Be Careful about Costs

Three confusions about the relevant marginal cost

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People will do something until the marginal cost exceeds the marginal benefit. This is the core proposition in price theory, which renders behavior sufficiently rational to allow us to make predictions.

Yet there is a lot buried in that idea. Costs and benefits are subjective, so who is to say what is a cost or benefit? Even if we simple propositions like most people view more money as a benefit and more work as a cost, it’s not always obvious what the relevant marginal costs and marginal benefits are. After all, as we’ve stressed many times, there is always another margin.

This week’s newsletter goes through three examples where our first guess of the relevant marginal cost may lead us astray. One example, about thermostats, is politically neutral. One example, about minimum wage, cuts against libertarian ideas. And the final example, about monopoly, cuts against progressive ideas.

Something to annoy everyone. Let’s dive in.

For Fun: Costs of Thermostats

Let’s start with an example from David Friedman’s 1987 article in the Journal of Political Economy, “Cold Houses in Warm Climates and Vice Versa: A Paradox of Rational Heating.”

Should you adjust your thermostat based on the outside temperature? For example, it’s a balmy 20 degrees Fahrenheit in Minnesota right now, but it was -20 degrees a few weeks ago. Should my thermostat have been lower when it was -20? After all, I would save on heating costs.

Friedman argues that the “rational” thing to do is to keep the indoor temperature constant. As always, we need to think on the margin about marginal costs, not total costs. Yes, when it is -20 degrees, I spend a 💩 ton on heating my house, but that’s not the relevant question. The relevant question is, do I value the marginal degree of warmth inside more or less than the marginal price I pay? He needs to make some simplifying assumptions about how heat escapes from a house, but the basic point is

since heat loss by conduction is proportional to the temperature difference between outside and inside, the marginal cost of interior temperature-the cost, say, of keeping the house at 70 degrees instead of 69 or at 65 instead of 64-depends on the characteristics of the house but is independent of both inside and outside temperatures. A utility-maximizing resident will choose that temperature for which the marginal utility of an additional degree is just equal to its cost; since the cost is independent of outside temperature, so is the optimal inside temperature.

Another way to think about it is that if the house right now is 69 degrees, the marginal cost of increasing that to 70 degrees is what matters. It doesn’t matter if it is currently 69 because that’s the temp outside or because the heater already pushed it up to 69.

I love this example. The math in the paper is simple, so that’s nice. But more importantly, it shows how the different notions of cost that we use in Econ101 to describe firm production of widgets (total cost vs. marginal cost) also play out in a context that seems quite different.

Friedman isn’t merely making a normative point about what is the rational way to adjust your thermostat. Friedman believes this is the proper assumption because it generates proper predictions. Here the predictions are that people will keep the thermostat (roughly) constant and that people in colder climates will keep their houses warmer. That’s the paradox in the title. Why? Since the characteristics of the house are not fixed, people in Minnesota will invest in better insulation, what Friedman calls “characteristics of the house,” which lowers the marginal cost of heating. With lower marginal costs, Minnesotans will choose a higher temperature. If this prediction is correct, then it means people do think about marginal costs instead of total costs, or at least people behave as if they do.

A Monopsonist’s Labor Costs

Now that we have the non-political example out of the way let’s move on to something where people get more heated: minimum wage.

If you follow minimum wage debates at all, you’ll likely run into a certain type of libertarian who is absolutely certain that raising the minimum wage must lower employment. After all, when you increase the cost of something, people do less of it. Therefore, if you raise the cost of hiring workers, people will hire fewer workers. It’s just basic economics! I’m not proud of it, but this may have been me a decade ago.

The most famous example of this confusion was James Buchanan’s reaction to the original Card/Krueger minimum wage paper. In one of his not-so-great moments, Buchanan wrote

The inverse relationship between quantity demanded and price is the core proposition in economic science, which embodies the presupposition that human choice behavior is sufficiently rational to allow predictions to be made. Just as no physicist would claim that “water runs uphill,” no self-respecting economist would claim that increases in the minimum wage increase employment. Such a claim, if seriously advanced, becomes equivalent to a denial that there is even minimal scientific content in economics, and that, in consequence, economists can do nothing but write as advocates for ideological interests. Fortunately, only a handful of economists are willing to throw over the teaching of two centuries; we have not yet become a bevy of camp-following whores.

My opening line said something similar to his first line. While it is absolutely true that the inverse relationship between quantity demanded and marginal cost is the core proposition in economic science, we need to be careful about what is the relevant marginal cost. It’s not always what we think it is.

Let’s take the standard monopsony model. The firm, by assumption, is rational and will hire workers up until the marginal benefit equals the marginal cost. Let’s assume the marginal benefit is fixed at $16 since that is the revenue each worker generates.

What’s the marginal cost of hiring an additional worker? The most obvious answer is the wage the firm needs to pay the worker, but that’s not right in the monopsony model.

I’ll avoid any graphs for simplicity, but the standard graph is here. Suppose there are two potential workers: Armen and Bengt. Armen will work for $10, and Bengt will work for $15. How many workers should the firm hire? It depends on whether or not the two workers must earn the same wage. In the baseline monopsony model, which may or may not be realistic, we assume the firm must post a wage and then hires everyone who accepts the job.

Under this wage setting rule, setting the wage at $10 and hiring just Armen generates $6 of profit ($16 of revenue - $10 of wages), while setting the wage at $15 to hire Armen and Bengt only generates $2 of profit ($32 of revenue - $30 of wages). The firm should set the wage at $10 to maximize profit.

We can think of the hiring decision in marginal cost terms. The marginal cost of hiring Bengt isn’t just the $15 that he requires to be willing to work; it also includes the $5 more the firm has to pay Armen. The marginal cost of the second worker is $20, which is greater than the marginal benefit of $16. That is why the firm doesn’t hire Bengt. Now if the firm can set different wages for different workers, the marginal cost of Bengt would be $15. But it’s not costless to do this type of price discrimination. After all, information is costly, so it’s not ridiculous to assume the firm can’t tell Armen and Bengt apart.

Now suppose the minimum wage is set at $15. The profit of hiring each worker is $1, so the firm will hire both workers. The minimum wage increased hiring! It did so in this concocted example by raising the average cost (and so lowering firm profits) but lowering the marginal cost. Since Armen is already making $15 with the minimum wage, the marginal cost of hiring Bengt is only the $15 he is paid. From the firm’s perspective, raising Armen’s wage is no longer part of the marginal cost of hiring Bengt. The naive libertarian (there are more sophisticated responses) only sees the average cost increase but not the marginal cost decrease.

The important part of the monopsony example is not that this pricing mechanism describes most labor markets. That’s an empirical question that is hotly debated. I would like to point out that there is new evidence from Priyaranjan Jha, David Neumark, and Antonio Rodriguez-Lopez that casts doubt on a famous paper arguing that minimum wage doesn’t decrease employment.

The point of this example is to point out that it is entirely plausible and not a rejection of economics that for some firms, the marginal cost of the worker is more complicated than just that worker’s wage.

To give Buchanan a bit of credit, we do need to worry about retaining scientific content in economics. If we can arbitrarily redefine costs in each new situation we study, we have no constraints on our theory. Buchanan’s own collection of essays on methodology is wonderful on this, including one of my favorites: “Professor Alchian on Economic Method.” One of the benefits of price theory is that it is a limited set of theories to explain a wide range of phenomena. But the classical monopoly and monopsony models have proven useful in enough context that they are no longer ad hoc theories.

Costs of Innovation

Now that I’ve annoyed my libertarian readers, let me annoy my progressive friends, especially those interested in antitrust.

There is a common idea within antitrust that once a firm pays some upfront cost that becomes a barrier to entry for new firms and creates a sort of natural monopoly that is hard to overthrow.

We can think of this story in terms of marginal costs. The common idea is that the incumbent has a lower marginal cost, since it has already paid the sunk cost. Since it has this advantage, the incumbent will be very difficult, maybe even impossible, to dethrone. Therefore, the logic goes, we should be very concerned about monopoly power in markets with these sorts of sunk costs.

A wonderful article at The Diff by Byrne Hobart (HT: Geoff Manne) explains the problem with this reasoning. His example is the renewed battle for search between Google and Bing, now with the large language model (LLM) based features of ChatGPT:

Where this gets really interesting is on the margin side. It costs money to run a search engine, and while that cost isn't entirely fixed, Google Search's maintenance cost is not 13x Bing's while its market share is. When Google looks at new LLM-based search features, it sees something that cannibalizes Google searches at a higher marginal cost. Whereas when Bing looks at those same features, it sees something that eats Google market share and spreads some of Bing's fixed costs over a larger base of searches. The same economics that make search such a great business ensure that a subscale search company has an incentive to embrace a less profitable search model.

Again, we can recast this in marginal costs terms. If there is only one search technology, then Google has the lower marginal cost today because it previously paid sunk costs to get the dominant position in the sole search technology. For Bing to compete on that exact dimension would be extremely difficult.

But when we realize there are other possible search technologies, such as the new attempt to incorporate ChatGPT into search, the relative marginal costs flip. For Google, the cost of developing a better search engine with LLM includes the costs of lost market share of their current form of search. Any LLM-based search that Google develops is taking money out of its left pocket to put in its right pocket. For Bing, they are taking money from Google’s left pocket.

I would argue that this type of competition for the new product is the more dominant form of competition in an economy. The world is more like a Schumpeterian endogenous growth model with different varieties than a fixed set of goods. Most firms are trying to secure market dominance, not by moving down a marginal cost curve of today’s technology, but by coming up with a new technology to leapfrog the incumbent. While economists tend to see sunk costs and barriers to entry, people in strategic management and entrepreneurship will see these sunk costs as barriers to change and innovation.

Does our competitor have a bunch of sunk costs in their current system? Great. They won’t keep up with us. Meanwhile, time and time again, the firm with a supposedly insurmountable position is left in the dust.

One reply I could expect from people really concerned about sunk costs-based dominance is that this example actually shows the problem. Google won’t innovate since it has a dominant position! Sure. If you’re going to compare this situation to some hypothetical planner, you may not have efficient innovation. In fact, the current monopolist doesn’t have the optimal incentives to innovate because they do not earn all the returns for their innovation. This is part of the general problem that monopolists don’t earn a high enough return, and so don’t optimally innovate.

Monopolies don't make enough money

However, in more applied policy work, we aren’t comparing to a benevolent planner. I’d argue we should be more interested in whether an incumbent will stay an incumbent. How often will the dominant firm be overturned? What sort of churn and business dynamism will there be? We don’t know the “optimal” level, but it seems like a good sign if firms change through time. It’s problematic that business dynamism has declined. The theory outlined by myself and Byrne Hobart and the example of Bing and Google give us a reason to believe jockeying for a dominant position still exists in a world with larger and larger fixed costs. Hope is not lost.

My usual retort that we need to think on the margin may not be entirely helpful. Which margin? There are a lot of them.