Those Pesky Fixed Costs

A lot of economic decisions require paying some type of irreversible fixed cost. Moving from one place to another requires substantial fixed costs both in terms of the monetary costs associated with moving, but also the opportunity cost of being farther away from family and friends. Moving back allows you to recover some of that cost (you get the benefit of being closer to family and friends), but requires new monetary costs. You cannot recoup the original cost. The same is true about building a factory. When a company is determining whether or not to build a factory, there is a substantial fixed cost associated with doing so. For example, the construction itself is costly and must be paid before any production is done. If the company decides to shut down the factory, they might not be able to find a buyer for the structure. Even if they do, they are unlikely to recover the cost of building the factory since the factory was built for a particular use that is likely different from the use case for the new buyer.

There are many more examples, but the basic lesson here is that there are things that people have the option to do that they might not want to do because of the fixed costs involved. For example, suppose I pay the fixed cost of building a factory in Vietnam to export to the United States. The dollar subsequently depreciates thus making my product more expensive to Americans. Meanwhile the cost that I pay the workers is paid in the local currency. Had I known this was going to happen, I might not have chosen to build the factory.

The same can be said for a long-distance move. I might pay the cost to move to take a new job. Once I get there, the company decides that they need to eliminate some jobs to save on costs and mine is one of them. I’ve now given up the connections with family and friends and paid a substantial amount of money to move and am unemployed. Had I known this was likely to happen, I would not have moved. However, moving back is costly. What should I do?

In these types of situations, it is best to think of people as having the option, but not the obligation, to take a particular action. That particular framing is useful because we have some idea about how to put a value on the option to take a particular action. We can rely on the same type of logic that we use for thinking about financial options.

One can think about the intuition as follows. One’s objective should be to maximize the value of the option, but how does one do that? Well, consider this example. Suppose that you want to build a new factory. Demand is rising, on average, over time. Some component of the demand for your product is predictable and some is not. Standard logic is that if the present discounted value of the factory is greater than cost of building it, you should build it. Uncertainty about future demand gives you an incentive to wait because the expected present discounted value is moving around with fluctuations in demand. Just because the expected present discounted value is greater than the cost today doesn’t mean that it will be a month from now or a year from now. Demand could decline unexpectedly. In other words, what you want is some kind of buffer between the expected present discounted value and the cost such that even unexpected declines in demand shouldn’t lead to losses. But how do you determine that buffer?

The way to think about this is as follows. The value of exercising the option on the day you exercise it (in this case the value on the day you build the factory) is the expected present discounted value less the fixed cost of building the factory. Since demand is rising, the longer you wait, the greater the exercise value. All else equal, this increases the value of the option. However, the longer you wait, the lower the present discounted value of the option to build the factory. You choose your threshold for demand to balance this tradeoff and maximize the option value.

Once you have chosen that threshold, your best course of action is to do nothing until demand hits the threshold.

Economic decisions that have these characteristics often result in lumpy empirical observations. What I mean by this is that if you are looking at a single decision-maker, it will appear as though the decision-maker is doing nothing for long periods of time, but they periodically make large economic decisions.

A prime example can be found by looking at data on investment. If you look at time series data for the U.S., investment trends upward like a lot of other macroeconomic variables in a growing economy, but it is fairly volatile compared to output. If you look at the distribution of investment in any given period of time, you can understand why. You will find that there is a very small fraction of firms that are investing in any given period. However, those firms that are doing the investment are spending very large amounts on the investment.

There are many other types of economic decisions that fit within this category. Let’s discuss some examples.

Some Examples

Why Do Exchange Rates Seem to have So Little Effect on the Distribution of Trade?

In the aftermath of the collapse of the Bretton Woods system when exchange rates started floating, real exchange rates became substantially more volatile. This matters because if the real exchange rate is fluctuating, the real purchasing power of the currency is changing. If there is a real appreciation of the dollar, then the cost of foreign goods have fallen. This also means that foreign inputs are cheaper. Thus, one would expect that significant fluctuations in the real exchange rate would alter the location of production.

However, people started noticing that the fluctuations in the real exchange rate seemed to be detached from reality. What they meant by this is that by the mid-1980s, despite some pretty wild swings in the real exchange rate, this didn’t seem to have a large effect on the location of production.

Paul Krugman’s explanation for why these fluctuations in the real exchange rate seemed detached from reality was based on this option value logic. Entry and exit from particular markets entails substantial fixed costs. Thus, the real exchange rate would need to appreciate above some threshold before it made sense to enter the export market. For those already in the export market, the real exchange rate would have to depreciate below some threshold to convince people to exit. However, what this means is that there are upper and lower thresholds for the real exchange rate. As long as the real exchange rate fluctuates within those thresholds, there is no entry or exit. Thus, there could be a lot of movement in exchange rates with little corresponding activity.

Why Don’t People Move When Things Get Bad?

The same logic applies to decisions about whether or not to relocate yourself. Sometimes people are living in areas that are on the decline. Labor market opportunities are declining. Nonetheless, people stick around. Why don’t they leave for better opportunities?

If you move, you give up the labor market opportunities you have now in favor of the labor market opportunities you have elsewhere. One might think that as long as the latter are greater than the former, you should move. However, moving entails a substantial fixed costs. The monetary cost of moving you (and possibly your family) and all of your stuff is significant. At the same time, you might also be leaving friends, family, familiarity, and local knowledge. When you move, the family who might’ve watched your child when you went to work is replaced by a daycare. You don’t know who to call when you have a leaky pipe. There is also uncertainty about the new location. What happens if you move and the market in your new area takes a turn for the worse?

As my colleague John Gardner and I have written about, moving is therefore best thought about in terms of option value. People will choose a threshold for how bad things need to get before they are wiling to leave. It is not sufficient for people to simply see better opportunities. There is uncertainty about the durability of those better opportunities and large fixed (and sunk costs) associated with moving. They want to make sure that it is really worth it before they make the move.

Do Unpopular Policies Survive?

We can even think about this in terms of non-market behavior. For example, how can we think about policy? People love to point to policies that purportedly have greater costs than benefits. They come up with all sorts of reasons why this is the case. A common argument is that policies that have a net cost to society get implemented and survive because the benefits are concentrated among a small group of people and the costs are dispersed within a large group of people. The people receiving the benefits have a strong incentive to keep the benefits flowing. Since each individual paying the costs is only paying a very small fraction of the costs, they don’t have as strong of an incentive to go out and try to stop or later repeal the policy. Furthermore, even if the costs exceed the benefits, the fixed cost of getting rid of an existing policy might be larger than the cost savings. In that case, the policy survives. (It also reveals a point of contention in this literature. The costs of organizing against the policy are fixed costs. Although they don’t count in terms of the flow of costs, they are costs nonetheless. Critics of these bad policies tend to ignore these costs and focus on the flow of benefits and costs. But we’ll leave that aside.)

However, in a dynamic environment when the net costs of a particular policy are changing over time, it stands to reason that if those net costs get large enough, there are rewards to political entrepreneurs to pay the fixed cost of organizing a coalition to eliminate those policies. Thus, we might think of political entrepreneurs as having the option to organize. These political entrepreneurs wait until the net costs are large enough to justify organizing a coalition.

On this topic, Brian and I wrote a paper with Alex Salter on the efficiency of policy. In that paper we start with the idea that the policy process works as follows. Interest groups are organized and negotiate over policy. Organizing a new interest group is costly. Nonetheless, political entrepreneurs representing potential interest groups have the option to enter and overturn a costly policy. They will enter if the net costs of the policy exceed some threshold. This entry point puts an upper bound on the net costs of any policy. In addition, policies that seem inefficient in a static sense are efficient in a dynamic sense (at least in the limit as the time horizon gets arbitrarily large). As a result, there might be long periods of time in which it might not seem like anyone is doing anything about a costly policy. Then, all of the sudden, there is a change in policy.

It’s a Post About Nothing

Seinfeld was a popular television show about nothing. It shouldn’t have worked, but it did. Doing nothing is also an important component of economic decision-making. It doesn’t like it would be all that interesting, but many economic decisions involve choosing the optimal time at which to make a decision and take action. In the meantime, empirically it appears as if you are simply doing nothing. That can be puzzling. However, if you understand option value, economic reasoning can not only explain the actions that people take, it can also explain the actions they do not take or why they wait so long to act.

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Sure. If another company comes along with lower costs, that will drive the price down. That’s always a possibility, and an important one in real markets. But is there anything else to do in the more traditional “entry takes time but eventually erodes profits” sense?

There’s one more way to compete. Suppose a company came along that’s not better in the technological sense. They don’t have lower costs.

Still, there is still room to compete on pricing. I said pricing, not competition on price in the usual sense of setting a lower price.

The rival can come in and change the pricing structure. They could charge an upfront fee, offer a bundled deal, or charge different customers different amounts. That last possibility takes us to price discrimination, which is usually described as a way for sellers to extract more from customers. The FTC appears to share that view; it just ordered nine companies to report whether they charge different people different prices. The FTC is worried data is being used “to estimate the highest price they can charge each consumer.”

But price discrimination can also be how a competitor offers a better deal and wins their business. To see how, we need to start with the problem of paying for fixed costs.

Fixed costs kill marginal cost pricing

Consider a customer buying electricity. The first unit is worth $120 to her, the second $30, the third $20, and the fourth $5. Producing each unit costs $10. If we have two suppliers with exactly the same cost, the price will be bid down to the marginal cost of $10.

If you charge more than $10, your competitor will offer a lower price to win the business. Charging less than $10 loses money, and we arrive at the usual competitive result that price equals marginal cost. This is the basis for so much of the way economists think about pricing.

Let’s make one small complication. Someone has to install the generator. There’s a fixed cost. Suppose install costs $100, but nothing else changes. Production still costs $10 per unit, and our customer still values the units at $120, $30, $20, and $5.

Suppliers compete by making binding pricing offers before installation, so the winning supplier installs the equipment and supplies the customer for the agreed-upon period.

The usual marginal-cost pricing no longer works because it doesn’t cover installation costs. At $10 per unit, the customer only buys $30 worth, which just isn’t enough. Notice I’ve rigged the numbers in such a way that installing a generator is still worthwhile. Those three units produce $170 of benefits at a total cost of $130. But we need something besides marginal cost pricing to generate those benefits.

So perhaps the equilibrium is a higher electricity price. A supplier charging $120 sells one unit, pays $110 in costs, and earns $10. That’s the offer. A rival can come in and offer $115 and earn $5, and so there’s room to undercut until the price is $110, where the supplier just covers its costs.

Zero profit! Competition has worked!

Except that the customer has bought only one unit, and the additional units, which are still worth more than their cost, go unserved. That’s not great.

There’s no room for more entry with further cuts in the per-unit price to come in and fix this problem. It’s not profitable. The firm is already earning zero profits. If you’d drop down to $30 to sell the second unit, you lose money, so no one does it.

It should be pretty obvious what the problem is here. You need to cover the fixed cost, so charge separately for that.

But now we are beyond simple marginal cost pricing. On the Econ 101 theory side, that’s not allowed in the simple model. You draw the line across at “the price,” which means the per-unit price. $10 per unit of electricity, each unit the exact same. You’re restricted to a single price (linear price) per unit in the standard Marshallian/Walrasian models that spit out our “price = marginal cost, so we have competition” conditions.

Maybe we need to be more creative. You’re actually selling two products: installation and electricity. Charge separately for each.

That can solve our numerical problem, but it raises a question about the theory. What exactly is the product whose price competition is driving down? Is it a unit of electricity, a connection, or an entire package delivered through the connection? Once we allow suppliers to compete over these different arrangements, the familiar instruction that “take the price as given” needs a little bit more explanation. That’s actually an area where firms can compete.

The competitor in the model is just as smart as we are, sees the fundamental problems, and offers a different pricing strategy. They don’t take the price as given. They offer a different bill to the consumer: $105 for install, then $10 for each unit consumed. Now we’re at the efficient outcome. The customer buys 3 units, pays $135 for electricity worth $170, and generates $35 worth of surplus for the consumer, compared to just $10 under the original per-unit of electricity price.

Just by changing the pricing—no technological improvements—the entrant earns a $5 profit, while also leaving the consumer better off. A rival can profitably improve the customer’s deal even when the existing supplier already earns zero profit.

Pricing is an avenue for competition.

The opportunity came for the usual reason: there was deadweight loss still on the table. Those second and third units still had room for gains from trade and the pricing was a way to generate those $30 that were being left on the table. The entrant gives $25 to the customer and keeps $5. Its total bill is actually higher than the old supplier’s bill, but the customer gladly switches because she gets more valuable service.

But other suppliers, seeing the crafty pricing strategy, can offer better terms. If the installation charge exceeds $100, a rival can lower that charge and still earn something. Competition pushes down the installation charge to $100, plus $10 per unit, and the consumer receiving all $40 of the surplus.

We could split this invoice to make it look different. Offering a package of three units for $130 would also do the same. No need to mess with install vs. electricity prices. Either way, competition is for the full contract. We need a broader conception of how competition plays out. Louis Makowski showed how nonlinear pricing can fit within a theory of perfect competition. Competition can discipline a whole pricing schedule, even when there is no single per-unit price to take as given.

Sharing fixed costs

Nothing above should be controversial or surprising once it’s laid out this way. But we can carry the logic further.

Suppose one generator can serve two customers. A workshop wants one unit worth $120, while a household wants one unit worth $40. Installation still costs $100, and each unit still costs $10 to produce. Suppose we start with the contract we just settled on, which has a $100 connection charge plus $10 per unit. Then the workshop would sign up and pay $110, but the household would decline. The supplier covers its costs.

Could a rival offer a lower connection charge to attract the household? The charge would have to fall to $30 or less, but collecting $30 from each customer would bring in only $60 towards the $100 install. Offering the same contract to everyone leaves us stuck again.

Imagine instead a rival offers the workshop an $80 connection charge and the household a $25 connection charge. Both still pay $10 per unit. The workshop’s total bill falls from $110 to $90. The household’s bill is $35. Their connection payments total $105, covering the install and leaving the entrant $5.

The rival has found another customer to help pay for the generator. The household pays $25 toward install, allowing the entrant to reduce the workshop’s invoice by $20 and keep $5. Again, a creative pricing system means both customers get a better deal, even though the supplier they displaced was earning zero profit.

These customers receive identical electricity. There is no cost-based reason for the difference; the seller regards the consumers as the same from a cost perspective. This is pure price discrimination. And still, everyone prefers the discriminatory pricing system to the uniform price.

Further competition can squeeze out the remaining profit, but it will never equalize the prices. Suppose one competitor has household and workshop rates of $33 and $87. That covers the $120 total cost. A rival cannot properly win both customers by offering lower rates. It wouldn’t cover its cost, nor can it properly serve the workshop alone for less than $87, so it can’t try to peel off one customer at a time. There are several divisions of the bill that could survive these tests, but they’re never going to equalize price.

Someone has to cover the fixed cost. That’s an ever-present thorn in society’s side. There’s no way around it. And in general, it’s going to be the people who value it more. Prices depending on value means price discrimination.

From a positive perspective, we should expect to see price discrimination where fixed costs are high. The fixed cost of a flight is high, and the marginal cost of an additional passenger is low, so airlines have done this for a long time, which increases the number of flights they offer. Software is another example. You have high development costs and low marginal costs, so the business model will involve charging some customers (business users) much more to finance the development while keeping software available for, say, students or other price-sensitive users. For drugs, this happens across countries.

From a normative perspective, fixed costs give price discrimination another potentially important benefit: making investment worthwhile. That’s why I always stress fixed costs when talking about price discrimination. The standard Econ 101 model of price discrimination, even when it is efficiency-enhancing, holds the product’s availability fixed, so it leaves out this investment margin. It’s also why I’ve proposed “more prices” in electricity to deal with data center concerns.

The constant struggle

Okay, let’s move from simple examples to why this matters. I was listening to an episode of Odd Lots, in which Lindsay Owens spends a long time worrying about pricing tools. For example, she doesn’t buy that charging some customers more would provide “a cross-subsidy for everyone else.” But the whole point of price discrimination is to lower the price for someone who isn’t buying at the uniform price. So that’s not right, even in the simple, no-fixed-cost case.

She also argued that targeted discounts for budget shoppers mean higher prices for everyone else. They could, yes, but they need not. In our example, attracting another customer lets a rival spread the fixed cost and lower the existing customer’s bill to win its business.

I’ve chosen these numbers, obviously, in a way to make the benefits clear and simple. Does it mean every pricing scheme helps consumers and raises total surplus? A seller can use price discrimination to charge more on average, leaving consumers with less surplus. There is an incentive for the seller to grab a bigger slice of a smaller pie. Maybe the title should be “Price discrimination can be competition.”

But trying to grab more is present in every market on both sides. Sellers want higher prices, buyers want lower prices. It’s also not the only force at play. Instead of just fighting for a bigger share of a fixed pie, there’s also an incentive to find a bigger pie. And pricing schemes, including price discrimination, can be one way of finding that bigger pie.

The entrant wants a profit. It finds one by changing the pricing arrangement, creating more gains from trade, and offering customers enough of those gains to win their business. Then rivals copy the arrangement and compete over its terms. That is competition at work. Even when profits under the old pricing system have disappeared, the search for a better deal continues.

Owens is a stand-in interlocutor. As I said, the FTC is making a big deal about personalized pricing. Many people come from the same perspective, which is why I spend so much time on it. They treat price discrimination as anticompetitive by definition (whether they use this framing or not), since it starts from a price that does not equal marginal cost. It’s a wrong view of the competitive process.

But it once was even more prevalent. Courts and economics said the same about exclusive dealing, tying, resale price maintenance, and vertical mergers. Their role was to reduce competition. Since then, economists have built large literatures showing how firms use each of these practices to win customers. In response, courts have dropped per se condemnation of several of them. That work begins at the same spot; a single price leaves units unsold that are worth more to the buyer than they cost to produce. Discounts, exclusive contracts, and two-part prices are ways for buyers and sellers to trade those units. Public discussion of price discrimination has not caught up.

Across those literatures, the expanding pie has been the more dominant force. Finding more gains from trade is THE big deal.

Money and Price Theory

There is a weird dichotomy in monetary economics. In fact, it is this dichotomy that originally attracted me to monetary economics in the first place. It’s even evident when I write about money (which I seem to do a lot) for the newsletter. Occasionally, people will ask me why I write about money for a price theory newsletter. I understand the perspective they are communicating. When people think price theory, they think microeconomics. When people think money, they think macroeconomics. What therefore does money have to do with price theory? Even within the monetary literature, there is generally a distinction between optimal monetary policy, using some type of efficiency criteria, and optimal monetary policy, using some type of macroeconomic stabilization criteria. One can stretch and say these are both about efficiency, but they are about two distinct types of efficiency.

In fact, what initially sparked my interest in monetary economics (although I probably didn’t know enough to articulate it at the time) is what appeared to be a disconnect. When we think about policy in almost any other area of economics, the general approach is to think about how the market would typically function. If there is some friction that prevents the market from getting the efficient allocation, then there is potentially a role for policy. This is the approach taken by Milton Friedman, for example, in his “Optimum Quantity of Money.” However, much of the rest of the literature focused on monetary policy as optimal stabilization policy. According to this view, the primary purpose of monetary policy is to minimize fluctuations in the economy. (If you believe that business cycles are inefficient, this is sort of similar, but there was another debate about how much of business cycles were inefficient and how much were efficient responses to random shocks. I’d rather not discuss that here.)

Friedman was one of the rare examples of people who not only did both, but integrated the two approaches together. For example, his k-percent rule (which called for the money supply to grow at a fixed rate of k percent per year) was based on the idea that monetary policy largely did more harm than good when conducting stabilization policy. In his “Optimum Quantity of Money,” he pointed out that his two proposed rules for monetary policy were perfectly consistent with one another. This consistency is now an implicit characteristic of a lot of modern models that focus on efficiency from the price theoretic perspective.

Another economist who did both was Bob Hall. In his paper, “Optimal Fiduciary Monetary Systems,” he attempts to address both the price theoretic approach to policy that mitigates the deadweight loss and the macroeconomic stabilization approach. In doing so, Hall contributed to a literature that was then called “New Monetary Economics.” Although many lament that this literature largely went stagnant over time, I am going to argue that Hall, in particular, had a significant impact in how we think about monetary policy today with his contribution.

Optimal Fiduciary Monetary Systems

As I have written about many times by now, many people fail to appreciate the rarity of the current monetary system. Although there are many exceptions, for a large amount of recorded human history, people traded physical objects (like gold and/or silver) as a medium of exchange that had positive value distinct from the value associated with the role as a medium of exchange. Even when paper money was introduced, the paper was often redeemable for these commodities.

When the Nixon administration closed the gold window, it did so as a temporary measure. The closing of the gold window was meant to bring other members of the Bretton Woods system to the negotiating table. Of course, the gold window never re-opened. The rarity of the current monetary system was thus much more appreciated in the years that followed. As time when by, many economists began to speculate about how to think about this system in which paper dollars circulated and were not redeemable for anything. This was a period of big contributions to monetary theory (at least in my view). People like Ben Klein, Earl Thompson, and Bob Hall wrote important contributions that helped one think about the uniqueness of our present monetary regime.

Bob Hall was careful to frame his work around “fiduciary” money. He did not call it fiat money. His stated reason for this is that U.S. law doesn’t require anything to be priced in terms of dollars or that contracts be written in dollars, but the dollar is nonetheless used for these purposes.

Hall identified several problems with our system of fiduciary money as he saw it at the time. The first is that fluctuations the demand for such money leads to instability in the price level as well as corresponding fluctuations in real economic activity. At the same time, the existing regulatory environment led to a lot of inefficiencies at the micro level. Meanwhile, although deregulation efforts could reduce or eliminate these inefficiencies, such deregulation would seem to exacerbate the macroeconomic instability of the system.

Given those challenges, how could one design an optimal system?

Hall begins by arguing that the critical functioning of this system is that there is a central bank that produces what he calls “reserve certificates.” Everything else is essentially redeemable for reserve certificates. He begins with issues that are of particular interest to price theorists. He argues that for such a system to minimize the deadweight loss inherent to the system, one would need to create higher-denomination reserve certificates or account-based reserve certificates coupled with deregulation sufficient to allow private banks the ability to supply both deposits and currency to the market. Similar to both Earl Thompson before him and David Glasner after him, Hall argues that this would lead to a perfectly elastic supply curve for claims to reserve certificates. As a result, the supply of claims to reserve certificates would be entirely demand determined thereby eliminating an inefficiency and also mitigating a source of macroeconomic fluctuations. The other element of tackling the inefficiency is for reserve certificates to earn interest. This eliminates the inefficiency typical of irredeemable paper money that pays no interest.

Nonetheless, this raises the question of how to set the interest paid on reserve certificates in order to promote macroeconomic goals, such as price stability and minimizing fluctuations in output.

Suppose that we normalize the price level to 100. Hall proposed having the reserve certificates pay the market rate of interest (on bonds) plus a premium that would be a function of the percent to which the expected future price level was above 100. Thus, when the price level was expected to rise (relative to 100), the interest rate on reserve certificates would automatically rise. The extent to which the expected price level fell below 100, the interest rate on reserve certificates would decline below the market rate. This created an automatic policy rule. What Hall was able to show with a couple of simple models is that such a rule would ensure that the price level only deviates from that initial price level when there are random shocks that hit the economy. Otherwise, the price level would be constant. Furthermore, his models imply that the more responsive that the interest rate on reserve certificates is to deviations in the price level, the smaller the effect random shocks will have on the price level and the faster that output adjusts back to its equilibrium level.

As a result, the model demonstrates how one can think about an optimal fiduciary monetary system both in terms of the efficiency concerns of price theorists and in terms of common macroeconomic objectives of central banks.

The Connection with Woodford and the Nobel Prize

Michael Woodford, who shared the award with Hall, is mostly known for his work on the so-called New Keynesian model. For better or worse, this has become the workhorse model for monetary policy analysis. Meanwhile, if you were to ask someone what Bob Hall is mostly known for, you would probably get nearly as many answers as the number of people you asked. In linking the two together, a lot of people have linked Hall’s work on consumption with the household component of the New Keynesian model. I think that there is more to it than that.

Not only have I seen a lot of people remark that the Hall and Michael Woodford are an odd pairing for the award, but I have also seen a number of people remark that it is odd that the award specifically mentions “macroeconomic stabilization policy.” However, I think that the paper I have highlighted in this post represents a link to the work they’ve done. The emphasis on feedback rules for interest on reserves that target the forecast, written in 1983, was clearly ahead of its time. And the central themes of that paper are themes throughout Woodford’s own work encapsulated in his book, Interest and Prices. While it is true that the paper only has 141 of Hall’s 77,000+ citations, it’s also important to note that three of those citations come from Michael Woodford and, in particular, the paper is cited in Woodford’s paper “Monetary Policy in a World Without Money,” which is the paper that kicked off this branch of Woodford’s work. Woodford references Hall specifically (and almost exclusively) as a precursor in thinking about the monetary system in the same way. In fact, where Woodford departs from Hall is that while Hall focused on keeping the price level constant, the feedback rule can be much more generalizable to Taylor-type rules for monetary policy. (And thus a shame that John Taylor wasn’t included in this award.)

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Suppose you get a $1,000 payment. How much do you consume? Before answering, we’d want to know a few things: Is this a one-time payment? The first of many? Can you borrow? Do you already have savings?

This year’s Nobel Prize went to Robert Hall and Michael Woodford for providing the theory to make this concrete, the empirical work to test the theories, and showing how policy, optimal, and realistic differ depending on how we answer the theory and empirical questions.

When co-authors win the Nobel Prize, like in 2024, it’s pretty simple to see why they’re paired together. It makes a lot of sense.

This one takes a little more squinting. Michael Woodford is a perennial favorite to win, and Robert Hall is one of the great economists of all time, but is less mentioned in Nobel discussions.

The Nobel Committee found a way to tie them together for “micro foundations of macroeconomic stabilization.” I would say it’s “microeconomic foundations of macroeconomics,” but my guess is that that doesn’t seem important, so they wanted a “why does this matter?” hook, so they went with “stabilization,” which immediately connects to policy.

This is a great macro prize. It’s partially a New Keynesian prize. Woodford is basically synonymous with New Keynesian economics, although Hall is less often described that way. As we’ll see, Hall’s equations and empirical approach became an essential part of the New Keynesian model.

I’ll go through some of Hall’s contributions: those directly connected to the prize, but also some that the committee left out that I think are equally important and interesting. Then I’ll talk about how that laid the foundation for Woodford’s work, which has been central to macroeconomics for 20+ years.

Consumption, today and tomorrow

Going back to the $1,000 question, every question I ask is really getting at the same point. What does the payment tell you about your future income? A household that can borrow and save will be able to spread that windfall, if it’s one-time, over many years. A temporary payment is really a small change in wealth. News that your income is permanently higher is a very different situation. It could generate a large change in your wealth.

That distinction between temporary and permanent is what killed the old Keynesian consumption function, which tied spending to current income. Milton Friedman’s Nobel Prize is partly awarded for this, for his permanent income hypothesis. One of Hall’s contributions was to make it precise and check it against the data. Hall is squarely in the Chicago price theory tradition with this micro-macro connection.

The hard part, empirically, is that expectations matter in the other direction too. Suppose you learn today that you’re going to lose your job in 6 months. You may cut spending now while your paycheck hasn’t changed. When you end up losing the job, the income drop may not be very large, and your spending may barely move.

By the late 1970s, economists had been writing down this sort of problem with rational expectations. A household that cares about consumption every period chooses a path so that giving up a dollar today and spending what that dollar generates tomorrow are worth the same on the margin. That condition is the stochastic Euler equation, which is drilled into you in economics education.

In English, the left side is about what a dollar of consumption is worth today (the marginal utility of consumption). The right side is what a dollar is worth if you save it, earn the interest rate r, and spend it next period, discounted by your impatience beta. At the optimum, the two are equal. This is just the equimarginal principle (on the margin, equalize costs and benefits). What makes it slightly unique, makes it slightly macro, is that we have time, and, therefore, we have expectations.

Testing the model

A version of the stochastic Euler equation falls out of every modern macro model. Is it true? Does it show up in the data? Hall’s 1978 paper, “Stochastic Implications of the Life Cycle-Permanent Income Hypothesis,” turned this theory into something you could check.

The hard part is that you can’t observe what a household expects about future income. That expectation operator in the equation above is tricky. Hall’s insight was that you don’t need to know expectations. Under his benchmark, the level of consumption will follow a random walk, so changes in consumption reflect news. The basic idea is that anything households already know is in today’s spending, just like what the market believes about future earnings is in today’s stock price.

Today’s consumption is a very good predictor of tomorrow’s consumption. Nothing else should be. It should follow a random walk. The question is: if anything else that households already know, like last year’s income, improves, then incorporating that improves the forecast. If the theory holds, those extra variables shouldn’t improve predictive power at all.

Rather than being a clear victory for this version of the permanent income hypothesis, the evidence was mixed. Past income added little once consumption was in the regression, but stock prices were the exception, so we didn’t have a clear vindication or rebuttal of the model. What Hall did show was how to turn the theory about some unobservable expectations into a restriction on observable data. That’s a powerful connection from theory to data.

Do interest rates matter?

Going back to the Euler equation, Hall’s 1978 paper is really looking at that expectations operator and putting the focus there. That’s not the only thing on the right-hand side. We can also ask whether there is anything else we can pin down, beta, the personal discount factor.

We can also ask about the interest rate. If monetary policy works by moving that price, the price between consumption today and consumption tomorrow, we can estimate the size of that response. A higher expected real return makes postponing consumption more attractive, and the elasticity of intertemporal substitution measures how much that occurs.

Hall’s 1988 paper on intertemporal substitution goes after it. Now let’s look at the very fancy plots that one sees in an 1980s economics paper.

Each point is a five-year average of the real return from Treasury bills, plotted against the growth rate of consumption. A strong response to the interest rate would show up as an upward-sloping set of dots. That’s not what we see. To be clear, this is just a descriptive illustration. It’s not how Hall actually estimates the elasticity.

This plot of prices (interest rates) and quantities (consumption) has the usual identification problem: you’re only picking up equilibrium price and quantity, which could be moving around as supply or demand shifts. We instead want to pick up how quantity moves around given an exogenous change in r.

Hall’s solution is the usual one for any demand curve. You can’t just regress price on quantity, but you need to find a variation in the price that has nothing to do with the shocks to whatever it is that you’re explaining.

This is where the theory helps, where the Euler equation matters. It says households act on expected real return. Any variables that happen before the consumption change that help predict that return, like earlier interest rates or earlier inflation, are themselves information that the households could have used. They are not shocks or surprises to consumption. You can use those as instruments and ask whether the part of the expected return they predict lines up with consumption growth.

The measure of price needs care, too. The return that matters is the expected real return after taxes, not the realized one, so you’ve got to be careful with that. Hall spends a lot of his time in his career being precise about these things. This isn’t a post about the details of measuring post-tax returns. The important thing is that Hall filled in the details, moving from the model to the empirical implication.

So did the interest rate matter? Not really.

The elasticity could be zero, and it is probably no higher than 0.2. But this was a start of measuring this, not the tightest estimate ever. A 1988 paper with aggregate data is not the end of the empirical discussion, and as with many prizes, this one is about launching a whole research program. Hall’s weak elasticity leaves a puzzle. If households barely shift consumption across time when the real rate moves, how does a rate cut raise spending at all?

The wide-ranging Bob Hall

If you go to Hall’s Google Scholar page, you’ll see that these consumption papers are only his second and sixth most cited papers. He has done so much, including things like a popular optimization algorithm. As Tyler Cowen rightly put it, “Every Bob Hall paper is interesting!”

Let me focus on two that I think are core price theory.

Even if you buy the machine, you pay the rental price every period, because you could be renting it to someone else. Owning does not make its services free. Hall and Jorgenson (1967), written while Hall was a graduate student, built an empirical investment model on that idea. The sticker price is not the cost of using the machine for a year. The firm ties up money, the machine depreciates, and its resale price may change. The cost of using capital is roughly the price of the capital good times the interest rate plus the depreciation rate, less expected capital gains.

The firm compares what the machine adds to output with that user cost, and the paper estimates how much investment responds and when. It is the household problem again, with the real interest rate as the price of time.

The other paper is Hall’s 1988 JPE article on price and marginal cost. This is cited in the scientific background, but I’m pretty sure it’s a typo.

What does producing one more unit actually cost? Firms don’t report marginal cost, but we can observe how their inputs change when they produce more. The problem is that this tests competition and constant returns together. We are always doing a joint test, but that’s a topic for another day. But that is classic Hall. Let’s take something we don’t directly observe and work out how to test it using choices we do observe.

The markup paper, while cited by the Nobel committee but in a very confusing way, also sets up Woodford nicely, which has sticky prices and markups.

Woodford puts the pieces together

Suppose the central bank wants to know what happens if it raises the interest rate by 1%. Instead of the old approach of estimating how inflation moves with unemployment, you want to start with a microfounded approach (as the Nobel prize points out) of how households and firms are making decisions. Then you can make causal claims. You need to know what causes what.

The problem with correlations is that people’s behavior changes depending on the policies that they live under. This is the classic Lucas critique. In the 1960s, higher inflation came with lower unemployment, so policymakers tried to exploit that. People came to expect inflation. The 1970s gave us high inflation and high unemployment together.

Woodford’s contribution is that he tied the pieces into one causal chain. The Nobel Committee’s scientific background lays it out following his book Interest and Prices.

The benchmark New Keynesian model has just three equations.

The first equation is Hall’s Euler equation with some bells and whistles. Add some things about the “natural rate” à la Wicksell, and you basically have it.

The second equation comes from firms. A restaurant that reprints its menu once a year (just assumed because of sticky prices) has to guess at costs and demand for the whole year its prices will be in use. Firms that can’t change prices every period face the same problem, so their pricing looks forward.

Then you close the model with an interest rate rule. It sets its interest rate in response to inflation and the output gap, as in a Taylor rule, thereby closing the loop.

So you have all these three equations feeding back into each other. Every link is a choice someone makes. Everyone is looking ahead and thinking about the future, and when you change the rules, people change what they can expect. That trickles into their behavior. This allows us to work through responses, without assuming people will behave as they did in the old policy. That is the benefit of microfoundations.

Does this particular microfounded macro model match the data? Yes and no.

Taking NK to the Data

Everyone knows the book, Interest and Prices, but the easiest way into the project is a 1997 paper with Julio Rotemberg. They built a quantitative model from optimizing households and firms and used it to evaluate monetary policy rules. The first question is whether the model can reproduce what happens after an unexpected Fed rate increase.

It’s a weird way of showing it, but the bottom panel shows the shock.

The interest rate rises and then returns to normal within a couple of quarters. In the top panel, the output falls with a delay and recovers gradually. The model’s solid line follows the estimated middle line closely for both. The middle panel is harder. The estimated inflation response stays negative longer than the model’s does. Matching how long inflation stays low is the weak spot.

They then asked what different rules would do. In their model, a better rule stabilizes inflation more and output less than the policy the Fed was estimated to follow.

The Zero Bound

The other paper I want to cover is Eggertsson and Woodford (2003), on the zero lower bound. Yes, 2003. It was in response to Japan already having near-zero interest rates, weak growth, and falling prices, but proved much more relevant after 2008.

What can a central bank do when its usual tool, cutting the rate, is gone?

We can think through this with the New Keynesian model. The zero bound is a price floor that the nominal interest rate can’t go below, but we have all these other parts of the equation. We have the distinction between real and nominal rates. We have to think about future policy expectations, and that turns out to be the key one.

The central bank can promise to keep rates low even after the zero-bound constraint stops binding. That changes the income and returns households expect, so they can spend more today.

We can’t run experiments on the Fed. We only see the policies central banks actually chose, never what would have happened under the others. A model that gets household and firm behavior right lets us change the rule and follow the responses through spending, prices, and expectations.

Overall, Woodford and the New Keynesian model are the benchmark for these types of thought experiments.

This is a long post already, so I’m not going to go through my gripes with the New Keynesian model. I’d simply refer people to John Cochrane on the issues with how the model determines inflation at all. The model has no money. See Ricardo Lagos on whether we can safely ignore money, and to Josh on whether we are measuring it right.

That is great price theory in the Milton Friedman tradition, and I’m especially happy with Hall’s half of this prize. The model is wrong in plenty of ways. But a model like this gives us something concrete to argue about.

For more on prizes in this series, read last year’s on Mokyr, Aghion, and Howitt, the 2024 prize, and the 2023 prize.

However, other times you will hear economists say that prices are substitutes for information. They invoke this in the context of discussing markets. They will say something like, “No one needs to know why the price of oranges has gone up. The fact that the price of oranges has gone up sends them a signal to buy fewer oranges.” Markets can work with minimal information.

But isn’t this a contradiction? How is it possible that prices reflect all available information, but somehow simultaneously act as a substitute for information?

To explain why this is not a contradiction, it might help to appeal to an analogy from cryptography.

A lot of people use online banking services. In order to do so, they have to connect to the internet and log in with a name and a password. This password is pretty important. Anyone who has your password can transfer your money and send payments. Choosing your password is important. You want a password that people would not guess so that no one can log in to your account. However, it is also important that your bank doesn’t just store that password somewhere. If they do, it doesn’t matter how good your password is, anyone who gains access to the database can log in to your account. But without storing this password, how can the bank know that it is you who is logging in?

One thing that the bank could do is to use your password as an input in a cryptographic hash function. Doing so produces an output called a hash value that is of fixed length. The output that is produced by this hash function is unique. It can only be generated by using your password as an input in the function. Any change to your password would change the output. But most importantly, while using your password as the input will always produce the same output, knowledge of the output cannot be used to recover your password.

Thus, what a bank could do is store a hash of your password. Anyone with access to the database will just see what looks like an incomprehensible string of letters and integers. There is no way for this person to reverse engineer your password from this information. Furthermore, entering this string of letters and integers as the password won’t help the person get into your account since that would require using the hash itself as an input in the hash function, producing a completely different hash. The only way for someone to log in would be to enter the correct password, which is then passed through the hash function and generates a hash that can be matched to what the bank has stored. If it is a match, you can get access to your account. If not, the person trying to login (including if it is actually you) will not be able to do so.

At this point you might be wondering what this has to do with prices and information. Recall the claim that prices both reflect information and act as a substitute for information. Now, think of the online banking example. Some valuable information (your password) was passed through a hash function to produce an output. This hash value reflects valuable information in the sense that it could only have been produced from your precise password. However, the hash value doesn’t reveal any of the underlying information that generated it. Anyone looking at the hash value would not be able to determine what generated that particular value. Yet, the hash value communicates something important to the bank since the bank can check this value against the stored valued to determine whether you should be granted access to its services.

Markets work in much the same way. There are people that populate markets who possess with their own unique knowledge, preferences, and constraints. When new information is revealed, this information is combined with the knowledge, preferences, and constraints of these people and that results in a change in their behavior. These behavioral changes manifest themselves in market interactions. The corresponding change in the price reflects the particular knowledge, preferences, constraints, and information of these actors. Nonetheless, one cannot use the price to recover the particular knowledge, preferences, constraints, and information simply from observing the price. And yet, the change in the price communicates a message even to those not privy to the new information that caused the price to adjust their own behavior such that the goods in the market are allocated to their most high-valued use.

When an economist says that prices reflect information, this is not meant to say that you can recover the information necessary to determine why a price is what it is or why a price changed (although it is sometimes possible!). What is meant is that we shouldn’t expect prices to change in response to information that is already widely known.

Markets are where information is turned into price changes, which in turn communicate incentives to get resources where they are valued most. It is precisely the fact that markets tend to coordinate the behavior of buyers and sellers in a market despite the fact that one cannot always reverse engineer changes in prices to obtain the information that precipitated the change that makes markets so remarkable and so worthy of study.

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The first two videos were on price controls (always) and tariffs (also always). Enjoy and thanks for the support!

Monopsony is usually told as a story about market power.

The textbook monopsonist is the sole employer in town. They’re the only job in town, so they are only competing with people who are desperate for work or those who can stay at home. Hiring more workers means raising the wages to attract more workers, and, by assumption, you have to pay all workers that new high wage. The monopsonist doesn’t like this, so “under hires.” A firm that’s a small buyer in the labor market doesn’t have this problem. It pays a going fixed wage. That’s sort of the setup we’re used to thinking about.

Instead of monopsony and all the baggage of “mono”/one buyer, economists often define buyer market power as the existence of a markdown. It’s the gap between the last worker’s worth to the employer and the wage. A competitive employer would have no gap, so any gap looks like something like market power.

Yet I’ve argued that we should think of these gaps as residuals, and different models leave them unexplained. There are lots of reasons for markups/markdowns, completely unrelated to market power. I’ve stressed that it is a return to some fixed cost.

Let’s consider a slightly different situation. Let’s assume the employer simply has to pay the same wage to all workers, either because of a union negotiation, social norms around it, or it’s just simpler from an implementation/HR perspective. Doesn’t matter. We also need it to bind every firm in the industry. That’s trivial in the monopsony example since there is only one firm, but it is important to be clear here. That’s going to do a lot of the work. We also need that they hire many different workers at that same wage. I’ll call that a uniform wage regime.

To be a bit more vivid, imagine a contractor who hires a laborer, a carpenter, and a plumber. Each has a going rate for their trade that the contractor can’t influence, but because of this uniform wage, everyone on the crew gets the same wage. Now, to add the plumber to the crew, the contractor has to pay the plumber’s wage to the laborer and the carpenter. Hiring one more worker means raising everyone’s pay. It should be clear that we have the exact same problem as the textbook monopsonist, except that we’ve assumed the firm has no market power and can’t move any trade’s market wage.

What’s the deal?

James Buchanan and Robert Tollison pointed this out in a 1981 paper (HT: Vincent Geloso). In both cases, the firm stops hiring while the last worker is still worth more than the wage, so you’re left with a markdown that looks like market power and an inefficiency. So what exactly does a markdown tell us about market power, if we can generate the exact same hiring decision without any?

However, the two stories differ in what closes the gap.

In the textbook, if entry is possible, monopsonists would face more competition among employers, which would reduce the markdown from market power. The markdown from a uniform wage survives free entry. Every contractor already takes each trade’s wage as given, and each one still has to raise everyone’s pay to add the plumber. Letting different jobs pay different wages removes it.

In this week’s newsletter, I want to walk through their argument, what it means for the basics of price theory, and then go one step further by correcting a mistake in their paper.

Hiring different roles for different pay

Buchanan and Tollison’s starting point is that jobs can be equally valuable to the firm internally but differently costly to fill externally. Equal value is a simplifying assumption. Each role adds as much to the crew as any other, though the trades still do different jobs. A real contractor may value a plumber more than a laborer, but assume it doesn’t, so that the only difference between them is what each could earn elsewhere. That outside wage is the worker’s opportunity cost, and anything paid above it is rent. For pricing, they argue, two workers are different inputs whenever their opportunity costs differ. So we have a clean separation between what a worker is worth inside the firm and the worker’s opportunity cost, what the worker could earn in the next-best job.

Let’s put aside uniform wages for a second.

The key restriction is that each role on the crew is a different job. You can’t build a house with five laborers. So adding a role means adding a different trade, and the contractor adds the cheapest trades first, hiring the people with the lowest opportunity costs, so each added role costs more than the last. The team’s supply schedule slopes up, but not because of buyer power. The firm changes no one’s wage. It just reaches into pricier trades.

If the firm pays each role the going market rate, that schedule is the firm’s marginal cost of labor, and each hire costs exactly its opportunity cost. The firm adds roles until the last one is worth its wage.

The outcome is efficient, because a role gets filled only if it’s worth more inside the firm than outside. That’s normal competition. There’s no discrimination, nothing nefarious, and no market power. Nobody thinks a contractor discriminates by paying a plumber more than a laborer.

Equal Pay

Now, let’s add this uniform pay schedule. Under a uniform pay scale, everyone is paid the wage of the last role filled. So the supply schedule stops being the marginal cost of labor and becomes the average cost of a worker. The cost of a hire is now

Cost of a hire = the hire’s wage + the raise for everyone already on the team

So now we have a clean divide:

1. The opportunity cost

2. The rent (surplus) that will be paid

It’s the same split between what a buyer pays and the real resource cost. I prefer surplus, but they use rent.

Now imagine that every firm in an industry follows this equal pay. Each firm’s cost per unit of output rises because it’s now paying rents to everyone below the top of its scale. Profits were zero before the rule, so firms lose money until the price rises enough to cover the higher cost. Relative to a world without equal pay, output falls, and we have an allocation problem where buyers lose output that’s worth more to them than it costs to make.

We also end up with winners and losers from this equal pay. Workers at the bottom of the scale who keep their jobs collect rents since they’re paid the top wage. Workers at the top lose little if they’re dropped; they take their market wage elsewhere, and consumers pay for the rents, mostly through higher prices. That’s why Buchanan and Tollison expect the push for one wage to come from low-wage workers who expect to keep their jobs.

We still have the same type of inefficiency, but the returns aren’t going to the firm.

Does a minimum wage work the same?

In many ways, this looks just like monopsony. With a monopsonist, a minimum wage can raise employment. Does a minimum wage in this industry raise employment too? Buchanan and Tollison say no, but they are wrong.

This is going to be a bit more subtle. Let’s try it without math.

Now let’s push the uniform wage slightly up from what firms would choose. A sufficiently high minimum wage will always cause problems. We are considering a marginal change here. We’re imagining a union contract with more aggressive bargaining, or maybe an industry-wide minimum wage. Again, we’re holding fixed what each tradesperson could earn elsewhere.

We need to disentangle what the higher wage means for the costs to each firm, how it changes decisions for the firm, and what it does to the industry once firms can enter and exit.

Buchanan and Tollison get the static inefficiency logic right. The uniform rule causes firms to stop hiring too soon, relative to the fully flexible, efficient benchmark. They grant that a higher required wage can make each surviving firm hire more because it lowers the marginal cost of a hire. That’s just like monopsony.

They claim this parallel doesn’t apply to the long run. In the long run, according to them, a higher wage gives workers more rent, and more rent raises costs. Since the industry was already at zero profits, higher costs are going to drive firms out. Firms will leave. Output will fall, and prices will rise. Less output needs fewer workers. Employment also falls.

There are a lot of connections, and we need to be careful. They slip up a bit. Costs do rise, and output does fall, but only a little. The missing steps are the next two. We can’t go from less output to fewer jobs or from more rent to more waste.

Cost per unit of output is U-shaped with respect to crew size. This is the standard textbook reason that bigger crews spread the fixed costs of running a firm over more output. Add that with an upward-sloping marginal cost curve, and eventually the cost savings per unit get swamped by the rising marginal costs, and so you get this U.

If firms are identical, free entry puts every firm at the bottom of the U, and the wage firms pick is the market wage of that crew’s last trade.

Now, raise the wage slightly via the minimum wage. Hold fixed the set of employees a firm has. Its cost per unit would rise in proportion to the rise. But they’re not stuck with the old crew exactly and their marginal costs have changed. Everyone already earns the new wage, so the next few trades, the ones whose market wage is below the new wage, can join without forcing a raise on anyone. That’s the Armen-and-Bengt logic from “Be Careful about Costs,” where hiring Bengt meant raising Armen’s pay. The higher wage raises the firm’s average cost of labor but lowers its marginal cost of a hire. So firms add roles.

The higher wage lifts the cost of every crew smaller than the one whose last trade earns the new wage. But that bigger crew costs exactly what it always did, since the new wage is just its last trade’s market wage. And it sits right next to the old bottom, where the U is flat.

So the bottom of the U barely rises, and that’s what sets the price. The old crew got more expensive, but nobody builds with it anymore, and the cheapest crew costs almost what it did before. Price barely moves, and buyers want about the same output.

.

Wait. Didn’t the rule raise costs and shrink the industry in the last section? It did. Imposing the rule raises cost per unit at every team size, so Buchanan and Tollison’s long-run story works there. It doesn’t work for a small push from the bottom of the U.

Firms do leave, though the industry barely shrinks. Its output is set by demand at the bottom of the U, and the bottom barely moved.

They leave because the firms that stay are bigger, so nearly the same output needs fewer of them. And bigger teams use more workers per unit of output, because each added role adds less than the average role already there. So teams grow. The number of firms falls. And employment rises.

Now think about what the exit costs, which takes us back to opportunity cost. Society’s cost of the industry’s output has two parts: every firm’s fixed cost, and what every worker could earn elsewhere. Society’s costs don’t include any of those rents since those are simply transfers. Since price barely moves, we can compare the cost of producing the same output.

Each firm that leaves stops paying its fixed cost. That’s a real saving to society. The firms that stay add roles, filled by workers who could earn more elsewhere than anyone already on a crew. The firms that close send their crews back to their outside jobs. Count both, and the industry uses more labor, measured at what those workers could earn elsewhere. That’s a real cost to society.

Near the wage firms pick, the fixed-cost saving is the bigger one, as long as rent per unit of output rises with crew size.

At the team size firms picked, growing a little would have cut fixed cost per unit by exactly as much as it raised payroll per unit. That comes from being at the bottom of the U curve above. To the firm, that whole payroll increase is a cost. But part of it is rent, which society doesn’t count.

In that case, the higher wage raises the firm’s cost but lowers society’s. Consumers pay about the same, firms still earn zero profits, and the gain shows up as higher rents for workers. So here, more rent comes with less waste.

The big idea is that we still have the normal gap between private and social costs. When that happens, we usually get an inefficiency. That’s the key disconnect. The long run doesn’t change that. The wage firms pick is the least costly wage for the firm, not the least wasteful one for society.

I think that the reason people equate price theory with markets is the word “price.” We tend to think of prices as being tied to markets. After all, most market transactions involved posted posted or some haggling over the price.

But prices are everywhere. When I buy one thing, I give up my ability to buy something else. When I wait in line for tickets to a concert, it is tempting to think that the cost of the concert is the monetary price of the ticket. However, the monetary cost of the ticket just tells me the amount of consumption of things other than the concert that I must give up. And that isn’t the entire price of the ticket. Since I had to wait in line to get the ticket, I also gave up the time that I was in line. That is time I could have spent doing something else. If I wait in line and I buy the ticket, then clearly doing so was preferable to me than what I have given up. I have given up something nonetheless.

Prices just measure what I have to give up to get something I want. The price is the opportunity cost.

This week, I want to talk about the importance of thinking in terms of relative prices (and therefore in terms of opportunity cost). Once you do that, you can start to see how price theory can be used to think about non-market outcomes. I will provide some examples to explain why wars end and why they continue to better make this point.

It’s relative prices that matter

I think that the prices most people have in mind are often money prices. But price theory is really about relative prices. Money prices just help us make those calculations. For example, if I go to the grocery store every week, I get well acquainted with the dollar prices of many of the items in the store. If I know a lot of the dollar prices, then I also have an idea of what the relative prices are as well. For example, if I know that the price of a gallon of milk is $4 and the price of a loaf of bread is $2, then I know that for every gallon of milk that I buy means I can buy 2 fewer loaves of bread. The two loaves of bed are the cost of the gallon of milk.

Because we are familiar with money prices, we often don’t realize we are doing relative price calculations when we make decisions. Money prices aren’t that helpful though when you’re not familiar with a lot of prices. For example, with apologies to my Norwegian readers, I’m not sure whether most readers of the newsletter could tell me whether paying 20 kroner for a gallon of milk is expensive or not. This illustrates just how much we think in terms of relative prices without even realizing it.

The Alchian-Allen Theorem really illustrates this point about relative prices. Suppose that there are two couples. Each couple is planning on going out to dinner. Suppose that each couple can choose one of two possible restaurants. There is a fancy restaurant that will cost $100 and a casual restaurant that will cost $50. The first couple has small children. As a result, they will need to hire a babysitter if the couple wants to dine alone. The other couple has no children.

If you focus on money prices, you would likely conclude that the couple without children is more likely to go to the fancy restaurant since the couple with children also need to pay a babysitter. Everything is more expensive for them in terms of money prices. However, the Alchian-Allen Theorem tells us that the couple with children is more likely to go to dinner at the fancy restaurant (all else being equal) because the relative price of fancy dinner is lower for them than for the couple without children.

Why?

The couple with children pay the babysitter no matter what. Suppose the couple pay the babysitter and buy the children fast food. This costs $50. Since they pay the $50 regardless, the cost of going to the fancy restaurant for this couple is $150 and the cost of going to the casual restaurant is $100. The fancy restaurant costs 50 percent more than the casual restaurant for this couple. However, for the couple without kids, the fancy restaurant costs double what the casual restaurant does. For the couple with kids the cost of two fancy dinners is that they have to give up three casual dinners. For the couple without kids, the cost of two fancy dinners is that they have to give up four casual dinners. In other words, the fancy dinner is more expensive to the couple without children when measured in terms of casual dinners and thus they are less likely to go to the fancy dinner.

Non-market behavior and, in particular, war

Once we start thinking about relative prices and therefore opportunity costs, it becomes straightforward to think about non-market activity. Prices are still lurking in the background. Every action entails some opportunity cost, regardless of whether there is any monetary payment involved.

For example, consider the decision to steal. Theft might take planning, which requires taking time away from some other activity. Efforts to conceal a theft are also costly. Furthermore, if one is caught in the act of stealing, there is some probability of being prosecuted and suffering the corresponding punishment. By committing theft, one avoids paying the monetary cost of the theft, but one nonetheless pays a cost in terms of the planning, the efforts at concealment, and the expected punishment. When those costs go up, attempted thefts should decline.

Some things that take place outside of markets are remarkably similar to market activity. For example, Donald Wittman takes this approach to assessing how wars end. The decision to end a war typically involves some type of settlement. If the parties involved agree to a settlement, this implies that there was some type of gain to exchange. Otherwise, the fighting would continue. This is true even if one side unconditionally surrenders since this implies that the alternative is worse. Perhaps the alternative is total annihilation.

This might sound obvious. However, thinking about the end of warfare from the perspective of price theory can reveal some non-obvious conclusions. For example, state leaders will sometimes say that they are engaging in a particular offensive or bombing campaign in order to bring the other side to the bargaining table. There is some logic to this. A successful bombing campaign might reduce the expected benefits of continuing the war to the side being attacked and thus make it less costly to reach a settlement. Nonetheless, it is not at all clear that this helps bring about an end to war.

To see why, consider that the benefit of a peace settlement has an opportunity cost. That opportunity cost is that you do not get to continue the war. The higher the cost of peace, the more likely war continues.

Returning to the example, as Wittman shows in his paper, a successful bombing campaign might discourage the side being bombed from wanting to continue the war. However, for the side doing the bombing, a successful bombing campaign can potentially raise the expected benefits of continuing the war by making victory more likely. Under certain circumstances, this can make the war more likely to end. Under other circumstances, the opposite is true. If the expected benefits of continuing the war were already high or rise sufficiently high, the side that is winning might end up emboldened to continue, with less of an incentive to negotiate.

Another common misconception about war can be understood if you understand price theory. A common misconception is that when you observe a reduction in the intensity of fighting that this might be a sign that the conflict is coming to an end. I think that the focus on intensity is often conflated with a sign of weakness. However, it is important to understand that if one (or both) sides decides to reduce the intensity of conflict, it is likely that they see this as increasing the expected benefits from continuing the war. Yes, a shift toward lower intensity conflict might reduce the probability of victory. However, it also reduces the costs of warfare (and thus increases the net benefits of victory). Again, as Wittman shows, if the cost of warfare declines significantly enough, a decline in intensity could be sufficient reduce the cost of warfare and thus increase the cost of peace. A decline in intensity might therefore prolong the conflict.

Prices are opportunity costs

Much has been written about Wittman’s work and people have a lot to say about some of his conclusions. Perhaps I will return to this work in a future post. However, the broader point here isn’t about war or Wittman’s perspective.

The main point here is that price theory is all about relative prices. Given that relative prices are about comparing among alternatives, when we are thinking about relative prices, we are thinking about opportunity costs. A lot of times when we think about markets, it is easy to focus exclusively on observed prices. Often, those prices are sufficient. However, when they are not sufficient for explaining how people behave, it is often because there are other (and perhaps not-so-obvious) costs involved. Once those costs are taken into account, one is able to see the correct prediction.

Outside of markets, observable prices might be missing, but opportunity costs exist. If you can correctly identify those opportunity costs, then you should be able to use the standard lessons from price theory to help you to understand and predict human behavior.

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When the price changes, people adjust. There are many margins of adjustment. The standard model assumes adjustment just by buying or selling less, just about quantity. But they can also change quality, wait longer, or buy different bundles. Half of price theory is asking what else can adjust when prices change.

(the ratio of a product’s price to its marginal cost) and call that a measure of market power. But interpreting that ratio requires accounting for the customer’s time, not just the firm’s costs. A paper with Thomas Phelan and Nick Pretnar, recently published in the Journal of Economic Theory, works out how time changes both firms’ markups and the incentives to create new products

Deriving demand from “experiences”

Gary Becker’s insight was to treat households as producers of the experiences they want. The thing you buy (say, a theater ticket) is one input into a household production function. You combine it with your own time to produce the thing you ultimately care about, an evening watching a show. You can think of the theater ticket as an ingredient and the production function as a recipe, as we’ve written about before.

In this framing, demand for the theater ticket is derived demand, similar to how a firm’s demand for labor is derived from what it can produce. You can decompose that demand into two parts: a scale effect and a substitution effect. If you raise the ingredient’s price, you do less of the activity. That’s the scale effect. If the recipe allows it, you also use less of the ingredient in each unit that you produce, putting in more of your own time per unit. That’s the substitution effect.

These are the same two effects behind Hicks-Marshall’s laws of derived demand, as we discussed with labor demand and AI. There the price that fell was AI’s, the input in question was labor, and the two effects pulled against each other: cheaper AI means more output and more work to do, but less labor in each unit of output.

Here the price that moves is the ingredient’s own, so both effects cut purchases. It’s a different horse race (terrible pun) between two effects but a different comparative static.

The meaning of markups when time matters

Before we think about margins of adjustment, let’s do some basic accounting and assume that the recipe is fixed.

This is the theater example. An extra hour in your seat doesn’t replace part of the ticket. A night at the theater takes one ticket and three hours.

Take two theaters offering different shows to the same customers, who value their time at $100 per evening out. One has a marginal cost of $20 a seat and charges $50. The other’s marginal cost is $4 and it charges $30. Price over marginal cost is 2.5 at the first theater and 7.5 at the second. That ratio is the usual markup, but it leaves out most of what the customers pay for their evening.

Each theater is going to price based on the demand curve it faces. Suppose attendance at either theater falls by about 5 percent for each 1 percent rise in the full cost of its evening out.

Let’s think of the second theater. The ticket is $30 against $100 of time, so raising the ticket price 1 percent raises the cost of an evening about 0.23 percent. That cuts ticket sales by about 1.15 percent. Demand for evenings is elastic and demand for its ticket is much less elastic, because the ticket is a small part of the evening.

The first theater’s ticket is a third of the evening, so the same 1 percent ticket-price rise costs it about 1.67 percent of its sales. Those demand elasticities give us the profit-maximizing ticket markups of 2.5 and 7.5, respectively. The second theater can charge a higher multiple of its marginal cost because customers are less responsive to percentage changes in its ticket price.

A dollar added to the ticket is a dollar added to the evening, and the time the evening takes doesn’t change, so in this fixed proportions case, it is like the firm is pricing the full experience. On the evening, both have the same “holistic markup,” as we call it. This is the full price of the experience over its full marginal resource cost: $150 over $120, and $130 over $104. Both are 1.25.1

This gap is not peculiar to these numbers. The usual markup in our model is always at least as large as the holistic one. With a positive markup and valuable consumption time, it is strictly larger—even with a fixed recipe

With a fixed recipe, this economy is equivalent to the textbook constant-elasticity model of differentiated products, with the full resource cost of a night out in place of a firm’s marginal cost. That model, with free entry, is efficient under the paper’s assumptions. This is Dixit-Stiglitz. The allocation in that model is efficient while measured markups differ by a factor of three. Dispersion in ticket markups does not by itself show that something has gone wrong.

Adjusting your time use

Now let’s imagine it is something where you can change how much time you allocate. Think of video games. (Let me know if you have a better example; I don’t love this one but its okay.) As prices rise, you can spend more time playing each one.

Raise the price and people consume less of the gaming experience. That is the scale effect. They can also buy fewer games and spend longer on each one to get a given amount of enjoyment. That is substitution.

With a fixed recipe, every lost ticket sale is a lost evening. With games, some of the lost sales come from people who are still gaming. They just replay more and buy less. We’ve seen a related distinction before: retirees can spend less on food without eating less, because they spend more time shopping and cooking.

That makes the game seller’s demand more elastic than the scale effect alone would imply. Keeping the experience-demand elasticity at 5, its holistic markup falls below 1.25. How far below depends on both the ease of substituting time for purchases and the purchase’s share of the full price of the experience.

Time therefore does two different things. It makes the purchase price a smaller part of the full cost. But it can also give customers another way to economize on purchases, another margin of adjustment. A small purchase share weakens the scale effect but it does not make the substitution effect disappear.

Do we get enough new products?

The paper closes this demand equation in a whole model with firm entry and other bells and whistles. So we can ask, does enough effort go into creating new products?

Usual markups are what pay for new products. Markups allow them to make profits to justify entering. Firms enter until profits cover the cost of starting up.

The question is whether the amount of entry that results is efficient. With a fixed recipe the answer is yes: the economy is equivalent to the standard model of differentiated products, and free entry gets the right number of them. When the recipe can change, every holistic markup falls below the fixed-recipe level, profits fall with it, and too few products get created.

The markup on purchases, but not on customers’ own time, pushes them toward a more time-intensive recipe than resource costs justify.

The paper also breaks the usual inference from markups to efficiency. We build two different consumer problems that produce the same demand curve for a product but imply an efficient allocation in one case and an inefficient allocation in the other. Different measured markups can coexist with an efficient allocation. Identical measured markups can coexist with an inefficient one. Even a perfectly measured markup is a residual that needs an explanation.

Measured markups systematically overstate the markup on the full experience, and the gap can be especially large for products where the customer's time is most of the cost.

Time is just one of those margins that adjusts when a price moves. I think it’s an important one.

I've argued before that markups are too low to get the right amount of product creation. Time use makes the problem worse and changes which firms it hits hardest. A high measured markup usually looks like a firm with too much market power. Here it can mean the product is a small share of the experience, the holistic markup is low, and the gap between measured and holistic is wide. The firms with the highest measured markups are the ones whose reward for creating products falls furthest short.

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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