 1, then this implies that living standards are 5.1 times better in 2024 than 1940. This is pretty close to the estimates implied by the growth in real GDP per capita.

However, Costa and Khan found much higher income elasticity of VSL. When Trammell and Jones use an income elasticity of 1.3, this implies that living standards are 21.1 times higher in 2024 than in 1940!

What this demonstrates is that it is possible that the growth in real GDP per capita might actually understate the rise in living standards associated with economic growth. This shouldn’t necessarily be surprising since its ability to measure living standards requires specific assumptions about preferences that might not hold.

Nonetheless, whether the real GDP per capita is a good proxy ultimately depends on measures of VSL. We need much more frequent and consistent estimates of VSL to make this determination.

Implications for Our AI Future

Why does all of this matter?

Well, one of the things that both Brian and I have been writing about recently is AI and the likely economic effects thereof. To some extent, Brian and I have spent a lot of time throwing cold water on the more provocative claims made by people with respect to AI.

In fact, one argument that I made based on the literature on economic growth is as follows. Some types of production might be easy to automate. AI might be expected to have a huge influence on those types of production. However, other types of production might be hard to automate. If production is a function of both easy-to-automate inputs and hard-to-automate inputs and the elasticity of substitution between those inputs is less than one, then the growth rate of the economy will be determined by the growth in the production of those hard-to-automate inputs.

Nonetheless, in a world of more advanced AI, living standards might increase substantially, in part due to all of that automation, but also due to inventions and innovations that humans might not have discovered in the absence of these AI tools. However, that might imply that real GDP per capita becomes a bad measure of living standards since total utility might be growing substantially faster than measured production.

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On its face, it seems like the answer to both of these questions is easy. The corporate income tax is a tax on the income made by corporations. Okay, easy enough. But that answer is superficial. Let’s dig into the details.

In a standard optimizing model of the firm, a corporate income tax increases the user cost of capital and therefore reduces the demand for capital. Thus, if you want a simple answer, you might say that the corporate income tax is a tax on capital – although that is also not a complete answer because it ignores the issue of tax incidence. However, let’s stick with calling it a tax on capital and see where that takes us.

Suppose that all firms are corporations and capital is homogeneous. Under that scenario, it seems permissible to refer to the corporate income tax as a tax on capital. Alternatively, suppose that there are two types of capital and two industries. One type of capital is used by one industry and the other type of capital is used by the other. If the corporate income tax is levied on one industry, then this is a tax on the capital of that industry.

However, if we assume that some firms are corporations and some are not and that both types of firms produce the same product, then calling this a tax on capital is not correct. It is not correct to call it a tax on capital because the capital is only taxed if the firm calls itself a corporation. It seems reasonable to me to think that both corporations and non-corporations produce the same goods and therefore use the same types of capital. Only one firm is subject to the tax.

What this framing reveals is that when both corporate and non-corporate firms produce the same good, a tax on corporate income is not really a tax on capital, but rather a tax on incorporation. Okay, now we are getting somewhere.

We know that if you tax something, you get less of it. If we tax corporate income, we should see fewer firms that call themselves corporations relative to the counterfactual of no corporate income tax.

To understand what this means, we first have to know what constitutes a corporation. According to the IRS, a corporation is a firm that has filed articles of incorporation with the state. (Thanks IRS!)

In general, corporations have some specific characteristics, such as shareholders with easily transferable shares and limited liability. Thus, if we think of a corporation as a firm that issues marketable ownership shares, then a tax on corporate income is actually a tax on the decision to issue marketable ownership shares.

This raises the question as to why a firm might sell marketable ownership shares and the corresponding implications of making it more expensive to do so. On this point, Laurence Kotlikoff and Jianjun Miao develop a framework for thinking about this. Their crucial point is this. The decision for the marginal entrepreneur about whether or not to incorporate depends on risk, the fixed cost of issuing ownership shares, and the cost of the corporate income tax. On the one hand, an entrepreneur would like to incorporate because adding shareholders allows for risk-sharing. However, to get the benefit of risk-sharing, the firm will have to pay a tax that it would not have to pay if the entrepreneur operated the firm on his/her own. Ultimately, whether an entrepreneur will decide to incorporate depends on whether the marginal benefits of incorporation are greater than or equal to the marginal costs. What this tells us is that there is some threshold for the skill or productivity of entrepreneurs. Those above the threshold will find it beneficial to incorporate. Those below it will not. Thus, when the government increases the corporate income tax, they are increasing the marginal cost of incorporating. As a result, the marginal benefit of incorporation must be higher than it was before the tax increase. This means that the skill or productivity threshold that the entrepreneur must cross to want to incorporate increases. In other words, fewer entrepreneurs will choose to incorporate.

In comparison to a world with no corporate income tax, the world with a corporate income tax will have fewer entrepreneurs who decide to incorporate. Since the benefit of incorporating is that it brings about risk-sharing, this also means there is less risk-sharing. Recall that when you tax something, you get less of it. What their model shows is that when you tax corporate income, you get less risk-sharing. Thus, it seems like the corporate income tax is a tax on risk-sharing.

To this point, I have focused on determining what is being taxed by the corporate income tax. We also need to know who is paying the tax. Politicians often complain when companies like Amazon do not “pay their fair share.” Of course, fairness is subjective. Nonetheless, what this highlights is that politicians often frame the tax as a tax on corporations, but corporations don’t pay taxes. Capital doesn’t pay taxes. People pay taxes. Do the owners of capital pay the tax through lower profits? Do firms pass along the cost of the tax to workers through lower wages and/or less employment? Who pays the tax depends on tax incidence. Of course, who pays the tax is related to what is being taxed. As it turns out, the assumptions made about what distinguishes corporate and non-corporate entities as well as some ancillary assumptions about the supply of capital have important implications for determining who pays the tax.

Maybe what politicians, like those I described, have in mind is that the owners of the firm (i.e., the shareholders) pay most of the tax. Arnold Harberger’s pioneering paper suggests that capital owners pay the tax — even those in the non-corporate sector. However, Harberger assumes that corporate firms produce a different good than non-corporate firms. In addition, Harberger assumes that factor inputs, like capital, are in fixed supply. The assumption that corporate and non-corporate firms produce different goods seems to violate casual empirical observation. In addition, since it assumes that the factor supplies are fixed, the model is unable to examine the effects of the tax on capital accumulation.

If we drop the fixed factor supply assumption, we get a much different result. Suppose that all firms are corporations and use the same capital. In this case, the corporate income tax is just a tax on capital. Here, the neoclassical model will suffice. The neoclassical model has a horizontal supply curve for capital. As a result, the equilibrium allocation of capital is entirely demand-determined. In the neoclassical model, since the supply curve is horizontal, a tax on capital is entirely paid by workers.

Of course, as I said before, there might be characteristics of corporations that make them different from non-corporations. For example, we could assume that corporations and non-corporations produce different goods and use different types of capital. We can now modify the neoclassical model to have multiple types of capital and assume that the corporate income tax is a tax on a particular type of capital. In the new textbook, Chicago Price Theory, the authors have a nice example of a corporate income tax as a tax on a particular type of capital. The conclusion that workers pay the entirety of the tax holds, but the cost of the tax to workers is higher than a tax on capital itself because of the additional distortion created by having different taxes on different types of capital. (Kevin Murphy provides an excellent discussion of this here.)

If we drop the assumption that corporate and non-corporate firms produce different goods, we can turn to Jane Gravell and Laurence Kotlikoff. As they show, this assumption results in a much larger deadweight loss than what Harberger finds because it distorts production within a sector that consists of both corporate and non-corporate firms producing the same good. In addition, capital owners are worse off from the tax at the expense of non-corporate entrepreneurs. Whether workers are better off or worse off depends on how the labor demand of entrepreneurs adjusts.

Finally, we could just abstract from capital completely like Kotlikoff and Miao do in the paper referenced above and examine the corporate income tax from the perspective of choices about being a worker, an entrepreneur, and incorporation. They show that the corporate income tax is a tax on high-skilled entrepreneurs who incorporate and workers who see lower wages due to the decline in the demand for labor as a result of the tax.

Are you following all of this?

If not, that is okay. Maybe the fundamental lesson here is that what and who is paying the corporate income tax and the size of the deadweight loss are issues of considerable disagreement because it depends on assumptions that we make about the differences between corporate and non-corporate entities as well as other ancillary assumptions. This disagreement is something to remember the next time your favorite politician (or economist) speaks confidently about the precise corporate income tax rate we should choose.

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We are beyond the point where we are asking if AI will be useful. It obviously will be. But the economic question is who will capture the returns, the benefits, the rewards?

The valuations suggest the big labs will, and the AI boomers and doomers (not the AI-will-kill-us-all doomers, but the AI-will-destroy-the-economy people) are in agreement on this. The boomers see a fortune waiting to be won by the companies that build the most powerful models. The doomers see the same fortune being taken away from workers, pushing labor’s share of income down. Both sides imagine a large pool of economic value moving toward AI. They disagree mostly about whether that is exciting or frightening.

In this newsletter, I want to think through whether that is true, and who else we can expect to capture the gains.

There is a distinction between creating value and capturing value. A technology, more generally, any good can generate enormous value while earning almost nothing for the property right holders of that good.

Water is essential to life, yet it is nearly free. Yes, the value generated, or the demand for what, does matter for prices,but only on the margin. Supply matters just as much. Supply and demand, after all. Water is plentiful, so water is cheap, no matter how much life depends on it. The holders of the property rights for water are not becoming billionaires, and those who are make money not from the actual essential part, but from bottling and marketing it in a specific way.

Returns go to goods with the right combinations of value generated and scarcity. We’ve known that basic idea since Ricardo, but the marginal revolution really tied it into a self-contained theory of value and price. Price does not measure the total usefulness of a thing. It measures the value of one additional unit, given how hard that unit is to obtain.

When we start thinking about prices and AI, we already see a water-like aspect going on. For example, the thing these companies are racing to build is collapsing in price. That’s not uncommon. Chips get cheaper. Computers get cheaper. Televisions get cheaper.

What is not ordinary is the speed. When GPT-3 became available in 2021, it was the only model that could score 42 on the MMLU benchmark, and running it cost about $60 per million tokens. Three years later, the cheapest model capable of clearing the same bar cost six cents. I’m not great with numbers, but that seems like a big drop. Epoch AI tracks inference prices and has prices falling to 1/9th the price each year up to 1/900th per year. I’m sure if I looked in the past week, these numbers would have fallen more for some models. Just today, Meta released a model (Spark 1.1) that further competes hard on price.

So we have two competing forces. A fixed level of intelligence is becoming abundant, and abundant things are cheap at the margin no matter how useful they may be in total. So you have a horse race, whether the moving out of the intelligence frontier will outstrip the plummeting price for a fixed amount of intelligence.

Nobody is paying nearly a trillion dollars because today’s frontier intelligence will remain scarce. Within a year or two, much of it will be cheap. Investors are betting that the leading labs can keep producing (and controlling) something that does remain scarce. Maybe that’s just the moving frontier, or other things like proprietary data, locked-up compute, privileged distribution, or the workflows that make their products habitual.

But what exactly remains scarce? Alex Imas asks a related question—that I’ll say more about—but focuses on the demand side more. I will focus more on the supply side and who owns the property rights to that which remains scarce.

AI makes intelligence easier to copy

Let’s think of intelligence as a kind of recipe. It is a way of combining ordinary things into something worth more than the ingredients. It is non-rivalrous. My knowing a recipe doesn’t hinder you from knowing it. A baker turns a few dollars of flour, water, butter, and heat into a croissant that people line up to buy. The ingredients are not especially scarce, so the baker’s intelligence, knowledge, his know-how, whatever, allows him to earn a profit.

But there are two different things hiding inside the word recipe.

One is the card. There’s a list of ingredients and steps, the kind of thing you could write down and hand to a stranger. But there’s also stuff that is missing from the recipe card, that the baker forgot to write down or is implicit, like the judgment about what matters, the sequence in which things should happen, the adjustments when conditions change, the tacit sense of quality that separates a good croissant from a mediocre one. I’ll think of the first one as tasks, just like task-based models, and then the second that lumps it all together to generate value, the intelligence.

Pre-AI, even the card was easy to copy. The know-how is not, and that is what makes it scarce. Anyone can buy flour and butter, and anyone can read a recipe card. They cannot easily reproduce the timing and the touch that make the croissant good. The baker earns a premium because the valuable intelligence cannot be separated from the person who has it.

For most of history, much of that recipe was trapped inside the person who knew it. They could teach others. They could write down the ratios and temperatures, but, still, there remained some unique ability (let’s focus on the knowledge side) around maybe timing and judgment. The true recipe remained scarce because it could not be separated completely from its owner, even if you could write down a word-filled recipe. Some important part of the know-how stayed embodied in people, teams, and firms. Knowledge was sticky.

That’s obviously not completely gone yet, but AI seems to loosen that connection between knowledge and where it is embodied. Because intelligence is nonrivalrous, it can replicate and disseminate much faster. That’s definitely true of the written layer, although it is starting to imitate the tacit layer too. It can pull out subtle parts of the craft that were never written down, maybe never articulated at all.

If you give the baker’s recipe to every shop in town, supply increases, and more people may eat them than ever. But no baker earns a premium merely for possessing the recipe, because every baker now has it. Just like on other dimensions, competition pushes the price of the croissant closer to the cost of its ingredients and production. The return to the knowledge drops.

Some of the old premium goes to customers in the form of lower prices. The remainder settles on whichever inputs are still scarce. Maybe there is still something to being on the corner with the foot traffic. Or maybe the oven (not written down) is the key. We could go down the list: the trusted brand, the financing, or the baker whose hands really are faster. Output rises, but the return to knowing the recipe falls. To stay ahead of this process, the baker has to continually come up with new recipes that aren’t copied and ahead of the market.

James Bessen called it the paradox of technical knowledge. Replicable ideas allow us to produce more with the same resources, but the resulting wealth does not automatically accrue to the people who once held the knowledge. When intelligence becomes abundant, bottlenecks matter more

So we get to a world where we have 100 million Einsteins in a datacenter. A huge amount of know-how has become copyable. But the model still has to run somewhere. It requires chips, electricity, cooling, buildings, land, and time. Unlike knowledge, those inputs are rivalrous. Two workloads cannot consume the same GPU-hour or the same megawatt at once.

So the cheapening of intelligence can raise the returns to the complements needed to use it. As intelligence gets easier to copy, users bid more aggressively for the scarce inputs required to run it at scale.

We see this already with physical complements. For example. OpenAI’s gross margin reportedly fell from 40 percent to about 33 percent in 2025. This is while its inference bill quadrupled. Upstream, Nvidia reported a 71 percent gross margin and $193.7 billion in data-center revenue in its latest fiscal year. ASML offers a physical version of this strategy. It is the only company capable of producing EUV lithography machines. The newest cost roughly $400 million each, and the company earned a 53 percent gross margin in 2025. ASML stays rich because competitors cannot simply copy what it makes.

Chips embody a lot of intelligence, but once produced they are rival physical goods. And those are not doing too shabby in a world flooded with intelligence. And those aren’t doing too shabby in a world flooded with intelligence.

Energy has the same structure. It remains scarce for the foreseeable future. The International Energy Agency estimates that data centers consumed about 415 terawatt-hours of electricity in 2024, roughly 1.5 percent of global electricity use. It projects a “demand” of approximately 945 terawatt-hours by 2030. (I can’t seem to tell what price this is assuming for the quantity demanded, which must depend on price, but let’s not fight that battle.)

Again, this is Ricardo in a nutshell. The rent goes to the scarce complement. Yes, it’s not conclusive but it suggests the value is spread around, not just to the frontier models. It seems related inputs are doing well.

Bottlenecks have clocks

That does not mean chips and electricity will remain scarce forever. High returns attract new fabrication plants, generators, transmission lines, and data centers. It means they are among the clearest bottlenecks today. Markets respond. I think we’ve mentioned that in this newsletter.

So any scarcity has a clock on it. It depends on what is scarce now and how fast it can respond. It depends on elasticities, as always. But those scarcities are responding. We can see that in the data center build out, which requires lots of these inputs into compute which is then an input into intelligence.

No all digital is replicable

Under open and competitive supply, the pure return to a copyable model is pushed toward zero. The service still has a cost because inference consumes scarce compute.

But the recipe itself earns no rent. So we have a distinction between the recipes return and the return to everyone in the supply chain.

Every company wants to avoid that, so they look to ways to exclude. If you prevent the recipe from being copied, you turn a nonrival capability into something rivalrous, which can become a priced asset. All of the physical production has this, ASML or chips, for example. offers a physical version of this strategy. The labs are trying to construct an informational equivalent. Can they have unique intelligence that no one else has? One possible way to get that is to input unique data. So you get that Reddit licensed its archive under contracts worth $203 million. And law may respond. In Thomson Reuters v. Ross, a federal judge rejected an AI startup’s fair-use defense for training on Westlaw material. Copyright and contract can manufacture scarcity around information that would otherwise be cheap to reproduce. So that changes relative scarcity.

This is basically the model in Cockburn, Henderson, and Stern. As algorithms diffuse, the return shifts toward the complementary assets that remain protected. OpenAI understands the distinction. As models improve, it argues, “the limiting factor shifts from intelligence to usability.”

What happens to workers?

So far, we haven’t really talked about workers. But I think we can easily extend the model. What parts of the job become replicable? What is exclusive?

We have to be careful about what the worker is selling. A worker sells an output, whether it be a diagnosis, a legal brief, a repaired machine, a lesson, a design, a relationship, a judgment someone trusts enough to act on. She does not sell “tasks” in isolation.

Let’s think about this in production function terms. To produce that output, she combines inputs. Some are personal, like her knowledge, judgment, taste, reputation, relationships, attention, and time. Some are external and bought over the market, like software, equipment, institutional authority, licenses, assistants, referrals, customers, and the firm or platform that connects her to demand.

Garicano, Li, and Wu work through this in more detail. Given markets price jobs, not tasks. A task only comes loose from the worker/job when it can be cleanly separated from everything bundled around it.

AI enters different places. It becomes an input into the worker’s own production. It makes research cheaper, drafting faster, scheduling easier, or diagnosis more accurate. In that case, AI feeds her work. Inputs become cheaper. If the rest of what she supplies remains scarce, her return can rise. She didn’t do anything more, but her productivity increased, and she captured (at least some of ) the gains.

At the same time, all of her competitors (and new competitors) are also using AI. Maybe some of that is much more “pure AI” and we can think of the AI as the direct competitors. The knowledge that you had is no longer scarce.

So we have a horse race between AI as an input and AI as a competitor. It’s not obvious which of those forces wins.

A decade after Geoffrey Hinton said in 2016 that we should stop training radiologists, the number of radiologists has risen by about 17 percent. AI became better at reading scans, but reading scans was only one input into the radiologist’s output. So far, a scan cannot be cleanly separated from the clinical judgment, the responsibility for the call, or the conversation with the surgeon. So AI did not reproduce the entire bundle of work performed by a radiologist.

Evidence from Upwork already points in this direction. Tracking 49,610 freelancers across more than two million contracts, Auyon Siddiq and Niuniu Zhang find that after ChatGPT, buyers in the most AI-exposed categories placed less weight on credentials and past performance and more weight on price. Demand shifted toward cheaper workers. As the work became easier to standardize, workers began to look more interchangeable. Interchangeable suppliers compete on price, not reputation. You could imagine that same thing happening even for relational goods.

Who owns the human premium?

Alex Imas approaches the same question from the demand side in his essay “What will be scarce?”

As standardized goods become cheaper, richer consumers may spend more on provenance, exclusivity, authenticity, and human connection. In one experiment, Imas and Graelin Mandel found that exclusivity raised the value of human-made art by 44 percent, compared with 21 percent for AI-made art. I think this demand-side argument makes sense.

There are two ways to extend it. First, “human” is too broad a category. A human premium can rise in some markets while falling for particular workers in others. The supply side still matters. If AI lets many more people provide an adequate human service, the premium attached to any one provider can fall, even though the service remains human.

Consider a relationship advisor. Her warmth and personal manner may be genuinely unique. But much of the service around that relationship, such as advice, scripts, interpretation, suggested replies, and emotional framing, can be separated from her and reproduced by AI. If AI cheapens her research and preparation, it feeds her work. She can spend more time on the relationship itself. If AI lets a thousand adequate advisors offer similar scripts, similar advice, and similar reassurance to the same clients, it floods her market. Her humanity remains real. The market is just as “human” as before, but the specific service she sells today will become less scarce.

This cannot be the aggregate story, since the supply of humans is basically fixed. The distributional story can still be true. If AI lets many more people provide an adequate human service in a particular market, the premium attached to any one provider can fall even though the service remains human.

This is the same ownership question we have been talking about all along. For workers, ownership often shows up as portability. Can the scarce human input walk away? Can it reach customers without the firm, platform, brand, license, or copyright wrapped around it? If yes, the worker has a claim on the premium. If no, the premium can show up somewhere else.

This isn’t a new problem. Things people think are separable aren’t always.

In the 1920s, a young Walt Disney built a studio around Oswald the Lucky Rabbit, only to discover that the character’s copyright belonged to his distributor. The distributor made the obvious move: keep the character, hire away Disney’s animators, and remove the man who appeared to supply only ideas. The distributor seemed to own every copyable part of the production process: the character and the hands that drew it.

But he did not own Disney’s sense of what was funny. That scarce input could walk out the door. It did, and as far as I can tell, had some success.

The rule

So what’s gonna happen? No idea. But I think we have a framework to think through it.

AI will create enormous value by making intelligence, and the diffusion happens by making it easier to copy. The returns go to whatever remains scarce once the intelligence is cheap. None of this is new. Right now, we see that the scarce thing is physical, like chips, megawatts, and land. Sometimes it is generated or manufactured, like data, distribution, a copyright, a brand. And sometimes it is a person whose judgment or relationships cannot be separated from the service she sells.

When the scarce thing is a person, there is a further twist worth thinking about. Does the intelligence AI is copying feeds her work or floods her market? Copied intelligence that becomes her input raises her return. Copied intelligence that creates her competitors lowers it, even though her own intelligence was never touched.

It is not enough to say intelligence goes brrr, so money goes brrr. Scarcity depends on ownership. Scarcity depends on property rights. What is AI making abundant, what remains scarce, and who owns it? That is where the returns to AI go.

This doesn’t always make me many friends. I occasionally make arguments that defend particular policies that my friends and colleagues dislike. They roll their eyes. They suggest I give too much credit to politicians or the political process or voters or … you get the point. In fairness to my friends and colleagues, their skepticism is often rooted in a basic fact of life. Because most people agree that national defense is an important function of the state, politicians love to invoke national defense in arguments that support their favorite pet project. Often, these claims are dubious.

Nonetheless, that doesn’t mean that all claims are dubious. In fact, one benefit of studying defense-based policies is that there can be clear evidence of failure. If a policy is particularly important for defense and one country chooses not to enact that policy, one would expect to observe military defeats and other defense-related setbacks.

Because of my interest in defense-related policies, I’ve been asked quite a bit recently about what I think of defense-related AI policies. To be honest, I haven’t fully formed an opinion on policies related to AI and defense. These discussions often make it difficult to interpret whether there is a legitimate issue or whether politicians are up to their old tricks of using dubious justifications to do what they want.

However, a recent AI-related policy has given me the opportunity to think through some of these issues. In this week’s post, I’m going to discuss this recent policy action and how to think about it in terms of policy and national defense.

Anthropic Can’t Let People Use Their Model

In June, Anthropic (the company behind Claude) issued a statement saying that the U.S. government had issued an export control on its Fable 5 and Mythos 5 models. This export control restricted access to all foreign users, including foreign nationals, from using these models. It is difficult to think about an export control for an AI model. Partly for that reason, Anthropic announced that it had decided to restrict access to these models for everyone because it seemed like the only way to comply with the export control. This week, they announced that the controls have been lifted and people can use the Fable 5 model. The Mythos 5 model is still somewhat limited.

The decision of the U.S. government and Anthropic sparked my interest. The reason is that not too long ago, Anthropic and the Trump administration had a very public spat about the technology and the government’s use thereof. This time around, there was no public spat, only an announcement.

It took a few days to get a sense of what was going on. However, according to reports, the head of the National Security Agency (NSA) informed the Senate Intelligence Committee that the Mythos model had broken classified systems within a matter of hours.

I have no idea how I, your humble newsletter writer, can independently verify the validity of these claims. In fact, I have some reason to doubt the specific claims. Suppose they were true. Would the NSA want to broadcast this to the world? That seems doubtful. Nonetheless, even if the specific claims isn’t true, that doesn’t mean that wasn’t some type of serious concern or issue.

With that in mind, let’s just assume that these claims are correct. This type of issue, or something like it, certainly sounds like a serious (not dubious) problem for national defense. A cybersecurity risk to the government’s intelligence operations (and who knows what else) certainly seems like something that warrants some type of action on the part of the government. The action taken by the government is a de facto ban on the use of a particular model (even if they are temporary, like this one).

How should we think about this?

The Economic Incentives, and Relating this Back to Other Policies

When we think about AI models in the context of current and recent events, AI models present both benefits and potential costs pertaining to national defense. AI is useful for drones. Unmanned sea-crafts are in development, if not already in use. AI can help military leaders assess a great deal of information and use it to analyze their options. It also aids with both the collection and use of intelligence. At the same time, advancements in AI that can help with things like cybersecurity can also potentially create threats to cybersecurity. A model capable of identifying your weaknesses might also reveal the key to exploiting those weaknesses.

If we accept the reports of what happened and we assume that this will be the way in which the government handles such problems in the future, we can start to think a bit about policy.

Suppose that any time a new AI model is introduced, there is a chance that the government shuts it down and restricts access to the public. This creates relatively lumpy returns to the development of new models and potentially costs firms a lot of money.

The training of new models requires the use of tens of thousands of GPUs. Those GPUs have to be produced by someone. The GPUs have to be located somewhere, which requires overhead and the access to and expenditures on the power necessary to run the machines.

Periodic shutdowns of models make the rate of return on each model lumpy. Ex ante, such restrictions lower the expected rate of return on a new model. Lower expected returns tend to result in reductions in investment. A decline in investment means fewer GPUs, fewer data centers, a decline in the production of computer memory, and less development of power infrastructure.

The restriction on output (in this case, the export control) makes it less likely than an existing model can harm national security, but also leads to a reduction in capital investment and therefore a slowdown the development of new models. Even accepting that the export control is the only appropriate policy, this still leads to an underinvestment in capital related to AI that is suboptimal. The reason for that is that the slowdown in the development of future AI models means a slowdown not only in AI-related threats to national security, but also to a slowdown in all of the benefits that would accrue to the national security apparatus from continued development of new models. In some sense, a policy that simply limits access to models creates an immediate benefit for the government, but a longer term cost.

The appropriate thing for the government to do (again, if it is intent on using export control-induced bans) is to couple the de facto ban with subsidies to AI infrastructure. Note that it is not appropriate to subsidize AI output, but rather to subsidize capital used in the production of new AI models. This would require subsidies for power-related infrastructure, data centers, and the production of memory and GPUs used in the training of models. The optimal policy resembles a bargain. The government offers subsidies to build up the infrastructure necessary to develop frontier AI models in exchange for limiting access to the models when national security threats arise. The policy thus mitigates the longer term costs of underinvestment that result from short-term bans on new models.

This sort of systematic policy would not be unprecedented. Earl Thompson once applied similar logic to rationalize other defense-related subsidies. In particular, Thompson pointed out that, during times of war, states usually adopt some form of price controls and that peacetime subsidies to particular industries could be rationalized by the cost of those wartime controls. He showed that wartime price controls result in intertemporal distortions in prices similar to a tax on capital and therefore result in an underinvestment in capital. Like the AI example, this theory argues that although regulation occurs at the level of output, the subsidies should be for capital investment.

When he looked at the data, that is precisely what he found in the postwar era. Wartime price controls on beef and dairy products did not result in peacetime subsidies for things like beef or milk, but rather for cows. The G.I. Bill can be rationalized as a subsidy for investments in human capital due to the tax on human capital created by conscription. In addition, he even found that where wartime controls were present and peacetime subsidies were absent, this could easily be explained by other characteristics of the market. For example, coffee was subject to price controls during WWII, but there was no peacetime subsidy. Thompson showed that there was no need. International coffee production was produced by a cartel. Thus, the high return to coffee during peacetime was enough to offset the low return during wartime and thus didn’t necessitate a subsidy. Overall, this general pattern was quite extensive.

There is already evidence of the U.S. government doing something similar for AI. The U.S. has taken steps to subsidize things like memory and GPUs through legislation like the CHIPS Act. However, despite executive orders from both the Biden and Trump administrations, there hasn’t been as much done to directly subsidize the build out the broader AI infrastructure.

Concluding Thoughts

For some time, there have been vague references to national defense and AI models. Recently, we got what I would consider the most concrete case of a threat to defense resulting from the development of new AI models. If the claims that have been reported are true (or even if they are strategic diversions designed to hide the true threats), then one can understand why the U.S. government might step in to try to prevent the use of a particular model. Nonetheless, there are broader implications associated with de facto bans (even temporary ones) on the use of particular AI models. Those implications include costs to the government in the form of foregone improvements in national defense on other margins.

What I’ve argued here is that de facto bans are likely to lead to underinvestment in AI-related capital infrastructure if such bans are standalone policies. Thus, if the government is going to use these de facto bans, they will need to couple the option for de facto bans with subsidies for AI-related capital. Otherwise, such bans are likely to produce short-term gains and long-term costs.

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If you ever come across an economic argument that seems to make sense but goes completely against conventional economic wisdom, it’s probably “reasoning from an accounting identity.” Run in the other direction. Accounting does not explain anything. That’s why we have price theory.

Take the following example. We all know that “Growth in real GDP depends on only four factors: consumption, government spending, business investment and net exports (the difference between exports and imports).” That comes from the definition of GDP as GDP = C + I + G + NX, so any growth in GDP comes from growth in one of those factors.

From there, one may mistakenly believe that, as Peter Navarro suggested, “Reducing a trade deficit through tough, smart negotiations is a way to increase net exports — and boost the rate of economic growth.” After all, there’s an equal sign there! Y EQUALS C + I + G + NX. It’s just math losers. QED.

No. Wrong.

Just as we never reason from a price change, we need to never reason from an accounting identity. My income equals my savings plus my consumption: I = S + C. But we would never say that if I spend more money, that will cause my income to rise.

It all depends on what caused the change. In my income example, more spending could cause me to work more to cover those expenses. Or I could save less. It depends. In the GDP example, we need to know what caused the change in net exports (or any other part of the equation). We need to be explicit about what actually caused the change in net exports. Exports don’t simply fall from the sky, and move up and down based on our wishes. We need to know the causes. There is an added complication in this example since the reason we subtract imports from GDP is that they are already part of consumption (C) and shouldn't have been since imports are not domestic production.

Did we discover a new fracking technology? Net exports will likely go up, as will GDP. Did we impose tariffs on imports from China? Those are likely inputs into other production processes and, therefore, lower “US gross domestic production,” aka GDP. Therefore, the tariffs cause an increase in net exports, but they cause a decrease in GDP. The reason is that the first mover— the cause of tariffs— pushed up NX, but it also at the same time pushed down something else, such as the C in C+I+G+NX. To say GDP moves up if net exports move up requires an assumption the C, I, and G are not changing.

For basically any macroeconomic example we are interested in, holding C, I, and G fixed is a ridiculous assumption. We need to think about how all of them are affected by a certain cause. Luckily, as I’ve explained before, economics helps us establish causation.

Economics—whether theoretical or empirical—helps us establish causal claims about the world. If X changes, then Y changes. If you prefer the framing of counterfactuals: If X had been different, then Y would have been different.

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3 years ago · 34 likes · 15 comments · Brian Albrecht

Yes, the accounting identity must hold, and we need to keep track of that, but it tells us nothing about causation.

Luckily, price theory allows us to trace out the myriad of effects that are caused by a single policy change. We must constantly ask, and then what? Suppose China (for political reasons) decides it doesn’t want its companies to trade with US companies and stops them from doing so. Now from here, we can try to trace out different implications. Chinese firms stop producing goods for exports. And then what? US consumers have fewer goods to consume (C goes down). And then what? They substitute partially to US manufacturing (C partially goes up). And then what? Workers produce fewer services (C goes down). And so on.

That’s just following the goods being traded. The policy change also means that Chinese firms have less demand for dollars. And then what happens? They weren't using those for purchasing US goods, so they must have invested in US debt or equities. And so on.

Every semester I make sure to include “Never Reason from an Accounting Identity” in my courses. The reason I’m mentioning trade policy today is that there was a recent “handbook for conservative policymakers” released by American Compass. One of their policy proposals was to eliminate the trade deficit. To accomplish this, we should:

Establish a uniform Global Tariff on all imports, set initially at 10% and adjusted automatically each year based on the trade deficit. After any year when the trade deficit has persisted, the tariff would increase by five percentage points for the following year. After any year when trade is in balance or surplus, the tariff would decline by five points the following year.

The essays defending this general position (although not necessarily the exact policy proposal) are just a series of reasoning from accounting. There is no economic content. As one essay put it,

For decades, the implicit and explicit subsidies to manufacturers that have driven surpluses in countries like China and Germany have caused global manufacturing to migrate from deficit countries to surplus countries, and from none more so than the largest deficit country by far, the United States.

The argument above supposes that there exist countries out there in the ether called surplus countries, and manufacturing moves to them. In reality, when you’re not just playing with definitions but looking at causation, Chinese subsidies increase manufacturing which increases the trade surplus (in some cases). The causal arrows point from subsidy to manufacturing and trade surplus, not from surplus to manufacturing.

The essay goes on to say that “American trade deficits force Americans to choose between higher unemployment, more household debt, or greater fiscal deficits.” Ignore the unemployment red-herring. The trade deficit doesn’t force (or cause) household debt or fiscal deficits. Something else causes both trade deficits and fiscal deficits to go up together.

For example, if people really want US treasury debt because there is a global financial crisis and US treasuries are the safest asset available, they will buy up more debt, driving down interest rates, and increasing fiscal deficits. They will want dollars to buy that debt, so they will need to sell goods to get dollars. The unique position of US treasuries in the global financial market causes both fiscal and trade deficits. They don’t cause each other. It’s a bit more complicated since we need economics to trace out causation and can’t just look at an equation, but it is vital.

The purpose of this newsletter is not to trace out all the implications of a trade war. The purpose is to point out that we cannot simply reason from the accounting identity. We need to take seriously all of the feedback.

Profits Do Not Cause Inflation

Before we mock the trade deficit people too much (who, in this case, are “conservatives”), there has been a more prominent example in recent years that has generally come from people on the left. It is the idea that profits cause inflation.

After all, any revenue PQ = Costs + Profits. So P = Costs/Q + Profits/Q. If inflation means that P goes up, it must be “caused” by costs or profits.

No, again. Stop it. This is like saying consumption causes income.

Instead, we need to ask, what changed? What actually caused things to be different? Did the Fed print a bunch of money? Then consumer spending will go up, which will drive up prices, costs, and profits. It may be that profits rose more than costs but that’s not a causal relationship. Or did prices rise because of an oil shock? Costs will probably rise, along with prices, but it could be that profits fall enough to offset that. We can do the decomposition, and that’s fun, but let’s not mistake that for economic analysis.

Instead, we need to use economic reasoning to think through what is causing profits and prices to move, sometimes in the same direction and sometimes in different directions.

Economic ignorance is omnipresent. Price theory is the answer. Economic Forces is the answer.

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The way that externalities are typically taught at the introductory level is as follows. A negative externality is a cost paid by a third party to normal market activity that is not reflected in the price of the good being traded. As a result, the social cost is greater than the private cost. Because this cost is not paid by market participants, no one internalizes the cost and the resulting equilibrium quantity is inefficiently high. The standard textbook argument is that the government should levy a tax on this activity equal to the marginal external cost (the difference between the marginal social cost and the marginal private cost). This tax is referred to as a Pigouvian tax. By doing so, this forces market participants to internalize the cost. The resulting equilibrium quantity in the market is the socially efficient quantity.

But is this policy really optimal? If so, in what sense? If not, why not?

Setting the Stage

Let’s imagine that there are 3 distinct groups. There are consumers, producers, and those who are not in the market at all but who suffer the external costs. Let’s assume that all costs are variable and the cost of production and the external cost are both linear in quantity. This implies that both the marginal cost of production and the marginal external cost are constant and equal to the average cost of production and the average external cost, respectively. The market is competitive and the supply curve is horizontal.

As any student of introductory economics knows, a tax drives a wedge between the price that buyers pay and the price that sellers receive. Since the supply curve is horizontal, the entire area to the left of the demand curve due to this tax wedge is a reduction in consumer surplus. Some of this area goes to the government in the form of tax revenue. The remainder is the excess burden, or deadweight loss, of the tax.

If the size of the tax is equal to the marginal external cost, this does in fact reduce the quantity traded to the amount that the market would choose if all the costs were internalized. This is often referred to as the efficient quantity.

Nonetheless, it is important to note that the consumer is worse off. This is true even if the tax revenue is used to make a lump sum transfer to the consumers, or otherwise paid to them in a way that doesn’t affect their choice in the relevant market we are discussing. The reason for this is that the total reduction in the consumer surplus is greater than the tax revenue.

It follows that the Pigouvian tax is not Pareto improving since consumers are worse off.

An Alternative Framework

Pigou wasn’t the only economist famously known for thinking about externalities. Ronald Coase is also famous for thinking about the problems of social cost. Coase emphasized property rights. These external costs we’ve been referencing often follow from an incomplete definition of property rights. For example, a frequently used example of a negative externality is a factory that pollutes a river upstream from a fishery. If either the fishery or the factory are assigned the property rights to the river, then the two parties could negotiate. For example, if the fishery is assigned property rights to the river, the fishery could prevent the factory from polluting the river unless the factory offers sufficient compensation to the fishery. That compensation forces the factory to internalize the cost of its pollution. Alternatively, if the property rights to the river are assigned to the factory, the fishery could pay the factory to limit its production in order reduce pollution.

Ideally, it would be great to be able to compare Pigouvian taxes to Coaseian logic within one coherent framework. Fortunately, the new edition of Chicago Price Theory contains an example that does just that. It requires thinking about demand a bit differently.

Consider the following example. Suppose that we have a demand curve as depicted in the figure below. The demand curve shows the typical negative relationship between price and quantity demanded. A tool that Kevin Murphy likes to use is to draw indifference curves in the price and quantity space. But what would an indifference curve look like in this context? As depicted in the figure below, for the price equal to 1, one can draw and indifference curve that is tangent to a horizontal line consistent with the price. Near this price, the indifference curve is relatively flat. This is because consumers are pretty indifferent about the quantity around the given price. They’ll take a little higher or a little lower quantity at a slightly lower price and be just as content as they are with the quantity demanded associated with a price of 1. The indifference curve is pretty steep to the left of the demand curve. This is because as the quantity the consumer gets to consumer declines, the consumer has to be compensated with a lower and lower price to keep them just as well off. To the right of the demand curve, the indifference curve is relatively flat because the consumer doesn’t need a much lower price to consume a little more.

Note that this also implies that lower indifference curves are preferred by consumers on this figure. This is because for a given quantity, the consumer prefers a lower price.

Now, let’s suppose that marginal private cost is 1 and the marginal social cost is

The figure below shows that quantity that would be chosen in the absence of a Pigouvian tax would indeed be q_u. A Pigouvian tax equal to the marginal external cost would result in the equilibrium quantity, q_e. This is the quantity demanded when consumers must pay the marginal social cost and is therefore the efficient quantity of output in the market.

Given what we know about the indifference curves plotted in price and quantity space, it is straightforward to see from this second graph that a Pigouvian tax makes the consumer worse off. This is a different way of illustrating the point I discussed above. A Pigouvian tax can make sure that the equilibrium quantity of output is efficient, but the tax isn’t Pareto optimal. In order for the tax to be Pareto improving, it would need to make some people better off without making others worse off. However, it clearly makes consumers worse off.

This begs the question: Is there a way to make sure that the efficient quantity is the equilibrium outcome while simultaneously being a Pareto improvement?

In order to think about this, we need to think about the welfare of the other people in the market, producers and those outside the market who suffer the costs of the externality. For simplicity, let’s lump both these groups together. In addition, let’s think of this group’s welfare as equivalent to the total surplus to the group. We can define the “other surplus” that goes to others in the market as follows:

Where the total surplus is the combined surplus to producers minus the external cost to those outside the market. To think about how this can be illustrated on our graph, consider the following example. Suppose that the marginal external cost is 1/2. It is possible to think about combinations of p and q that provide the same surplus. To see, why let’s consider some examples. Imagine that when the p = 1, q_u = 48. This implies the surplus is -24. Now, consider that if the price is 1/2, the quantity that provides the same amount of surplus is 24. If the price is 3/10, the quantity that yields the same surplus is 20. If the price is 0, the quantity that produces the same surplus is 16. Thus, one can illustrate the “other surplus” in the figure as the curve OC.

Now, we are prepared to think in Coaseian terms. Note that for any given quantity, the “other surplus” is increasing in p. It follows that any point above the line denoted OC, the combined group of producers and those who suffer the cost of the externality are better off. At the same time, we know that any point that lies below U_1 makes consumers better off. It must therefore be true that the area between the indifference curve labeled U_1 and the OC curve represents potential gains from trade between the consumers and the others.

The Pareto optimum solution is achieved at the point at which the others’ surplus curve is tangent to the consumer’s indifference curve. Consider the following example. For the OC curve as it is drawn, a lower indifference curve tangent to the OC curve would make consumers better office without making the others worse off. The tangency point between these two curves is a Pareto optimal outcome because in comparison to that tangency point, there is no other point that can make one group better off without making the other group worse off.

It is also important to note from the graph that there are many points on the graph between U_1 and OC associated with the efficient quantity. This not only tells us that the efficient outcome is possible, but that we can get to the efficient outcome without the Pigouvian tax and in a way that consumers would prefer to the Pigouvian tax.

Of course, there are a couple of things to note here. The efficient outcome is not possible if the marginal price is set below 1. If the marginal price is uniform to all consumers and set below 1, the quantity demanded would be even greater than q_u. Implementing the efficient equilibrium outcome without Pigouvian taxation would require that the marginal price is greater than 1 and the average price is less than 1. This entails some non-linear pricing scheme.

To turn this back to Coase, there might be some voluntary solution via bargaining that implements a non-linear pricing scheme that is Pareto improving. This would likely require setting up some type of organization that can impose this type of non-linear pricing in order to generate a Pareto-improving outcome.

Whether or not the efficient quantity can be achieved and how close such an organization can get to the efficient quantity depends on cooperation costs. As Coase alluded to with regards to transaction costs more broadly, coordination costs limit the ability to achieve the efficient outcome.

Some Concluding Thoughts

The standard argument that negative externalities can dealt with by implementing a Pigouvian tax ignore some of the welfare implications of the tax. Such taxes might produce the socially efficient quantity, but these taxes are not Pareto improving.

In fact, externalities are substantially more complicated if we take Pareto optimality seriously. The Coaseian logic that bargaining can produce a better outcome is illustrated by thinking about the total surplus from trade of all parties involved, including those who bear the external costs. Furthermore, as Coase himself emphasized, the ability to reach the efficient outcome through a voluntary solution is limited by transaction (in this case, coordination) costs.

This is just one more example of why we spend so much time on externalities here at Economic Forces. The average introductory textbook often makes externalities seem straightforward and the policy solutions seem easy. When it comes to providing caveats to the Pigouvian policy solution, textbooks might acknowledge the difficulty of estimating the true marginal external cost. Some textbooks might even mention that there can be a tension between the Pigouvian tax that implements the efficient quantity of output and the Pigouvian tax that generates the most revenue. Nonetheless, this is only part of the story. A bigger limitation is that Pigouvian taxation isn’t Pareto-improving.

If you want the efficient quantity of output and you want to make sure there is a Pareto improvement, a Pigouvian tax simply won’t do.

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One idea is to tax computer processing capabilities, sometimes called a “compute tax.” Andrew Yang is pushing it, so you know it must be serious. John Arnold captured the general sentiment on Twitter:

As Anton Korinek told the WSJ: “Half a year ago, it was something you would hear about only in very select circles. It really has become much more mainstream in the last three months.” That piece has a lot of great quote, so I will keep comping back to it. It also has Nobel laureate Simon Johnson saying a compute tax is a “sensible policy lever to slow down automation.”

Is it sensible?

We agree that when you tax something, you get less of it. That would slow automation down. “Sensible” is not the word I would use, though. If you just hate AI and want less of it, then maybe Simon Johnson is right, and a compute tax is sensible.

A compute tax is about as bad as a tax can be, by the standard benchmarks used in public finance. If you care about things like increasing output, total surplus, minimizing deadweight loss, those types of things, stay away from this.

This newsletter explains why. In many ways, this will mirror what we’ve discussed before about tariffs, so I’m going to keep bringing them up in this piece. I know. Sorry. But, as Herbert Spencer said, “Only by varied iteration can alien conceptions be forced on reluctant minds.”

What is a compute tax?

A compute tax is a levy on computational resources. Think GPU hours, processing power, data center electricity, or some similar proxy for AI work. But “compute tax” bundles two quite different proposals, and the difference matters.

Korinek and Lockwood have written the most careful framework on this in a Brookings working paper on public finance in the age of AI. They draw the key distinction: there is a stock version and a flow version.

A stock tax is if you tax the GPUs, the data centers, the training clusters. This is basically a form of capital taxation (which we will talk a lot about below). My reading is that this is the most commonly proposed tax. The idea of banning data centers is an extreme tax on the stock of compute.

In principle, you could also tax the output. This is a tax on the flows, through the tokens generated, the images produced, the AI services consumed. Korinek and Lockwood are more sympathetic to this form of taxation. But once you add the B2B exemption that they suggest, you’ve described a regular sales tax or VAT on AI consumer services. I don’t think we should call that a compute tax.

Taxing the wrong thing

There are a few main results in optimal taxation that show up again and again. People can quibble over the exact ordering but I’d say the most important comes from Diamond and Mirrlees.

The takeaway is don’t tax intermediate goods. Keep the production side of the economy as efficient as possible, then redistribute from the output. That’s why it’s called Diamond-Mirrlees production efficiency.

Compute (again, as a stand-in for computer processing) is huge now but going to be the intermediate input of the modern economy. It goes into drug discovery, weather forecasting, fraud detection, medical imaging, logistics, customer service, and, yes, generating cat pictures. When you tax compute, you raise the cost of every single one of those downstream applications. You shrink the economic pie before anyone gets a slice.

Korinek and Lockwood have a great line about how a compute tax is like “taxing steel during the industrial revolution.” You don’t make people richer by making steel expensive.

This was also the core problem with tariffs on intermediate goods. As I’ve explained before, a 10% tariff on imported car parts compounds through the supply chain and becomes a 30% effective tax on the finished car.

The supply chain aspect may not be as extreme as if you’d say tax something even further up the supply chain, like semiconductors, but a compute tax compounds in the same way. Tax the GPU hours that train an AI model, and the cost cascades through every product that uses the model. The drug company, the weather service, the fraud detection startup, the accounting firm, they all pay more. Pascual Restrepo told the WSJ: “Why do you want to increase the cost of all of that?”

This feeds directly into another one of the main results in optimal taxation: don’t tax capital. The original Chamley-Judd result says that you shouldn’t tax capital. The original result said “in the long run,” but, really, even in the short run.

Data centers are capital. Training clusters are capital. The entire AI infrastructure buildout is a massive capital investment.

A compute tax discourages precisely the investments that make AI cheaper and more widely available over time. This is the equivalent of taxing ladders to protect the people climbing trees with their bare hands. You don’t help the bare-handed climbers by making ladders expensive. You help them by making ladders cheap enough that everyone can afford one. Then, if you want to redistribute, tax the coconuts.

It also doesn’t make sense to tax capital from a redistribution point of view, as John Arnold seems to worry about in his tweet. I made this exact argument about AI and capital taxation in my response to Trammell and Patel. The features of AI that people worry about (easy substitution between capital and labor, mobile capital, self-replicating infrastructure) are exactly the features that make capital taxation counterproductive. With elastic capital supply, a capital tax doesn’t stick to capital owners. It falls on workers through lower wages. The more mobile and substitutable capital becomes, the worse taxing it gets for the workers you’re trying to help.

The optimal rate is below zero

So far, Diamond-Mirrlees and Chamley-Judd say a compute tax is a bad tax at any rate. It’s not obvious that we shouldn’t even go further. Maybe we should subsidize compute?

The Pigovian principle (1920) says the optimal corrective tax on an activity equals its marginal external damage. When an activity generates negative externalities (pollution, congestion), tax it at the marginal external cost. When an activity generates positive externalities, the optimal “tax” is negative. A subsidy.

It’s plausible that compute has positive externalities from at least two distinct sources.

There’s a learning-by-doing element. If we’re training models and other people are learning from that process, the industry supply curve can be downward sloping, so my production actually helps your production. The firm producing the millionth GPU does not capture the full social value of pushing the technology further down that curve. Everyone who uses cheaper GPUs in the future benefits from that producer’s accumulated experience without paying for it. That’s an externality. We may want to push producers down the supply curve to lower everyone’s cost

There seems to be something to that when we see GPU performance improving, but it could be this is almost all internal to NVIDIA so its not ’s not an externality.

There’s a slightly different angle around general-purpose technology (GPT) spillovers. Bresnahan and Trajtenberg (1995) defined a GPT as something that is pervasive across sectors, improves over time, and has the capacity to spawn complementary innovations. So things like steam, electricity, semiconductors, and now AI compute all qualify. GPTs generate two-sided externalities, where users don’t capture the value of pushing the technology down its cost curve, and producers don’t capture the value of enabling downstream innovators they never anticipated. So it’s like learning-by-doing combined with when people use your good, you don’t get all the benefit.

In practice, I don’t think we have a good enough sense of exactly how to subsidize it to make it work. I’m skeptical of externality-based arguments. If we are going to start saying externalities for anything we want, that becomes a huge mess of just asserting AI is wonderful or going to kill us.

I’m saying it’s not obvious, from a Pigovian perspective, that we want to tax.

You can’t even define it

Above is all in the land of standard economic theory. It’s at a level of abstraction. But let’s take practice a bit more seriously.

Now suppose the legislature sits down to write the statute. What counts as taxable compute?

It seems like we definitely want to count a GPU training a large language model. How are we going to track that? What about a GPU rendering a video game? When my laptop is running code or my phone is autocorrecting, is that compute? Probably not. What if it is happening on the cloud through data centers?

Tax practitioners flagged this same problem with robot taxes (also a dumb idea for the same reasons). Are we going to tax ATMs?

Any definition will be either so narrow that firms route around it by relabeling their compute, or so broad it taxes everything with a processor. Both outcomes are terrible.

Let’s not forget about all those lovely exemptions. Will where get to the point where we have that “U.S. data” (undefined in statute) must be “processed” (also undefined) on “U.S.-made motherboards” (also undefined). Will medical AI get a carve-out? Climate modeling? National security applications? Each exemption is a lobbying target.

A broad consumption tax doesn’t have this problem. It taxes the final transaction. It doesn’t need to know whether an AI or a human produced the good. It doesn’t need to distinguish between “AI compute” and “regular compute.” It’s technology-neutral by design.

The revenue isn’t there

If you want to just slow down automation like Johnson, that’s one thing. But if you want revenue, say for redistributing to labor (ignoring the problems above), that’s another thing. Here’s the part that compute tax advocates don’t want to talk about. Korinek, who takes the AI displacement concern seriously, points out that the numbers don’t work, and a compute tax “would raise a little bit of money but would not really make a significant impact.”

U.S. compute spending is large in absolute terms but small relative to GDP. A tax high enough to fund meaningful UBI payments would need astronomical rates, generating enormous distortions. I’ve worked through the math before. When a tax base is narrow, you need sky-high rates to raise real revenue, and the deadweight loss grows with the square of the rate. That’s bad enough for tariffs, where imports are about 10% of consumption. For compute, the base is even smaller.

And let’s not forget those pesky elasticities, always causing problems for central planners. Compute infrastructure can relocate (unlike land, unlike most labor), a unilateral U.S. compute tax pushes training runs to Canada, the Gulf states, or wherever electricity is cheap and taxes are lower.

So what are we to do?

It’s not like we are starting from some optimal tax code. So can we fix it? Erik Brynjolfsson argues the current U.S. tax code already implicitly penalizes labor relative to machines. A company with 1,000 workers pays more in total taxes, including payroll taxes, than a company making the same revenue with 1,000 machines. I’m not sure that’s even true—and to the extent it is, we may want it, since capital taxes should be zero for the reasons above. If you still think the system tilts too far toward automation, the fix is to cut the tax on labor, not to add one to a particular form of capital.

Perhaps it is different now, but when I lived in Michigan, there was a combination of two laws that really confused me. On the one hand, it was legal to buy and sell fireworks. On the other hand, it was illegal to set off fireworks. Violations were subject to a fine. (In fairness, this isn’t completely true. There were certain days in which one was exempt from fines. I believe that New Year’s, Memorial Day, and Independence Day celebrations were exempt from fines.) It seemed contradictory to allow people to buy and sell fireworks, but that lighting off the fireworks on most days of the year resulted in a fine. Why allow people to buy something and then fine them when they consume it?

Another thing that I’ve long found perplexing is the parking situation on university campuses. I’ve spent a lot of years on university campuses and the one thing these campuses have in common is that there never seems to be enough parking to satisfy demand. This is such a problem that universities often have meetings about how to solve the parking problem that involve discussions about whether to build a new parking garage, but rarely about price. One would think if the objective was to solve an excess demand problem, the obvious solution would be to increase the price. Yet, somehow this never comes up in the meetings.

What is going on here? My conjecture is that both of these examples represent applications of something like a two-part tariff.

In price theory, a two-part tariff is a type of price discrimination. This particular type of price discrimination refers to a scenario in which the price of a good includes two parts: a lump-sum amount and a per-unit price. This type of arrangement applies to a variety of circumstances. Some major retailers like Costco or Sam’s Club are known for selling large quantities of goods at lower prices per unit than their competitors. However, they also charge a fixed annual fee to be a member and receive that lower per-unit pricing. Another example would be to think about bars that have a cover charge. The cover charge allows you to get in the door, but then they charge you for each individual drink you order.

Okay, but how does this relate to the examples that I started the post with?

University Parking

Let’s start by thinking about university parking.

One thing about university parking is that there always seems to be excess demand. This would seem to suggest that parking passes are priced below their market-clearing level. However, that doesn’t really make sense. Why would the university do this?

For example, imagine that the university has a fixed number of parking spaces available. In addition, suppose for simplicity that each person with a parking pass comes to campus every day and demands one parking spot. It would make sense to charge a price that is just high enough that the number of people who buy a parking pass is equal to the number of spots on campus. Charging a higher price will result in empty parking spaces and foregone revenue. Charging a price below this amount will lead to excess demand. There will be more people on campus each day who want to park than there are parking spots available.

Of course, if there are more cars on campus than there are spots to park them, these cars will have to park somewhere. Universities tend to have a common way of dealing with that problem: parking tickets.

Herein lies the solution to the puzzle of pricing for parking. The university is price discriminating when it comes to parking in order to maximize revenue. The university price discriminates via a two-part tariff: a fixed entry fee (the parking pass) plus per-unit pricing (parking tickets).

Let’s think about how this might work. Let’s imagine that there are a fixed number of of parking spots, denoted by Q_s. Furthermore, the inverse demand curve for parking spots is given as p = a - bQ.

Let p* denote the price that clears the market such that

Now suppose that the university sets the price equal to p_u such that

Note that by lowering the price of a parking permit from p to p_u, the university has the following foregone revenue:

where the first term is the lost revenue from lowering the price at the previous quantity and the second term is the increase in revenue from increasing the quantity sold at the lower price.

The excess demand for parking is a source of parking tickets. Suppose that there is some probability, $\lambda$, that the people parking illegally get caught and that enforcement is costless. Those caught parking illegally must pay a fee f. It follows that the university will generate revenue from parking tickets equal to

The university benefits from the two-part tariff if the revenue from parking tickets exceeds the foregone revenue from the lower price of the parking pass:

Given the demand curve, this simplifies to

Recall from the definition of the price elasticity of demand, evaluated at the market-clearing price, we have:

Thus, in order for the university to generate more revenue from the two-part tariff than from the market-clearing price for parking permits, the university simply needs to set the expected fine such that

where $\delta$ is the difference between with market-clearing price and the actual price of the permits. What this shows is that if the fines and/or the probability of getting caught is sufficiently high, then the university is actually better off with the two-part tariff. The necessary magnitude of the fine depends on the elasticity of demand for permits and the magnitude of the discount. All else equal, the bigger the discount, the bigger the necessary fine. Furthermore, as demand becomes more inelastic, the magnitude of the fine has to get bigger. The intuition is easy to understand. The university is selling a number of permits that is equal to the quantity demanded at the price it sets. When demand is inelastic, they lose revenue from reducing the price of permits because the percentage decrease in the price is bigger than the percentage increase in the quantity demanded. Thus, one needs a bigger fine per violation to make up for the lost revenue from permit sales.

As a result, it is possible for the lump-sum permit and the per-violation fines can maximize revenue. The basic idea here is that the university is able to price discriminate. Those who have a higher willingness to pay will not only buy the permit, but they will continue to park on campus even when there are no spots available and incur the fine whereas those with a lower willingness to pay will tend to arrive earlier to make sure that they get a spot.

Interestingly, this also seems to have an added benefit for the university. If parking is in short supply, high parking permit prices might draw the ire of students and their parents. High permit prices might make it prohibitively costly to park on campus. However, by reducing the permit prices and instituting fines for violations, the cost of parking on campus is now endogenous to the behavior of the driver. Parents are therefore likely to blame their children for the high cost of parking due to repeated violations instead of the university since the fines could have been avoided with better preparation. This tendency of parents to blame their child for the high cost of parking will be true even if the university has itself engineered excess demand with lower permit prices, which increases the likelihood of violations.

Fireworks

When it comes to the fireworks example, our analysis should consider the objective of the state government. Why would they allow you to buy fireworks, but fine you for lighting them? Aren’t they sending mixed signals?

Suppose that their objective is to raise the maximum amount of revenue possible. One way for the state to generate revenue would be for the state to charge a tax on every unit of fireworks that they sell. However, there are limits to how much tax revenue can be raised.

For example, consider the case in which all consumers are identical and the supply and demand curves are linear. In the absence of the tax, quantity supplied is equal to quantity demanded and the market clears at some equilibrium price. In this case, the total surplus from trade (consumer surplus + producer surplus) is maximized.

When the government levies a tax per unit of fireworks sold, this drives a wedge between the price that consumers pay and the price that sellers receive that is equal to the size of the tax. Because of this wedge, both consumer surplus and producer surplus are lost. The distribution of the foregone surplus depends on the relative price elasticities of supply and demand. For our purposes, we don’t need to worry about the burden of the tax. The more important point is that the foregone surplus is exactly equal to the amount of tax revenue raised plus the deadweight loss.

Tax revenue is easy to understand. The tax revenue generated is the tax per unit multiplied by the number of units sold given the tax. Tax revenue increases in proportion to the tax.

The deadweight loss is the residual. It is the total loss in surplus to consumers and producers minus the revenue that went to the government. Given this definition, it is not hard to understand why it is referred to as a deadweight loss. It is the foregone surplus that is lost and goes to no one. It is the value of the gains from trade that are simply foregone because of the tax.

What is particularly important about the deadweight loss is its relationship to the tax rate. With linear supply and demand curves, we know that the deadweight loss can be illustrated graphically as a triangle. What we know about triangles and this triangle in particular can actually generate an important insight about the costs of taxation.

Recall the following. The area of a rectangle is (Base x Height)/2. The base of the triangle in this example is equal to the size of the tax. The height of the triangle is the change in the quantity traded because of the tax. We can then use the definition of elasticity to derive a precise equation for the deadweight loss of a tax as a function of the tax itself. Allow me to explain.

Note that the price elasticity of demand is defined as follows:

Solve this expression for dQ and note that dP = t, where t is the tax. It follows that

Now, using our definition of the area of a triangle, we have:

Note the important insight here. Tax revenue is proportional to t, but the deadweight loss is proportional to t^2. What this means as a practical matter is that the deadweight loss from taxation grows much faster as the size of the tax grows than tax revenue grows. This is where the Laffer curve comes from. For low levels of taxes, an increase in the tax will tend to increase revenue. However, as the magnitude of the tax gets larger, the deadweight loss grows faster, which implies that tax revenue will eventually start to decline.

Now, think about this from the perspective of the government. Imagine that their objective is to collect as much revenue as possible from fireworks. What they would want to do is choose the size of the tax that maximizes the amount of revenue that the tax generates. In the state of Michigan, they collect the normal 6 percent sales tax, but also collect an additional 6 percent tax that applies to fireworks.

Nonetheless, it is important to note that when choosing the tax to maximize revenue, there is still consumer surplus and producer surplus to be captured. If you are a government and your objective is solely to maximize tax revenue, you would also like to figure out a way to collect all of that surplus as well. Of course, you know that you cannot vary the size of the tax to generate more revenue because it would distort behavior in the market. If the state has already set the tax rate at the height of the Laffer curve, then this would be self-defeated.

All is not lost for this revenue-maximizing government. What it could do is institute a two-part tariff. The government could combine a lump-sum tax with the per unit tax. Given that the per unit tax maximizes revenue, the government could levy a lump-sum tax on consumers less than or equal to the remaining consumer surplus and a lump-sum tax on producers less than or equal to the remaining producer surplus.

Again, the state of Michigan appears to do something like this. The fine for setting off fireworks is the same no matter the quantity of fireworks that have been lit. One way to interpret the fine is as a lump-sum tax to collect at least some of the remaining consumer surplus. Michigan also levies a lump-sum license fee on retailers who sell fireworks. In order to sell fireworks, retailers effectively have to pay an entry fee. This is a flat fee that is again independent of the number of fireworks sold.

Concluding Thoughts

When I lived in Michigan, the rules on fireworks were initially confusing to me. Why would the state allow people to purchase them, but then turn around and fine people for actually consuming them? Furthermore, one persistent problem on college campuses is that universities tend to lack adequate parking. Yet, despite the excess demand, there is little discussion of raising the price of a parking permit.

Hopefully, what I have shown in this post is that both of these examples can be explained through some very basic price theory. If the objective of the state and of the university is to maximize revenue, then something like a two-part tariff can be optimal. In the case of the university, this is a straightforward application of price discrimination. The two-part tariff allows them to charge more to those with a higher willingness to pay. For the state, this is a way for the state to capture as much revenue as possible from a sometimes dangerous recreational activity.

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So, a little context. In 2006, Boeing and Lockheed Martin combined their launch divisions in a joint venture into United Launch Alliance. That’s what I mean when I say they combined. It’s not actually a merger, and there are important differences when you get into the weeds of antitrust, but let’s think of this as a merger to a monopoly for simplicity. This seems bad and extra bad in an industry that handles national security payloads.

By every static measure, this is the textbook nightmare.

Economic Forces readers will know I think the textbook metrics are a bad starting point. So I was intrigued to see a recent paper by Ruibing Su, Chenyu Yang, and Andrew Sweeting, which argues it was probably a good idea.

Their key mechanism that is missing from the basic model is that every launch teaches you something. The engineers who fly the fiftieth mission know things the engineers on the first mission didn’t. And before the “merger,” that asset was being duplicated across two separate programs with separate engineering teams, separate supply chains, separate everything. So we have a clear possibility (not sure if its plausible yet) for an efficiency in a specific sense.

Is that efficiency enough to outweigh the standard monopoly problem?

Su, Yang, and Sweeting argue yes. They use a full structural model, lots of bells and whistles, modern industrial organization stuff. They look at the space launch industry from 1985 to 2024 and argue the learning synergies were real and large enough to outweigh the market power. They also find that when the government committed to multi-year block buys rather than shopping launch by launch, costs fell dramatically. Forward-looking procurement gave the supplier incentive to invest in getting better, even without a competitor pushing them.

That’s a serious empirical study for one industry. The harder question is what regulators were supposed to do at the time.

We usually punt on dynamics

Every merger in a learning-intensive industry raises the same questions. Will the merged firm keep innovating, or get comfortable? What happens to entry when the incumbent has a decade of accumulated know-how and the challenger starts from scratch? Will the firm use its position to lock up inputs and foreclose rivals?

In practice, regulators mostly punt. They evaluate mergers on the static margin and treat “dynamic efficiencies” as a vague thing out in the ether, too speculative to count for much. That bias always cuts the same way. It cuts against mergers in the industries where dynamic effects are biggest.

It’s fair. Studying dynamic efficiency is hard. Full dynamic models can deliver answers, but the people who build them admit they come with lots of costs. Doraszelski and Pakes in their handbook chapter on “Applied Dynamic Analysis in IO” caution the framework “delivers very little in the way of analytic results of applied interest.” Berry and Compiani, in another summary of the dynamic literature, aren’t really any more positive. “[T]he attempt to add dynamics may create enough compromises that the result is not better than the static model.”

So, yeah, if the only way to engage with dynamics is a five-year structural project, most merger reviews will keep ignoring them.

Turning static to dynamic to static

Let’s work through some other options. Instead of going full structural IO, let’s think in simple price theory times. Strip away the details. I think there’s a simple way to capture a lot of the interesting dynamics here.

The key idea here is that output today affects costs tomorrow. The firm that produces more accumulates something.

That’s a reduced form way of capturing lots of different things. The learning-by-doing example of rockets makes sense, but it’s only one case. Retailers do the same thing with distribution density. Airlines do it with routes. A manufacturer that keeps producing refines its tooling and supplier relationships in ways a competitor running smaller volumes can’t match. The platform version is an installed base.

The engineering details differ. Don’t let that obstruct things. The economics is the same. Output today builds a productive stock, and that stock lowers future cost.

Notice this is not standard capital accumulation. That is a separate decision that sort of fights with production. Cash spent on a new machine is cash not spent directly making product. Time spent building the next semiconductor line is time not spent producing the current one. In your basic dynamic model with capital accumulation, production and investment compete for the same scarce resources in a more direct way.

The productive stock here works differently. You can’t write a check for a year of launch experience or a denser route map. The only way to build it is to produce. So output and investment don’t compete. They’re the same decision. Producing more today is investing more today.

Circling back to mergers in particular, of course, this doesn’t cover every dynamic merger claim. Some dynamics are about patent races, product repositioning, entry timing, demand-side network effects, or strategic investment chosen separately from output. Those may require different tools.

But most merger-efficiency claims are more mundane. They’re about scale, experience, density, know-how or having some installed base. For example, when T-Mobile and Sprint argued in 2019 that combining their spectrum holdings and cell sites would let them build a higher-quality 5G network than either could alone, that’s a network-density claim. The “stock” is network capacity. Producing more output builds that.

Always some tradeoffs

A merger with this type of capital does two things at once, pulling in opposite directions.

Of course, we still have the standard worry of the drop in competition. The new firm doesn’t worry about product diversion. If Boeing’s launch business raises price before common control, some lost business goes to Lockheed. After common control, those sales stay inside the same organization. The combined organization recaptures customers it used to lose. That weakens the incentive to fight for the marginal customer, which means higher markups and less output.

We can draw this out. Common control rotates the marginal benefit curve in. Before the combination, winning a launch from your rival is a gain. After the combination, winning a launch from your other division is partly stealing from yourself. The combined firm internalizes cross-product diversion, so the marginal benefit of expanding output is lower. Quantity falls.

That’s the normal merger logic.

But here we have a competing force. If producing today builds capability for tomorrow, each extra launch is also a little more experience and operating capability. That lowers the effective marginal cost of producing today. When the effect is large enough, the supply curve slopes down. The firm is paying the current cost of the launch, but it is also buying future cost reductions.

If consolidation means the combined organization captures a larger share of the returns from building productive capability, it has a stronger incentive to produce today. Combined production volumes mean faster learning. More internal coordination means the cost savings actually show up rather than getting duplicated across separate programs.

Draw the picture

To see the two forces in one picture, we need to think about the marginal cost of this productive stock. How does it change the marginal cost curve? What’s the price?

Capital has a rental rate, what you’d pay per period to use it. Jorgenson called it the user cost of capital; it’s the implicit rental on an asset the firm owns rather than rents. We can think of experience and operating capability have the same structure, even though no one cuts you a check, just as most firms own their capital so don’t pay a rental/user cost.

What’s the value of owning that capital? Each unit of output today adds to the stock and lowers tomorrow’s cost. The present value of that future saving is the implicit rental rate on the stock. Producing one more launch is cheaper than the accounting cost suggests, because part of what you pay “buys” future productivity.

Call the normal accounting cost per launch the static marginal cost. Call the static cost minus the rental rebate the dynamic marginal cost “net of rental”. Static MC is what shows up on the invoice. Dynamic MC is what actually drives the firm’s output decision once it values the stock.

Pre-merger, in the top panel, the firm faces residual demand for its own product and a single-product marginal revenue curve. Static MC sits at 3. Dynamic MC, net of the rental rebate, sits closer to 2. The firm produces where MR meets dynamic MC. We can read off the price and quantity.

Post-merger, two things change at once. MR rotates inward to “owned-product MR.” This is the standard diversion effect in picture form. If that was all that happened, mechanically, the merger would reduce output and raise prices.

Here, second force is that the dynamic MC rotates further down to “post-merger dynamic MC.” The combined firm captures more of the rental value of producing today. Less duplication across two engineering organizations. Higher combined volume moving up a learning curve (or moving down the cost curve). More of the future cost reduction stays inside the firm rather than leaking to a competitor. The rebate gets bigger, so the firm’s perceived marginal cost falls.

In the figure, the dynamic-MC shift dominates.

The picture also tells you when the result flips. If the learning curve is flat, dynamic MC barely moves and the MR rotation wins. Quantity falls, price rises, cats and dogs, living together, mass hysteria.

In some sense, this is all trivial. If the force that pushes up quantity is greater than the force that pushes down quantity, quantity goes up. Not exactly a deep insight. The figure can help us think through when the result flips.

But we can think even more about how learning works and how that maps to the figure. If experience spills over to competitors, the merger doesn’t change how much of the rebate the firm captures, and again dynamic MC barely changes. The industry already has that downward sloping curve, even if each firm doesn’t. Which one dominates depends on the slope of learning, how private it is, and how durable. The theory can guide your investigation into these questions.

Then we can start thinking about alternatives. A merger is one way to change the return to producing today. It is not the only way. Su, Yang, and Sweeting find that when the government switched from buying launches one at a time to committing to multi-year block buys, which is a way of guaranteeing the supplier a stream of future orders, costs fell sharply. The mechanism is the same one the figure shows. A bigger committed order book raises the value of investing in learning today, because the firm knows it will be producing the launches that benefit from that learning. The rental rebate gets bigger. Dynamic MC rotates down.

Is the stock the harm?

The figure shows when a merger generates real cost savings: steep learning curve, private experience, durable stock.

We need to be careful here. Those same parameters make entry hard. A new entrant starts at zero experience while the merged firm sits on years of accumulated know-how. If learning is steep, the cost gap is large. If learning is private, the entrant can’t catch up by hiring engineers away. If the stock is durable, the gap persists.

It’s tempting to call the entry barrier the offsetting cost of the efficiency and try to net them out. I’ve argued before that this gets the analysis wrong. Achieving scale is not an antitrust harm. Preventing a rival from achieving scale through better products or lower prices is not an antitrust harm either. Both are what competition on the merits looks like.

The same goes for an accumulated learning stock. If ULA’s experience makes it harder for an entrant to win contracts, that’s the productive stock doing its job. The merger that built the stock faster did so by combining output, not by doing anything to competitors.

The harm has to be a specific mechanism. The restraint is the harm, not the stock. Foreclosing key inputs. Locking up distribution. These raise rivals’ costs in ways that have nothing to do with the merged firm’s own productivity.

In this case, it turns out ex post that entry was possible and SpaceX completely changed the game and this all seems almost irrelevant. But not every market will have that type of entrant to switch things up.

Again, we have the tools to think carefully through it. This quick analysis doesn’t replace the structural model but gives you a way to think about the question before you build one, and a way to see what the model is doing once it’s built. It forces you to be specific about trade-offs and mechanisms. Which curves are shifting? What’s moving which way? Which ones can you see ex ante, and which ones only show up after the fact? If we can even clearly articulate that, we are a long way toward understanding a market.

What if demand isn’t downward-sloping? Isn’t this a problem for price theory? After all, if both the supply and demand curves are upward-sloping, it is possible to get very different price responses when the supply or demand curve shifts. For example, for a Giffen good, it would be possible that sudden reduction in supply might cause a reduction in the price, depending on the slope of the demand curve relative to the supply curve. This seems counterintuitive and empirically false. Nonetheless, the fact that this is a theoretical possibility seems like it could be a pretty significant problem for price theoretic analysis.

A lot of people dismiss Giffen goods as sufficiently rare that we don’t have to think about them. Others suggest that it is a theoretical possibility, but not not empirically relevant. I would like to take a much stronger stance on the issue and argue that upward-sloping demand is entirely the result of certain assumptions of the price theoretic framework. If we take uncertainty about prices seriously or if we allow for intertemporal decision-making, then the demand for Giffen goods is actually downward-sloping like all other demand curves.

Where Does the Theoretical Possibility Come From?

Let’s start by thinking through the theoretical possibility of a good for which the quantity demanded increases in conjunction with the good’s price. Recall that in price theory, there are two ways of deriving demand curves. One way of deriving demand is by starting with a utility-maximizing framework. In that framework, the set of possible choices available to the consumer depends on their income and the prices of the goods that the consumer would like to purchase. The consumer will choose his or her basket of consumption, given those prices and given income, so that the choice maximizes the consumer’s utility.

From this framework, we can use a hypothetical set of all possible prices of a particular good and determine the precise quantity demanded for that particular good at that price (holding all of the other prices constant). The plot of those combinations of prices and quantities demanded is referred to as the Marshallian demand curve. The Marshallian quantity demanded depends on the prices of the goods and the consumer’s income. In other words, as one moves along the demand curve, utility is changing, but income is not.

Alternatively, one could derive a demand curve by starting with the idea that the consumer wants to achieve a particular level of utility. Given the prices of the goods, the consumer chooses the quantities of each good to buy that minimize the expenditure necessary to achieve that level of utility. Holding all other prices constant, one can figure out the quantity demanded by the consumer at each possible price. The plot of this combination of prices and quantities demanded are referred to as the Hicksian demand curve. The Hicksian quantity demanded depends on prices of the goods and the utility of the consumer. In other words, as one moves along the demand curve, utility isn’t changing.

The reason that all of this is important is that there is a distinct relationship between Marshallian and Hicksian demand. In particular, let e^m denote the Marshallian elasticity of demand (the percentage change in the quantity demanded from a 1 percent change in the price). It follows that

where e^M is the Hicksian elasticity of demand, s is the share of expenditure on the good, and N is the income elasticity of demand (the percentage change in the quantity demanded from a 1 percent change in income). This is known as the Slutsky equation (in elasticity form). What it shows is that the Marshallian price elasticity consists of two effects. There is a substitution effect (captured by the Hicksian elasticity) and there is an income effect.

To understand these two effects, think of an increase in the price of apples. The substitution effect says that apples are more expensive and so the consumer should buy fewer apples. The income effect says that the higher price of apples makes the consumer feel poorer, which creates an additional effect on the quantity demanded.

How the quantity demanded responds to income depends on the type of good. Most goods are “normal” goods. By that, we mean that when income goes up, people buy more of the good. However, some goods are inferior goods. For those goods, when income rises, people demand a lower quantity of those goods.

The theoretical possibility of an upward-sloping demand curve should now be apparent. Note that when goods are normal, we don’t have to worry about a Giffen good situation. e^H is negative. As long as N is positive, we know that e^M is negative. However, consider the case of an inferior good. In that case, N is negative. Now, whether the Marshallian elasticity is positive or negative is going to depend on the magnitude of the Hicksian elasticity and the income elasticity. If the income elasticity is sufficiently large (in absolute value) or if the share of expenditures spent on the inferior good is sufficiently large, then the Marshallian demand curve could be upward-sloping.

Now that we have seen the theoretical possibility, we should assess how seriously we should take this claim.

The Demand for Giffen Goods is Actually Downward-Sloping

As I stated earlier, some people are dismissive of Giffen goods as a mere theoretical possibility, but the conditions are unlikely to be met (even in theory). After all, how many people are spending a large enough share of their expenditures on an inferior good? How sensitive are inferior goods to changes in income? Others concede that Giffen goods are a theoretical possibility, but not empirically important.

I think that both of those arguments concede too much. Instead, we should recognize that the demand for Giffen goods is downward-sloping like all other goods. However, to make that point, we need to discuss what is missing from our analysis.

The exercise that I just described for generating both Marshallian and Hicksian demand curves generates demand curves by considering the quantity demanded associated with a set of hypothetical prices. If the price equals Y, then the consumer will choose a quantity X. If the price equals Z, then the consumer will choose a quantity W.

It is important to note that this is not always the same as saying that when the price changes from Z to Y, the quantity demanded will change from W to X. That might be true, but it is not guaranteed. Whether or not these two things are the same depends on the expectations of the consumer. Only in the case in which a change in the price is completely unexpected would these things be the same. If, on the other hand, the consumer knows that there might be a change in the price, we should expect that to factor into the consumer’s decision-making process and that the consumer makes contingency plans.

It might help to illustrate this with an example.

Consider a Giffen good. Suppose that the prices of all other goods are constant, but that the price of the Giffen good could be high, with some positive probability. Otherwise, the Giffen good’s price is low.

Given the uncertainty over prices, the consumer might want to purchase insurance against the fluctuations in price. The reason is as follows. In the state of the world in which the Giffen good’s price is high, this will make the consumer feel poorer (and thus the marginal utility income will be high). In the state of the world in which the Giffen good’s price is low, this will make the consumer feel richer (and thus the marginal utility of income will be low). However, an optimizing consumer would like to equalize the marginal utility of income across these states. This requires transferring income from the low price state to the high price state. It is better to have an extra dollar to spend in the high price state than the low price state. How does one do that? Buy insurance.

Now, let’s think about the implications of the insurance.

If the consumer insures against these price changes, then income will be high when the price is high and income will be low when the price is low. Recall also that Giffen goods must also be inferior goods. One consumes less of the inferior good when income goes up and more of the inferior good when income goes down. Thus, with insurance, since income is high when the price is high and since the good is inferior, the consumer will consume less of the Giffen good when the price is high and more of the Giffen good when the price is low. In other words, the demand for the Giffen good is downward-sloping.

Critics might argue that this logic only applies when there is insurance to buy. There are two responses to this. First, this moves the goalpost. An upper-sloping demand curve would now require not only the typical Giffen good characteristics, but also would require incomplete markets.

Second, and more importantly, insurance isn’t even necessary here. Suppose that we allow for intertemporal decision-making rather than one-period decision-making. Now consider a world in which the Giffen good is storable. If you can store the Giffen good, then storage actually replicates the insurance policy. Why? Buffer stocks are a form of insurance. In periods when the price of the Giffen good is high, the person storing Giffen good now has more “income.” In periods when the price of the Giffen good is low, the person storing the Giffen good will now have less “income.” Since the good is inferior, we get the standard result that quantity demanded is lower when the price is high than when the price is low.

This can be extended further to intertemporal substitution more generally, although it requires more technical details. As Yoram Barzel and Wing Suen show in their paper on the topic, if a consumer is maximizing over both different goods and time, one of the maximizing conditions is that the marginal utility of income is constant across all periods. Thus, what we need to think about is how the price of the Giffen good affects the marginal utility of income. Barzel and Suen show that the marginal utility of income is high when the price of the Giffen good is high because this is true of inferior goods more generally. Thus, just like the case of insurance, the quantity demanded of the Giffen good is lower when its price is high than when its price is low.

It is important to note, however, that this intertemporal result is not deriving a structural demand curve. It is a time series of price-quantity pairs that shows a negative relationship between price and quantity demanded for the Giffen good.

There is one final caveat here is that the change in the price must be anticipated. People cannot plan for things they don’t expect to occur.

Concluding Thoughts

The theoretical possibility of a Giffen good is something that many students are taught, even in introductory courses. Economists are often quick to dismiss this theoretical possibility as unlikely to hold or empirically irrelevant. Yet, there is a broader lesson to be learned. People optimize on many margins. If prices fluctuate over time, people might take actions to mitigate the costs of such price fluctuations. The very actions that people take to mitigate those costs actually result in negative relationships between the price and quantity demanded of a Giffen good. All of this follows from straightforward applications of price theoretic logic and concepts that any student who has learned about Giffen goods would understand. The problem with the analysis of Giffen goods seems to be that it doesn’t take the price theoretic logic far enough.

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And every major AI builder seems to agree that humans are next. Musk says AI will “replace all jobs.” Amodei is out there talking all the time about everyone losing their jobs, grounded his framing of AI as “a general labor substitute.” OpenAI investors are out there talking about “80% of all jobs by 2030.”

While these are important people in the space, not some random blogger, they may not exactly be a random sampling of the most knowledgeable people. But it’s certainly not a new fear, and not just an AI thing. Wassily Leontief of input-output fame (more on input-output in a minute) had a few pieces in the early 1980s expressing this worry.

If AI really is a perfect substitute for human labor, any cost advantage drives to 100% AI. You don’t need an essay to prove it. But “AI will eventually be a perfect substitute” is doing all the work.

But that’s hiding a lot, lots of margins of adjustment and differences, heterogeneity that makes the world the world and not a simple model. How substitutable is AI right now? What would it take for that to rise high enough? What else has to hold?

Even the historical example that “tractors could do what horses did, therefore horses became obsolete” sounds like one step, but it’s actually several. And “AI can do what humans do, therefore humans become obsolete” is hiding even more.

So let’s go through those steps. This newsletter is based on a new working paper that goes through the math and economics, really MOSTLY basic accounting, in detail.

What collapse of human labor actually means

For a quick recap for those unaware of the history of horses in the US, the US horse population rose from 4.3 million in 1840 to 27.3 million in 1920. Then we get the fall with farm horses and mules dropping to roughly 3 million by 1960.

Horses basically had one job that came and went. For humans, we need to be more careful. Let’s make sure we have our accounting right and be clear about what a collapse actually means.

For simplicity, suppose human labor demand goes to zero. Not low. Zero. What does that require? It means no dollar you spend, anywhere in the economy, passes through a human hand at any point in its supply chain. Not the person who made the thing. Not the person who shipped it. Not the person who designed it, sold it, maintained it, or cleaned the building where it was assembled. Zero human labor embodied in final expenditure. That’s the target. That’s what I’m going to take “humans become horses” to mean, stated precisely.

This is the input-output idea Leontief built his career on. You can trace any final purchase back through its supply chain and add up all the human labor that went into it, direct and indirect. A cup of coffee has the barista, but also the roaster, the trucker, the farmer, the person who made the truck. “Embodied labor” means all of it. For labor demand to collapse, every one of those links has to go to zero, in every product anyone buys

The economy is not one production function. It is many activities. When AI makes some of them cheaper, people don’t just buy more of the same thing. They buy something else.

Every dollar you spend lands somewhere. Some dollars land in activities with lots of human labor inside them: a restaurant, a therapist, a roofer. Some land in activities with almost none: a streaming subscription, an automated checkout, cloud storage. So when we are tracing out what happens when AI gets cheaper, it’s not just “Can AI do my job?” It is “When everyone saves money because AI did my job cheaper, what do they buy next?”

Aggregate labor demand depends on three things: how much people spend in total, how much of that spending lands on activities with human labor inside them, and how much labor is embodied in each of those activities. For human labor demand to collapse, it’s not enough for AI to displace workers inside some activities. Every dollar of spending, wherever it lands, must lose all its embodied human labor. That’s three channels, and the horse argument needs all three to go wrong simultaneously.

The important starting point for thinking about labor is te idea that nobody wants labor. A restaurant doesn’t want waiters; it wants orders taken, customers reassured, mistakes corrected. So labor demand is derived demand. How does AI change how much firms demand?

When AI can do the things firms are actually buying, cheaper AI does two things at once. Firms substitute AI for workers, which reduces labor demand per unit of output. But cheaper AI also lowers output prices, output expands, and the expansion pulls labor demand back up. Whether labor demand rises or falls depends on which effect is larger. This is the Hicks-Marshall decomposition of derived demand into substitution and scale effects.

This is going to be the organizing principle for everything. When a dollar is saved, where is it redirected? To new tasks? To new jobs? To new sectors? It must go somewhere.

“AI can do the tasks.”

This is obviously true for many things. Early models had this even. For example, the early GPT exposure paper by Eloundou, Manning, Mishkin, and Rock estimated that roughly 80% of the U.S. workforce could have at least 10% of tasks affected by LLMs. With complementary software, 86% of occupations cross the 10% exposure threshold.

And lots has been done on this. The task-level evidence backs this up. In a large customer-support setting, access to generative AI raised issues resolved per hour by about 15%. In a professional writing experiment, ChatGPT reduced average task time by 40% and raised measured output quality by 18%. In a controlled GitHub Copilot experiment, developers completed a coding task 55.8% faster. These aren’t tiny effects.

But they’re effects on tasks. The saved dollar doesn’t vanish when a task gets automated. It creates new tasks within the same job, such as more review, more client management, more judgment calls. Just as there’s not some fixed amount of demand so the scale effects matter, there is not some fixed job.

“A job is more than a task list.”

There’s a ritual in AI discourse where someone posts a demo, the demo does a task associated with a job, and people conclude the job is doomed. Sometimes they’re right. But the inference skips about fifteen steps. What does it actually cost to deploy, errors included? Do customers trust it? Does management know how to reorganize around it? A chatbot demo can appear overnight. A hospital reorganizing clinical liability around AI cannot.

We need to think not just about jobs but organizations. Often the result is a team, not a replacement. A human-AI pair produces output. But complementarity is not free. A pair that produces only slightly more than the AI alone doesn’t justify the human wage. The human has to add something the AI can’t replicate cheaply.

Surgery, aviation, structural engineering, fiduciary advice, for legal reasons alone are areas where we can expect the damage from an error dwarfs the savings from cheaper production. Again, that can always change one day but not soon. When failure on one component destroys the value of all others, you don’t care about the sticker price. That’s the O-Ring logic. You care about cost per unit that actually works. When damage stakes are high enough, human-supervised production wins regardless of how cheap AI becomes.

“Fine, the current jobs go. Where does the spending go?”

Suppose substitution wins inside most jobs. The saved dollar escapes the workplace entirely. Where does it go? Most standard models aggregate into a single final good, so this question plays no role. The real economy has many sectors, and the dollar has to land somewhere.

Start with software as a microcosm. This is a sector that has already been heavily automated by digital inputs for decades. If substitution were going to drive labor out of a sector, this is where you’d see it first. The chart below groups industries by how much software they purchase relative to their value added — low, medium, and high software intensity. What do you see?

The most software-intensive industries don’t just retain human labor;they have a higher labor share (67%) than the least software-intensive ones (55%). Heavy digital inputs didn’t drive out human labor. If anything, the industries that automated the most are the ones that spend the most on workers. BLS projects U.S. employment to increase by 5.2 million from 2024 to 2034. Software-developer employment? Up 17.9%, despite direct AI exposure.

The scale effect won within the sector most exposed to digital automation. The BLS could be completely off but the evidence so far points strongly toward the scale effect dominating in software-intense industries.

Software is one extreme but we basically have the same pattern holds across the whole economy, over a much longer period.

For another angle on the problem, let’s go bigger and look across the biggest sectors in the economy: services vs. goods. In 1929, most consumer spending went to physical goods. Today, roughly two-thirds goes to services. As manufacturing got cheaper, people didn’t just buy more stuff. They shifted spending toward healthcare, education, restaurants, personal services. That’s the saved dollar in action at a more not-quite macro but close level — the savings from cheaper goods flowed toward services.

In terms of our guiding decomposition, coods got cheaper. I’m going to be a bit fast and loose here but the scale effect didn’t show up in goods. Demand for physical stuff didn’t explode. Instead those freed-up dollars migrated to services, and the scale effect showed up there. The substitution effect won inside goods-producing industries. The scale effect won across sectors. Output overall expanded. So if you’re thinking as a macroeconomist, the scale effect dominated.

But migration alone doesn’t help workers unless the destination still has human labor inside it. Did it?

This chart tracks what fraction of each sector’s value goes to workers — employee compensation as a share of value added. Services consistently pay a higher share to labor than goods-producing industries. Spending didn’t just migrate. It migrated toward sectors where more of each dollar ends up in someone’s paycheck.

Again, so far, yes. We are moving toward services.

So you say sure, this actually supports the horse outcome. The price of goods fell and we bought fewer goods. What I’m saying is that there is a margin of adjustment, there is an escape hatch when you are looking at an economy as diverse as the modern U.S. economy.

And comparative advantage always pops up fighting against this. When automation makes some things cheap, the things that remain expensive tend to be the things that are hard to automate. And the things that are hard to automate are, almost by definition, the things where humans still have comparative advantage. The saved dollar drifts toward where humans are still worth paying. That’s not optimism. That’s what comparative advantage means.

Bessen showed this sector by sector. In early textiles, power looms cut labor per yard of cloth. But cloth got so cheap that demand exploded, and total employment in textiles rose for decades. Same in early steel, early autos. Eventually demand saturated, prices stopped falling fast enough, and automation reduced employment in each sector. The question for AI isn’t “does automation destroy jobs?” It’s “which phase are we in, for which sectors?”

Where might the AI-saved dollar land today? Healthcare is already 18% of GDP and rising. Elder care will grow as populations age.

Mokyr, Vickers, and Ziebarth have a great JEP piece that makes the historical case for why this time isn’t different: new tasks appeared, comparative advantage held, products we couldn't imagine created new work.

Horses had no equivalent destination.

“Fine, spending chases automation.”

The saved dollar found human-intensive sectors last time. The best argument for why this time is different comes from Philip Trammell’s “Is labor a luxury in the long run?“ His answer is probably not. Even if people initially spend more on human services as they get richer—live music, handmade goods, personal care—four forces erode that over time. AI-produced variety keeps expanding, competing for every dollar that lands on human-made goods. Consuming human services has an opportunity cost: time spent at a live concert is time not spent on a superior AI experience.

Other scarce goods—beachfront land, status goods, R&D—compete with labor for the “scarce thing people pay a premium for” slot. And capital goods keep getting cheaper to produce, so the investment share of spending can grow without limit.

Trammell’s Coca-Cola analogy is the sharpest version. Original Coke held 50% of the soda market. Then Diet Coke, Cherry Coke, Pepsi Max, energy drinks, sparkling water. Even with brand loyalty and supply restrictions, the share fell below 20%. If AI keeps inventing new varieties of goods that compete with human-produced ones, even a strong initial preference for human labor gets diluted by expanding choice.

I take this seriously. It’s a possible scenario.But notice what it requires. Not just that AI-produced variety expands (which it will) but that it expands fast enough and broadly enough to pull spending away from every human-intensive category at once. The question isn’t whether AI competes with some human goods. It’s whether any human-intensive island survives. Does anyone still spend money on something with a person inside it?

The numbers still have to be extreme. Suppose AI eats 85% of the economy. Software, accounting, law, medicine, logistics, most management, most media. All gone or nearly gone as human labor categories. Suppose the remaining 15% of spending goes to things with at least 30% human labor inside them. Elder care, in-person education, surgery, live performance, skilled trades, therapy, status goods. Then the aggregate human labor share is at least

S ≥ 0.15 × 0.30 = 0.045

That may not sound great but I’m literatlly just putting a bound. Knowing nothing else, we can sustain this. Not large. Not utopia. But not zero, and that’s the absolute lowest possible bound. And remember, labor share declining is not the same thing if the pie is growing much larger.

But is it just sentimentality to think spending stays on human-intensive stuff? Alex Imas argues no. As AI makes commodities cheap, real incomes rise, and richer people systematically shift spending toward what he calls “relational” goods.

There's a huge literature in economics on structural change, the long-run pattern where spending shifts from agriculture to manufacturing to services as countries get richer. The big question is why. Is it because prices change and people buy more of whatever got cheaper? Or is it because incomes rise and people just want different stuff? Comin, Lashkari, and Mestieri, for example, decompose the two and find that income effects account for over 75% of the shift. That matters here. If spending migration were mostly about chasing cheap goods, AI making things cheaper would pull dollars toward AI-produced stuff. But it's mostly about what richer people want. And richer people have consistently wanted more services with humans in them.

In experiments, when subjects learn that others will be excluded from purchasing an identical product, willingness to pay roughly doubles. Pure exclusivity premium. Anonymous, no status signaling possible. The premium is stronger for human-made goods. Human-created artwork gains 44% in value from exclusivity, versus 21% for AI-generated artwork. AI-made goods feel copyable. Human-made goods feel scarce even when they aren’t. People want what other people can’t have. That wanting doesn’t run out, and it sticks to things a person made.

Maybe the point is to wait long enough and AI variety erodes even that. Maybe. But the structural change evidence says income effects dominate price effects by three to one. When basic needs get cheaper, humans don’t say “good, I’m done wanting.” They invent new ways to compare themselves with neighbors. Whether the new wants land on human-made goods or AI-made goods is the open question, and the experimental evidence so far favors humans.

A falling labor share is not falling labor demand. There is a range where labor’s share of income is declining but total labor demand is still rising, because the pie is growing faster than labor’s slice is shrinking. That range may be where we are right now. It would look like “AI is taking over” in share terms while employment keeps growing. The popular argument runs these together and they are not the same claim.

We already see that. Higher income people consume more services. Services tend to be high labor share. Again, that can always flip in the future but this is the evidence we have.

I think humans have a shot

Going through all of the layers, from tasks (where we are just starting to see some substitution) all the way up to the macroeconomy, leaves me pretty skeptical of the horse outcome. I know I’ve hidden it really well up to this point, but that’s where I’m at.

AI will do many tasks. It will reorganize jobs, probably painfully. Some sectors will lose most of their human labor. Spending can chase automation. All of that can happen and still not get to zero. Because at every step, there’s a saved dollar looking for somewhere to land. And the question is always the same one. Where does it go next?

For the horse outcome, you need that saved dollar to find nothing with a human attached to it.

That’s a very specific future. It might happen. But it has to happen everywhere at once, and the evidence we have, the structural change evidence, the revealed preferences, the experimental results, keeps pointing the other way.

I also like examining topics like this precisely because they highlight what price theory is and is not. Price theory is a framework for understanding, explaining, and predicting human behavior. Price theory is not a theory of mind.

A different way of thinking about this is as follows. In the early days of behavioral economics, a number of researchers focused on finance. The reason that they focused on finance is that financial markets tend to be populated by professional finance people who have an incentive to get things right and acquire information. Financial markets are also characterized by frequent trading and highly liquid markets. Given those characteristics, the thinking was that if behavioral assumptions could survive financial markets and not simply be arbitraged away, this would be strong evidence in favor of these behavioral assumptions. We can debate whether that turned out to be true. Nonetheless, the sentiment itself is useful.

I take a similar view of using price theory to analyze things like drug use. The stereotypical view is that drug users don’t behave in predictable ways. If price theory can explain how people respond to changes in drug policy or even what types of drugs that people use, then this would seem to be a pretty strong indicator of the usefulness and broad applicability to price theory.

With that in mind, I would like to continue with this theme of exploring price theory in a context where one might otherwise find it lacking: panhandling.

Competition, Entry, and Profits

Price theory, at least the Chicago brand, tends to focus a lot of its attention on the so-called competitive model. A basic idea of the competitive model is that competition will tend to drive economic profit to zero. This does not mean that competitive firms don’t earn a profit. Instead, what this means is that the accounting profit earned is equal to the opportunity cost to the owner(s) of operating the firm.

In finance, there is the idea that variation in returns of different assets can be explained by the risk characteristics of the different assets. A higher expected return is simply compensation for taking on more risk. A useful concept that follows from this logic is that equilibrium is characterized by the absence of risk-free arbitrage. Again, competition should see to it that this is true. If one can earn income from risk-free arbitrage, then we should expect people to enter the market to capture some of those profits. Furthermore, we should expect that people will continue to enter the market until the only arbitrage opportunities left require taking on some degree of risk.

This is not to say that these outcomes will always prevail. The basic assumption lurking in the background, but unacknowledged explicitly to this point, is that these outcomes are predicated on free entry. The presence of positive economic profit or risk-free arbitrage could be the result of the fact that it is costly to enter the market. This could be true for a variety of reasons. There could be legal or regulatory barriers to entry. There could be significant fixed costs associated with entering the market. In that case, one has to make sure that the profits from day-to-day operations are large enough to offset that initial fixed cost.

Suppose that you wanted to test this idea that, all else equal, competition tends to equalize rates of return on particular types of investments or activities. How could you do it?

One way to test the theory would be to estimate the rate of return on investment in various industries. In a competitive market with free entry, one would expect that the rate of return on investment would equalize across industries. Any failure to equalize these rates of return should be explained by some sort of barrier to entry.

This is easier said than done. For one thing, there is no reason to think that at any particular moment in time, we are in equilibrium. This is a challenge in finance. Sure, there are a lot of papers that seem to show evidence of clear arbitrage opportunities. However, the fact that trading is happening by the second in financial markets seems to indicate that there are a lot of people who believe they have an arbitrage opportunity. Even if one were to observe that an arbitrage opportunity exists at a moment in time, this would not tell us whether the absence of risk-free arbitrage is a useful equilibrium concept because we might simply be on the path back to equilibrium.

Although I’m not sure that David Laidler ever wrote this down, I’ve heard him say that every economist should have to revisit their dissertation at the end of their career and see if it holds up. In our context, this would mean that if you had evidence of risk-free arbitrage or the failure to equalize returns across industries, you would have to replicate your result after approximately 30 additional years of observations. If you could replicate it, that would be pretty strong evidence that you were correct.

But all is not lost. We need not wait 30 years for people to update their data. There are alternative ways to test the implications of the competitive model.

For example, think of a situation in which there is (a) free entry, but (b) some reason to believe that the competitive model might not apply. If one finds evidence in favor of the competitive model under those conditions, then that is pretty strong evidence in support of the model.

One such example is that of panhandlers. It seems pretty clear that there are places in which panhandling is perfectly legal and there is no restriction on panhandling. The absence of those restrictions suggests that anyone can show up and panhandle. As a result, if panhandling turns out to be quite lucrative, we would expect to see people switch to panhandling from some alternative use of their time. In fact, competition in panhandling should drive down the rate of return on panhandling until it reaches the opportunity cost of the marginal panhandler.

At the same time, casual observation suggests that panhandlers might suffer from the same erratic behavior attributed to drug users. This shouldn’t be surprising since many panhandlers tend to be drug users. Given their erratic behavior, a common retort would be that panhandling isn’t the best example. Sure, there is free entry. However, we are not dealing with rational actors. We are dealing with people who are on drugs or desperate. They aren’t calculating where to panhandle to get the highest rate of return. They’re panhandling because they need all the help that they can get, possibly to buy a meal or perhaps even to get their drug fix.

It is not despite those objections, but precisely because of those objections that this is a useful testing ground. There is free entry, but panhandlers aren’t crude, calculating maximizers. So what happens?

Evidence on Panhandlers

Fortunately for you, dear reader, there are people who get paid to think about such things. A recent paper by Peter Leeson, August Hardy, and Paola Suarez used data they obtained by observing panhandlers in Washington, D.C. to test this very hypothesis.

Specifically, they observed panhandlers outside the D.C. Metrorail stations. The places where the panhandling takes place around these stations appears to be legally permitted based on local statutes. Regardless, at the very least, it is de facto permitted. They were able to observe the panhandlers and get information about how much they collected by asking the panhandlers to count their earnings in exchange for five dollars. They are also able to get data on the number of customers that pass through that area using publicly available data from the Metro system. They also used a standardized process to examine the friendliness of passersby.

One possible barrier to entry is the ability to get to a particular Metro station. Not all homeless are panhandlers, but most panhandlers are homeless. If that is the case, then a basic barrier to entry might be the ability to get to a particular Metro station.

Setting aside whether competition equalizes rates of return across different stations, one simple test would be to see if panhandlers follow basic economics incentives. For example, one would expect that there would be more panhandlers at the busier stations and the friendlier stations. One would also expect that there would be more panhandlers where the barriers to entry are low, such as at stations where there is a shuttle stop for the homeless nearby.

This is precisely what they find for the full sample.

Nonetheless, it is important to remember that the main thing that they want to test is whether the rates of return equalize. Yes, all else equal, one should expect busier stations to have more panhandlers. When Willie Sutton was asked why he robbed banks, he replied “because that’s where the money is.” The same principle applies here. Busier stations mean more people to ask for money. The more people one asks, the more likely one is to receive some money from a passerby. At the same time, this tendency will cause rate of return equalization between Metro stations. Busier stations have more competition, which drives down returns. Less busy stations will have less competition, which boosts returns.

Because they were able to obtain data on how much the panhandlers earned per hour directly from the panhandlers themselves (and verify the information by having the panhandler count for them), they are able to test whether the mean, median, and variance of the returns are similar across stations. Using the data that they obtained, they cannot reject the null hypothesis that the mean, median, and variance of returns across the stations are equal.

This is especially strong support for the competitive model. Panhandlers are much more likely to suffer from mental health disorders and substance abuse problems than the rest of the population. In addition, panhandlers are often thought to have less self-control and be deemed erratic or irrational. Yet, the prediction of the competitive model prevails even in those circumstances.

Conclusion

I bring up examples like this because it allows me to address criticisms of price theory that largely miss the mark. Critics of economics generally, and price theory in particular, tend to argue that we assume that everyone is a hyper-maximizer, only concerned with self-interest and that the world is more complicated than that. People aren’t walking around all day solving utility- and profit-maximizing problems in their head. Not everyone is a rational calculator.

I think that we can reject these criticisms. I am not saying that we should reject them on the grounds that they are false characterizations of the real world, but rather that they are a false characterization of price theory. As I wrote in my previous posts, price theory is about providing rational frameworks to understand, explain, and predict human behavior. It is about rational frameworks, not rational people.

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