Favorite Models: Spence on Monopolies, Harberger on Incidence, Solow on Growth

Alex and Tyler put three classic models through their paces. Alex starts with Spence on how a monopolist chooses quality and applies it to how the New York Times’ paywall flipped its audience incentives. Tyler pushes back, arguing that network effects and loyalists matter more than marginal customers. They move to Harberger on tax incidence and the hidden winners and losers of corporate taxes, minimum wages, and congestion pricing. Finally, Solow’s growth model frames a conversation on why some countries catch up and others stall, including what it gets right about China, and what it misses. Together, their debate shows why the best models keep earning their place—not because they’re perfect, but because they still shape how we think even when they’re wrong.

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ALEX TABARROK: Good morning, Tyler.

TYLER COWEN: Good morning, Alex.

TABARROK: Today we’re going to be talking about our favorite models.

COWEN: Economic models. Not our favorite models. That’d be a very different podcast.

TABARROK: I was going to spare you the lame joke, but okay. We’re going to talk about our favorite economic models. Let’s get right into it.

One of my favorite models is how a monopolist chooses the quality of output. We all know that the monopolist produces a lower quantity of output. The monopolist wants to reduce the quantity in order to raise the price and increase revenues. But what about quality? Does the monopolist also produce a lower quality of product, or does the monopolist produce an inefficiently high quality of product? You could have too high as well as too low.

This intriguing question was first explored by Michael Spence in 1975. This is the same Michael Spence who won the Nobel Prize for his work on signaling. He had some very productive early years coming—I think a lot of it came out of his dissertation.

COWEN: Then he became a dean. I never understood that at the time. Like, “Michael, why are you becoming a dean?”

TABARROK: Good stuff at the time, though. So Spencer’s answer about monopoly quality is pretty intuitive. The monopolist cares about revenue, which means the monopolist is always thinking about the marginal consumer. Will this change in quality, will this change in the characteristics of the good, will it make this marginal consumer more likely to buy? The guy who’s not buying it now, will this change in quality, will it induce him to buy? The change in quality affects all consumers, but the monopolist only cares about the marginal consumer.

Let me give you a simple numerical example and then we’ll give you some intuition and then we’ll do some applications of this model, which is really why I like the model, is the applications.

COWEN: Then I’ll tell you why I don’t like it.

TABARROK: Yes. Okay.

COWEN: A part of it I do like, part of it I don’t. All right.

TABARROK: Simple numerical example: We have Tom, Dick, and Harry. And Tom values the good at nine, Dick values the good at five, and Harry values it at three. The monopolist could sell one unit for nine, or they could sell two units for five, or three units for three. Clearly, it is best for the monopolist to sell two units for five and have revenues of 10. We’ll ignore costs, just simplify things.

Now let’s imagine that there’s a change in the characteristics of the good, which makes Harry willing to pay four for the good. Well, that’s great for the monopolist because now the monopolist can sell three units of the good at four each for total revenues of 12. As long as it costs a monopolist less than two to increase the quality or to change the characteristics of the good, the monopolist can make more money by selling three units at four by increasing the quality of the good and selling three units of four.

Now, notice in this example that the monopolist only cares about Harry. Suppose, in fact, people differ about what they think about quality. Maybe Tom doesn’t like this change in the characteristics of the good. Tom used to value the good at nine, but suppose that because of the change in the so-called quality of the good, Tom now values it at six. Monopolist doesn’t care. Monopolist can still sell three units at four each for total revenues of 12. Even though, and here’s the key, the social value of the good has actually gone down because Harry only values the change in quality at one more, Tom values this change in the quality of the good at three less.

If there were a social planner, the social planner would say, don’t do this, but the monopolist only cares about the effect on Harry, he can increase his revenues by selling one more unit, three units at a price of four each, total revenues of 12. The monopolist does this. What this tells you is that the monopolist isn’t thinking the same way as the social planner and it could be increase in quality, could be decrease in quality, depending upon what Harry thinks about this change in the characteristics of the good.

Let me give you a sort of some intuition and then we’ll do some applications. Imagine the good we’re talking about is whether there should be smoking in the restaurant. Again, we have Tom, Dick, and Harry. Harry is a smoker, he will only go to the restaurant if there is smoking. For the restaurant to allow smoking, that increases Harry’s utility from three to four, but say Tom really hates smoking, and that’s why it goes from Tom’s value of the restaurant goes from nine to six. Because it’s a monopoly, all three consumers still consume, and so this is good for the restaurant to allow smoking, even though it’s bad for society.

Now, this doesn’t prove that we should prohibit smoking in restaurants or allow smoking in restaurants. There’s a lot of other things going on, but the point is that the monopolist thinks about the marginal consumer, not about Tom, the inframarginal consumer. So that’s the model. Should we give some applications, or do you want to say why you don’t like it or shall we give some applications first?

COWEN: Let me first tell you what I do like about the model. So often you hear people say, well, the quality of that is crummy. It’s because they’re a monopoly. It might be true, but it’s not in general going to be true and the Spence model shows you that, that a monopolist could choose higher quality or lower quality, and neither follows a priori.

To give you a simple intuition, if you could have a monopoly over the supply of yachts for very wealthy people, or a monopoly over a little plastic speedboats for kids, which would you rather have? Well, it’s going to depend on the numbers, of course, but it may well be you prefer a monopoly over the higher-quality yachts that sell for more money. The simple identification of monopoly with low quality, which you just hear all the time, even from people who should know better, it needs further justification. Clearly, it’s sometimes true, but you can’t just say that’s why quality is low and the model on that is great.

TABARROK: Exactly. Yes, I agree with that entirely. It could go either way. Let’s give an application of the model. Why has The New York Times become more left wing over time?

COWEN: Though it’s becoming more centrist in the last year, it’s going to be complicated.

TABARROK: Clearly one thing which changes is that consumer tastes change. You just might think, well, maybe the consumers have become more left wing over time and now Trump is elected, and so now they could be less left. Well, blah, blah, blah, consumer tastes. I want to argue that the Spence model explains this. Here’s how I would do it. The New York Times used to get most of its revenues from advertising, a little bit over a majority of its revenues came from advertising.

Now, what do the advertisers care about? Well, the advertisers, they care about the number of readers. They care about eyeballs. How many people are reading The New York Times. The advertisers, they’re not interested in the left wing, the right wing, blah, blah, blah. They just want readers. The advertisers put a moderating force on The New York Times. In other words, the advertisers, they care about the marginal consumer. They want as many eyeballs as possible, and that means, tends to mean just stick to the middle.

However, technology changed. Newspapers went online, and at first, this was a big shock to the newspaper industry, advertising revenues fell. The New York Times started to lose money because they couldn’t make enough money from advertising. What did they do? Well, they put up a paywall, 2011, and then the paywall started to get stronger and stronger over time. Advertising revenue continued to fall, but subscription revenue went way up, and with the advertisers no longer having the same force, no longer being the same power, The New York Times is no longer pushed to the middle. Instead, they were pushed to cater even more to the subscribers.

COWEN: Why weren’t they pushed to the centrist subscribers? Because there’s more of them, right?

TABARROK: Well, I don’t know if there’s more of them. What do the subscribers really want? Do they really want the news or do they really want the red meat which serves up their view of the world? News has always been packaged with entertainment, and I think by going to the subscription model, what it showed was that the entertainment value of The New York Times is, let’s have another article attacking Donald Trump, people love that, it got the most repeats, the most passed on and so forth. That is what increased subscription revenue.

COWEN: I view those people as the inframarginal buyers, not the marginal ones. They’re the ones who will subscribe to The Times, anyway. What you want to get them to do is to put the article on Facebook or send it around so you’re repealing to your dedicated hardcore, the marginals, who many of them left, or the centrists. The New York Times, at least for a while, until lately,ignored the centrists, who were the marginal buyers, and went after the loyal ones who would lead to this contagion effect.

I think that’s the key problem with the Spence model. It ignores the fact it’s your dedicated buyers who are going to spread word of what you’re doing. That’s why you want to appeal more to them, not the marginals.

TABARROK: The advertisers were the ones appealing to the marginals, and those guys went away. It’s the subscribers. It’s the same reason why television got better once you had HBO, is because HBO made its money from subscription revenue. You got a higher so-called quality of product. Now, in this case, the quality of product you may differ, but for the people who were subscribing to The New York Times, it was feeding to them their own worldview back to them and enhancing it and increasing it.

That’s, I think, why The New York Times got more left wing. Because the subscription revenue, those are the guys that you want to make them love The New York Times. People, I think, love The New York Times in the left-wing era more than they loved it before when it was just all the news for the print.

COWEN: You fed more to the inframarginals. Look at so many other sectors. They cater to people who join the club, people who get rewards, people who keep on buying, people who keep on going. There’s just a lot more of that. Now, some of that is segmenting your market and colluding. I think a lot of it is in the world, attention is more scarce. You just need dedicated consumers who will talk up what you’re doing, review it well, send around links. Again, at first, put it on Facebook. Now could be TikTok, whatever. That’s the opposite incentive from the Spence model. It’s the person who barely is willing to buy your thing, who’s not going to talk about it. You need people to talk you up.

TABARROK: Right.

COWEN: Look at Marginal Revolution.

TABARROK: Yes. I think we’re agreeing. You agree that the advertisers care about the eyeballs and they went away?

COWEN: Yes.

TABARROK: The subscribers, they’re the ones who are more likely also to send the article to their friends. You want to appeal to them, and how do you do that?

COWEN: Of those subscribers, there’s some people who over the years write me and tell me they got fed up and stop. Then there’s the dedicated hardcore who want to look at the culture page and see so many articles about, my goodness, whatever. For so many years, there was more and more appeal to them. I just think they’re the people who are not going to leave The Times no matter what.

TABARROK: I don’t know. Why do you think The New York Times got more left wing?

COWEN: I agree. It’s disappearance of advertising. That’s not exactly the Spence model. The Spence model is taking that as fixed, and then saying, as market power increases, do you appeal more to the marginals or inframarginals? It’s saying you appeal more to the marginals. I just don’t see that empirically. I get there’s some cases where it’s true, but I think this other publicity effect has become more and more important.

TABARROK: I am twisting the Spence model a little bit. Because I’m thinking about the Spence model not so much as growing monopoly power, but as just thinking about the marginal versus the inframarginal consumer, and how you pay for the product can change that. In the pure Spence model, there’s only one actor, the monopolist. In the model, which I’m talking about, which is also the model of HBO, we’re actually talking about—or the artist model like on the margin, the artist has to meet the consumers, but the inframarginal, the artist wants to support their own taste.

I’m talking more about, there’s two different groups here, and they have different views of what quality is. The marginals care more about just the news and the inframarginals care about the red meat. I think I am changing the Spence model a little bit, but only a little bit. It’s more just understanding that there are these two groups, I think, which is the key to the model.

COWEN: If that’s all it is, I agree. The notion of when the marginals become more important, I don’t agree with Spence. Even HBO, I think of them as facing the following problem. They have all these loyal subscribers, but those people expect a really good show once every two years, and you’d better give it to them, or they’re going away. HBO, at least for a while, kept on delivering that consistently. Maybe not anymore, but they did for many years.

They were never so much, “let’s dumb down the HBO thing and try to bring in some newbies.” At least not after a while. They’re like, “We’ve got to come up with another Boardwalk Empire or Sopranos,” and always trying to do something hardcore.

TABARROK: Yes, exactly.

COWEN: Now it’s when they lost track of that, that they started failing, which is more recently. During the heyday of HBO, it was just hardcore. Let’s appeal to the inframarginals.

TABARROK: Exactly. Because it’s subscription revenue.

COWEN: That’s not the Spence model.

TABARROK: I think it is. It’s the Spence model in the sense that when you had broadcast television, you are much more interested in the marginal consumer than when you have subscription television.

COWEN: That’s the Coase model, which makes sense to me.

TABARROK: Which Coase model?

COWEN: His piece on payola. That’s what, 1972?

TABARROK: Yes.

COWEN: That when it’s ad driven, it’s least common denominator. If it becomes “payola” or subscription or just upfront money, pay for service, you serve the more intense preferences. Totally true.

TABARROK: You call it the Coase model, I call it the Spence model. Let me give another example, which you are very familiar with. Dare I say, this comes from our lived experience. Our lived experience is writing a textbook, Modern Principles of Economics. When you and I started to write this textbook, we had the goal pretty explicitly of not writing the most popular book.

COWEN: That’s right. We did succeed, but it’s in fact become a very popular book.

TABARROK: It has become a popular book. Our goal was to write a textbook, which the inframarginals, if I could put it that way, would love. That some people would really love. We wanted to write an Alchian and Allen, we wanted to write a McCloskey. We wanted to write a book which would last. To do that, we had to make some choices, like not including a lot of things which people wanted. We had to get this by our publisher.

COWEN: That’s right. Over time they want you to put everything in an appendix as a compromise.

TABARROK: Exactly. Every new edition, we face this battle or this conflict with our publisher, who’s otherwise a great publisher, Macmillan Press. In that Macmillan, they don’t get the love. They only get the revenue. They don’t care that people love our book, they only want it to be popular. We get this, “If only you had a chapter on indifference curves, then more people would use your book.” We’re like, “Indifference curves shouldn’t be taught in principles. We are a supply-and-demand book.”

Supply and demand, supply and demand, supply and demand. Teach supply and demand better, give more applications. Don’t throw the students who, most of them, are never going to take another economics class, don’t throw them into indifference curves and explain why indifference curves don’t cross, blah, blah, blah. Then you just give them one application and then they forget it. The company is like, “Oh, well, but some places, they have to teach this model.” We have this battle. Sometimes we give in.

COWEN: Sometimes we don’t. I’ve been on these phone and Zoom calls where I’ll say, “If you want to teach indifference curves in the latest edition, that’s in an appendix.”

TABARROK: Yes, exactly.

COWEN: It is.

TABARROK: There’s a real trick that you don’t want to make the book worse for the people who love it. You do sometimes want to appeal to the marginal consumer. It’s amazing to me, but one of the most popular economic textbooks, even to this day, is McConnell.

COWEN: It’s easy to test, based on it.

TABARROK: Easy to test. No dirt on McConnell, but no one has ever said McConnell is the greatest textbook ever written. How is it so successful? One of the reasons that book is so successful is that you can get it through a committee. A lot of economics education, you have to have one textbook for the entire department, and everybody has to agree on it. I think we will have in any committee, some people who love our book, but some people, they don’t like it so much. They can only agree on McConnell as a compromise.

COWEN: It’s also interesting to me, as texts become more and more online, which has happened with ours as well, it’s harder to resist the pressures. You could say in the old days, “Oh, but if we put in another appendix, the book will be too bulky. The paper will cost you money. The point of the book won’t be clear.” With everything a click away, the complaint, in a sense, sounds a bit more like, “We don’t want to have to do the work,” rather than, “Oh, the book will be worse,” and you’re more likely to lose the battle and content will proliferate.

TABARROK: It’s interesting because you can always mix and match the author, the chapters, but a lot of people don’t do that.

COWEN: That’s right.

TABARROK: A lot of people don’t do that. They think if the authors have written it this way, we must do it in the same order and cover exactly the same material.

In any case, I see this as an application of the Spence model because the company is interested in the marginal consumer. We’re interested in giving love to the inframarginal consumer. It’s my lived experience which makes me like this model.

The Harberger Model

COWEN: Let me tell you about one of my favorite models.

TABARROK: Please.

COWEN: This is not a partial equilibrium model. It’s a general equilibrium model. That’s another of my worries about the Spence model. You’re just looking at one firm or one sector or one thing. Arnold Harberger, who, by the way, is still alive, I believe he’s 100 years old. He’s at least 100, still deserves a Nobel Prize. In 1962, he wrote what is now a famous piece called “The Incidence of the Corporate Income Tax.” This piece teaches you how to think about tax incidence, what then was a new and better way. Now it’s quite standard.

The point Harberger makes is tax incidence up until Harberger had been about a single company or a single sector. He built the modeled equivalent of a whole economy. What economists mean when they say general equilibrium is instead of one sector, we’re going to have two.

TABARROK: Usually, we’d say for partial equilibrium, it depends upon the elasticity of demand.

COWEN: That’s right. It depends partly on that, to be sure. In the Harberger model, it depends on how the sectors interact. One thing we learned from the Harberger model is that simply from moving from one sector to two sector, you get a lot more richness. A lot of people might have thought, to mimic a real economy, you need 7,000 sectors. Otherwise, you don’t know what you’re doing. There are people who try to do that. The Harberger model is the simple Chicago School economy. Only two sectors, you get a lot more richness.

TABARROK: You have a corporate sector—

COWEN: And a noncorporate sector.

TABARROK: —and a noncorporate, which is still large in the US economy.

COWEN: It can be nonprofits. It can be residential real estate, which is huge. It can be household production, which is hard to measure, but very large. Partnerships.

TABARROK: Small companies.

COWEN: Right. Also, the other sector can be overseas activity, not in his first model, but that’s turned out to be one of the most important applications.

TABARROK: You have an increase in the corporate tax. What happens?

COWEN: One lesson of the model is actually anything can happen. Who bears the burden? Is it capital, is it labor, or is it consumers? In the simplest versions of the model, what you have is both a substitution, capital versus labor in the taxed sector, and you have substitutions across sectors. You have a whole series of different effects. One of the first and simplest lessons from Harberger, which is really neat, but people just hadn’t gotten it before, is if you tax the corporate sector under a lot of reasonably general assumptions, the rate of return on capital goes down equally in both sectors, which to us is standard fare.

What will happen is capital flows out of the corporate sector into the noncorporate sector, that lowers the marginal rate of return on capital in the nontaxed sector, and simply the notion of capital can suffer in both sectors. Again, a revelation, maybe self-evident to us having written this principles textbook, but it shocked people. The partial equilibrium models never show that.

TABARROK: When you tax the corporations, you’re also taxing the mom-and-pops.

COWEN: And the nonprofits and whatever, wherever else the capital might flow.

TABARROK: Yes. This was one of the first useful applications of general equilibrium.

COWEN: That’s right. On that, it’s really held up. International affairs, one of the lessons is if you turn the other sector or add another sector that’s international, basically small economies cannot afford to tax capital at very high rates because so much of the capital will flow elsewhere.

TABARROK: Instead of it flowing to the noncorporate sector, it just flows out of the country.

COWEN: That’s right, which is like the other sector not affected by this particular tax. In 1962, a lot of small economies treated their capital very badly. Many still do, but there’s been a real revolution where even fairly statist economies—like the Nordics over time shifted to treating capital income pretty generously. Singapore would be another example. Again, it’s simple once you know it, but the Harberger model taught us that.

TABARROK: What about the labor margin?

COWEN: The debate since then has been how much of the tax is borne by capital and how much is borne by labor? On one hand, the Harberger model teaches you anything can happen. That’s useful intuitively. In fact, when you investigate it empirically, it’s what you would expect to happen that mostly happens. That is, capital does bear more of the tax than labor.

TABARROK: Labor bears a chunk.

COWEN: Yes. A typical estimate might be a third. There’s no free lunch from the point of view of labor. Furthermore, a lot of the capital is owned by labor through pension funds. If you take that into account, I don’t have an exact number for you, but I think it’s plausible to think labor might bear half the burden of the corporate tax. Again, you can show that pretty simply. The estimates are not exact, but just a big advance for economics. If you ask me, what ideas do I use all the time, that’s one of them.

The Harberger basic model, it doesn’t have land, but there’s the issue of what if you have three factors in the model, you would start with the Harberger model. If you’re a NIMBY who thinks there’s this kind of land monopoly in a city or land rents are very high because we stifle building, the incidence of a lot of taxes, even in general equilibrium models, can fall on the land for a city.

TABARROK: Yes, because the land can’t escape.

COWEN: That’s right.

TABARROK: As we say in the textbook, elasticity is equal to escape, right?

COWEN: Yes.

TABARROK: If you have high elasticity, you can escape the tax. If you have very inelastic demand, going to partial equilibrium now, which is land, you can’t escape the tax.

COWEN: You may not like this point, but like the congestion tax in New York City, it depends on a lot of things. At least think through the possibility that much of that tax will fall on the landlords, and prices for what you drive into the city for will fall by about as much to offset the $9 toll. This adjustment takes some time. Over time, you may not discourage commuting or driving very much, and the landlords will be worse off and the state of New York will have more money.

It doesn’t have to work out that way. Depends on what you’re taxing. Plenty of complications. Even to have that thought, even today on Twitter, very good economists, they don’t want to entertain that thought. It’s fine to say, “No, the elasticities are such, but that’s not the dominant effect.” People just want to say, “Oh, there’s an externality. We should tax it. There’ll be less traffic in New York. This is clearly good.” Still it’s better, on net, to tax the congestion, but you need to think through where is it really going to fall?

TABARROK: Yes. You’re making a good case for Harberger for a Nobel Prize.

COWEN: Now, some other points in the model. First, the basic model assumes that both capital and savings are fixed. Now, over time, as you would expect, this has been modified as one of the great contributions of Larry Summers, that he led many of those modifications. Just to understand, what was it that Larry did that was important? Many different things. You don’t understand the importance of Larry without knowing the Harberger model, because he, Martin Feldstein, Jim Poterba, some other people, started looking at this being more elastic. You get cheaper, less academic versions of that from the supply-siders, but same basic idea. That can change the results.

The notion that you want your tax system to encourage accumulation, it’s not in the Harberger model, and still the model is useful, is a funny mix. You might not expect that, as a market-oriented economist, but that it’s true is a little sobering. The effects you might think are most important, you don’t always need to have in your model, is a useful lesson for modeling in general. It doesn’t mean you shouldn’t have other models for those. You should.

Now, here’s another thing about the Harberger model. Does this lower it or raise it in status? The basic model is sweeping under the rug, consumer price effects. It’s like there’s two sectors, Harberger’s like, “Some prices will go up, some will go down.” This is not a model about consumer prices. Fine, you can limit it that way. There’s some later papers, there’s this one in particular by Scott Baker and co-authors, came out last year from NBER. It looks at changes in state corporate tax rates, and it finds that, really, so much of the burden falls on consumers, and that some of the core results where it seems to be 70% on capital and 30% on labor, it can be up to 50% of the total gets translated into higher prices for consumers.

Now, that doesn’t quite make economic sense. There’s a lot of different cases where these cost-push or cost-plus theories of prices seem empirically sounder than you might like to think as a microtheorist. This is one of them. That’s not a final word, but the notion that we need to think about pricing more seriously, it may not just be elasticities in the simple sense. There’s some coordinated add-on to average cost maybe that actually could stick.

I’m not defending that, but the recent add-ons to Harberger investigations are putting that on the table back again, it makes the corporate tax look worse. It makes some parts of traditional micro look worse. Not resolved in my opinion, but a puzzle. The papers that find these big consumer price effects, I don’t see anything wrong with them. They may not be general, but I don’t think they’ve been refuted.

TABARROK: It’s always been a little bit puzzling to me that in the big literature on the minimum wage, all of the focus is on how much, or does it reduce? How much does it reduce the demand for labor? Yet a big effect is a lot of it is just passed on.

COWEN: Those are some of the best papers. Consumers pay for it.

TABARROK: Exactly. You have a minimum wage, and the price of McDonald’s goes up. You may hire almost as much labor as you did before, but now that increase in labor costs, you’ve passed it on to consumers, many of whom eating at McDonald’s are not rich. They’re not the rich. It definitely changes the distribution in not a particularly beneficial way.

COWEN: Maybe another lesson is we should listen a bit more to business people as Alan Blinder and some others have done. They’ve said for ages, “Oh, you put a tax on us, we’re just going to pass it along.” As an economist, you roll your eyes a bit and you want to lecture them about elasticity. Yes, they should learn about elasticity, but there may be a bit more to that crude response than we thought at first.

TABARROK: It’s certainly true that every business thinks that that is what is going to do, but in general equilibrium—

COWEN: Correct. We go full circle. Do we really have the true general equilibrium model in any of these cases?

TABARROK: It’s very hard to do a general equilibrium model and, as you say, still come up with useful advice. Often in those models, not just in the Harberger model, but often in the general equilibrium model, lots of things, maybe everything can happen.

COWEN: Can happen. That’s right.

TABARROK: Which is upsetting.

COWEN: The Harberger, it was this very successful balancing attempt to put more into the model. Anything can happen, but doesn’t have to happen. It was still simple enough, you could believe some of what came out of it. That delicate balancing act, we’re always in danger of it being disrupted, that there’s too many results or too few results. It’s a very good way of thinking about modeling and economics.

TABARROK: The art of economics.

COWEN: To trace the Harberger debates. This is not something that will end. Like I said, I don’t think there’s a final word. The last word I know of is the price effects are really important, but again, the degree of generality there is unclear.

One other thing I like about the Harberger model, you see how different parts of economics relate to each other. The Harberger model, it comes in part out of the Heckscher–Ohlin model, which has two countries: capital and labor. Harberger redoes it. The countries become sectors. This is known that it comes from Heckscher–Ohlin. You see how one model—you might think Heckscher–Ohlin is very flawed. Maybe that’s a separate podcast, but whatever its flaws may be, it gave rise to the Harberger model. That’s high praise right there.

Then the Harberger model over time gives rise to the Krugman, Dixit, Norman models. People start trying to put firms into the Harberger model more explicitly with more structure, which is a good thing to do. That led to new ways of thinking about trade and Nobel Prizes in that area. It comes full circle, starts with trade, ends up reforming trade theory, improving trade theory. Really a very striking powerful development from Harberger.

The Solow Model

TABARROK: Very good. Shall we do a macro model?

COWEN: Let’s do a macro model, which, in fact, also is going to be related to the Harberger model. It’s very general equilibrium and it’s going to have capital and savings explicitly modeled in a way Harberger does not. Alex, why don’t you introduce that to us?

TABARROK: One of my favorite models in macroeconomics is the Solow model. The Solow model of economic growth. I like this model because much like supply and demand in microeconomics, that’s a workhorse model. It’s a very simple model, but you change it around. You do it in different ways, has a lot of implications. The Solow model is a workhorse model in macroeconomics. You can view it and apply it in different angles, different lenses, and it yields lots of different insights.

The model, at its root, it’s pretty simple. I explain it this way. Look, there’s really two factors. One is diminishing returns to capital, which relates to Harberger: your first tractor is very, very productive, it allows you to increase output a lot. Your second tractor is less productive, the third is less productive, and so forth. Same with your railroads, your airports. We in the DC, Northern Virginia region, we have three major airports, we’re about to get a fourth. Did you know this?

COWEN: No. Where?

TABARROK: In Manassas.

COWEN: A good airport?

TABARROK: It’s going to be, it’s going to have some direct flights. I’m pretty happy about that. It’ll be where I live. I’m hoping to get out of Dulles sometimes. However important the Manassas airport turns out to be, it’s not going to be as important to the productivity of the Northern Virginia region as Dulles was. You have diminishing returns to capital. That’s point one.

Point two is, again, pretty obvious, capital depreciates. The roads get potholes, the ports get silted up, the tractors rust, and so forth.

COWEN: That’s really expensive. People underestimate that.

TABARROK: Absolutely.

COWEN: Visit Alexandria, Egypt, and you will understand capital depreciation.

TABARROK: Exactly.

COWEN: It’s a great economics lesson.

TABARROK: Yes. Alexandria, Egypt, or you look at Rome and the Colosseum.

COWEN: That’s doing better than you might have expected compared to Alexandria. The library’s gone altogether, they tried to rebuild some version of it, but books are gone.

TABARROK: The library’s totally gone.

The more capital you already have, the more investment you need just to keep the old capital going. What this means is that poor countries, at least ones with decent institutions, can grow rapidly because two reasons. One is they don’t have a lot of capital to begin with, so the initial capital they apply is very productive. The second reason is they don’t have much capital, so there’s not much depreciation. All of their investment can go to new capital.

Why do I like the model? Well, I like the model because it can explain, first of all, a seeming paradox. That is, Adam Smith said, “Little else is requisite for growth, but peace, easy taxes, and a tolerable administration of justice.” We’d put a little different spin on it. Acemoglu would say, “Don’t have extractive institutions,” that’s like, have low taxes. He would say rule of law, that’s a tolerable administration of justice, but it’s all in Adam Smith.

Now here’s the problem, here’s the paradox. China was growing at 10% for year after year, decade after decade. Even though its institutions are much worse than the institutions of the United States, which is growing at 2%.

COWEN: Highly corrupt, right?

TABARROK: China, yes. Just to be clear, exactly. It doesn’t have tolerable administration of justice. It has better institutions than it did before Mao died, but still does not have great institutions. How do you explain this? Well, the Solow model explains this. China had very little capital. The capital that it first applied was very productive. And it didn’t have a lot of ports, it didn’t have a lot of airports, it didn’t have a lot of railways, so it didn’t have a lot of depreciation.

However, Solow model tells us that you’re going to continue to invest until all of your investment is needed just to make up for the depreciation of the capital you already have. Now China has lots of high-speed railroads, but it’s got to fix them up. They start to depreciate. It’s got ports, but they start to silt up. China’s got to devote more and more of its investment just to keeping up, and because of that, it slows down.

Now where does it slow down? Well, that does depend upon institutions. I think China is slowing down right now, and they’re not going to come up to US levels of GDP per capita because their institutions are so much worse. The Solow model does tell us that there’s a big difference between catching-up growth and cutting-edge growth. That might seem obvious today, but at the time that Solow was writing, it actually wasn’t obvious at all. In fact, it was Solow’s model which first created this distinction between the catching-up growth and the cutting-edge growth.

COWEN: There wasn’t as much catching-up growth then. That’s one reason why it wasn’t obvious.

TABARROK: Exactly. It had taken hundreds of years for the developed economies to grow, and we didn’t see the fast catch-up of the less-developed economies.

COWEN: The one case that maybe we saw, Soviet Union, was controversial for other reasons and is still debated and the data were not good, right?

TABARROK: Exactly. A lot of stuff.

COWEN: The Solow model actually applies a bit to the Soviets, I think. There was some real gain in living standards that was explained by this low-hanging fruit and you can just build some apartment blocks and people will be much better off.

TABARROK: Adopting mass manufacturing. You bring in Ford, you build a mass manufacturing model, you grab that from the West. You can do quite a bit.

COWEN: Put a subway in Moscow, right?

TABARROK: Exactly.

COWEN: It still works pretty well.

TABARROK: That’s one reason I like the Solow model. It explains the seeming paradox. Another reason I like it is it actually gives us quantitative predictions. I said that the Solow model predicts that the poor economies will catch up to the richer economies. Again, assuming they have similar institutions. But the parameters of the Solow model, you can easily find them in the economic data. The labor share of national income, you can just grab that, put it into the Solow model, and then it’ll give you a quantitative prediction of how quickly a country or a region, like a state, how quickly will the South catch up to the North. It’ll give you a quantitative prediction of how quickly the catch up will happen.

COWEN: Mostly those are wrong, right? To be clear.

TABARROK: Yes.

COWEN: They’re wrong predictions, it’s the problem with the model. We’re very poor at predicting future rates of economic growth.

TABARROK: We always have to add some twist to the model, but it’s a place to begin. And for a very simple model, it’s a great place to begin. Because then you know what doesn’t work and then you can start to look at what do we need to explain this? If you don’t know that to begin with, you have no idea that you need to look somewhere else. I think even when a model fails, it can still tell us a lot and that’s true for the Solow model.

COWEN: Let me tell you what I do and do not like about the Solow model. The first thing that I find deeply intriguing is it tells you there’s a real analytic gain or at least change from thinking about capital and ideas as fundamentally separate. I’m not even sure I agree with that. It’s very different from what you get, say, reading Ayn Rand or a lot of free-market boosterism.

In fact, people who only have ideas, they’re parasites. Real growth is embodied in capital goods and it’s things investing with capital with ideas in it that matter. Solow was saying, if you separate those two completely, you’ll get a much better theory. It’s a bold claim. I’m not sure it’s true, but I think it’s actually the core innovation in the model, and it was brilliant to see it was at least worth investigating.

TABARROK: See, that’s what I don’t like about the model, because I would say embodied capital is huge.

COWEN: Yes, that’s also what I don’t like about the model. Empirically, you try to estimate TFP, total factor productivity, you’re separating out investment. What if the ideas are embodied in investment, which, of course, they are all the time, especially with tech, and the TFP measure becomes worth less and less. I’m not sure we should separate capital and ideas so cleanly.

TABARROK: I agree with you. It is interesting, you can get pretty far by doing that. Again, with just a few pretty simple parameters, you can actually do growth accounting. You can use the Solow model to say, “How much of growth is coming from more capital? How much of growth is coming from more labor or better labor? How much is coming from ideas?” I do agree with you that it’s tough to separate ideas from capital since so many new ideas are embedded in new ways of doing things. I’m still pretty impressed by how far you can get with growth accounting even by not making as many of these distinctions as you have to make.

COWEN: I would say it’s a Soviet model, doesn’t have to be a bad thing. Remember this is, what, 1956?

TABARROK: Right.

COWEN: In the Soviet Union, it was so clear what was capital and what was ideas. There were ideas in chess and so on, but, basically, the capital was new subway and Moscow, and it was capital, not really a new idea. It was super clean for them. Now it’s super blurred because of tech, but I think that makes the model worse for today.

TABARROK: It’s super blurred, but that also is the distinction between the catching-up growth, which is just more and more capital and the cutting-edge growth. It is true, the Solow model itself tells you very little about cutting-edge growth. It does allow you to see that, “Oh, cutting-edge growth is not coming from more capital or more labor. It must be coming from more ideas.” And it does tell you, “Well, because of that, I need to think more about research and development, about intellectual property, IP, education. Where do these ideas come from?” It points you in the right direction.

COWEN: Here’s a related worry. I’m not sure catching-up growth is a thing. Convergence on average is not true. In the last five years, it’s become less true.

TABARROK: Ehhh...

COWEN: There’s only five years, but it’s not all falling into place. “Oh, give us some time. You’ll see, Tyler.” We’re moving further from convergence. My inclination is just to think the countries that haven’t developed by now, for whatever reasons, maybe they’re not going to. They’ll limp along, they’ll have smartphones, they’ll have this, that, and the other, but they’re just never catching up. Solow model doesn’t at all explain that. In fact, it tells you that’s impossible.

They don’t all have terrible institutions. If it’s North Korea, fine, I get that. There’s plenty of places, like Uruguay has reasonable institutions. They’re not catching up anytime ever. I don’t even think they’ll grow faster than the US on average for the next 200 years. I could be wrong, but you can’t even make sense of that in the Solow model.

TABARROK: I wouldn’t count Uruguay out.

COWEN: I wouldn’t count them out, but I’d say, it’s like 50/50 at best if they catch up much.

TABARROK: If it’s not catching-up growth, then it’s not institutions, what is it which explains why these countries are not growing?

COWEN: I think it’s Solow or maybe Samuelson—they have this famous remark about things degenerating into clichés about sociology that don’t really make any economic sense. Whenever people invoke a methodological argument to address a substantive point, I think it’s usually bad. I do think it’s culture and ambition and aspiration, and I know those are hard to model, hard to test. But Uruguay, it’s democratic, reasonable amount of free speech, not at war. If you want to pull the, oh, European settlers’ card, a lot of Swiss blood in that country, it’s fine. But something about it.

TABARROK: Culture is an idea?

COWEN: Yes.

TABARROK: I do agree with that. I was in Argentina recently, and there’s this big literature. Argentina was one of the richest countries in 1900, and it’s just become poorer and poorer, relatively speaking, over time. Yet when you go to Argentina, it’s a pretty nice place. I think one of the reasons why Argentinians have put up with this relative decline is that actually it’s not so bad. It’s not so bad. Now, maybe with Milei, we’ll see. Maybe it’s the bringing the chainsaw out. Maybe this is the revolution, or maybe it’s just the pendulum swinging back and forth. I agree that culture makes a huge amount of difference because it’s the title of another book you wrote, The Complacent Class, right?

COWEN: Right.

TABARROK: It’s very easy to be complacent when you’ve satisfied most of your Maslow’s hierarchy. Do we really need to go to Mars to satisfy another—

COWEN: Where does Elon migrate? Western Europe is not catching up to the US. They’re falling behind somewhat and they’re free enough, right?

TABARROK: Yes. I think it’s too early to say with Western Europe.

COWEN: It’s always too early to say. There’s an infinite amount of data in the future, but you see no signs of them catching up.

TABARROK: I think tech has made a very big difference in the last 15 years or so, but that’s a pretty short-run thing.

COWEN: The notion that scale matters is also not in the Solow model. For a lot of things, scale doesn’t matter, but the more you’re in a tech age, at least so far, and the growth of China illustrates this, scale really matters. If you look at the data of the world as a whole, Peter Thiel makes this point, the two big trends are Europe share decline, China share up, US share, which everyone thought would decline, is fine. Scale has become a lot more important than it was 30 years ago, I think.

TABARROK: Yes. The US share has still declined a lot. China’s share has gone way, way, way up.

COWEN: The rest of the world often has declined. US has held up just fine against lots of countries, in many cases, gained on them. Most cases, I think.

TABARROK: Yes, most cases. China’s the big exception. Maybe India following behind.

COWEN: That may be.

TABARROK: Slower, but yes.

COWEN: The simple point that for the last 20, 25 years, scale has been key. Solow is obliterating that possibility, and I think it’s probably true.

TABARROK: One of the problems with a very simple model—I like very simple models, you can do a lot with them—but you can’t do everything with them. Let me give you one more reason why I like the Solow model.

COWEN: I’ll give you one more why I don’t like it.

TABARROK: All right. Once you think about the factors which generate growth in the Solow model, like better capital or more capital, more labor, better ideas, you realize that these things, they don’t come at you smoothly. Sometimes I’m working at my office and sometimes I have a good idea and sometimes I’ll go for weeks and there’s no good ideas at all. All of these things, they come with noise to them.

COWEN: Fischer Black.

TABARROK: We have a big fire in Los Angeles. That’s a negative technology shock. That’s a negative shock to capital. Negative shock to labor. All that labor is not going to be used productively for quite some period of time. When you add noise, when you add errors, and you add the fact that your capital could be jumping up and down, your labor moving up and down, your ideas move up and down, the Solow model actually turns into a model not just of economic growth in the long run, but a model of business cycles. The Solow model with errors, that turns into the real business cycle model.

COWEN: I like that point and it relates to your comments on Argentina. Fischer Black stressed luck. I think early Argentina had very good luck. Not that many people, resource-based economy, they made huge bets on meat and refrigerated box cars at exactly the right time. I’m not saying there was no wisdom behind that, but that it paid off also involved luck. That luck is gone, and now they’re not making any especially good bets. In the data, so many countries are small countries, and their fates can be so governed by luck. That, too, Fischer Black points us in the direction of luck. Solow, it’s buried in there, but not really.

Here’s the final thing I don’t like. Some days I like it. I’m 50/50 on this one. The Solow model suggests there’s a distinction between once-and-for-all changes and ongoing changes in the rate of economic growth. This ultimately stems from the split between ideas and capital as being separate. John Cochrane wrote a great blog post on this criticizing it. So much of economic growth is just that every period you get a new once-and-for-all change. You can always get new ones, there’s plenty of fruit to be plucked. Maybe so much of growth is just the once-and-for-alls. The Solow model pushes us away from that distinction, it trivializes the once-and-for-alls. You’re going to cough them back up because later on you’ll accumulate less rapidly because there’s less catch-up.

For the Solow model, it’s all the ongoing changes that matter in the long run. That might just be wrong. I’m not sure. I tend to think I agree with John, loved his post, but what do you think of that issue?

TABARROK: Ultimately it is ideas. Ideas, they don’t depreciate.

COWEN: They do, though. In our podcast on In Praise of Commercial Culture, we see ideas very much depreciate. We cannot compose great baroque music today. We do other things.

TABARROK: Yes.

COWEN: It’s not that they all depreciate.

TABARROK: We can’t or we don’t want to.

COWEN: Mix of both. We can’t build in certain styles anymore. Ideas have to be maintained. They’re embodied in networks of people, Solow model—

TABARROK: That’s true.

COWEN: —depreciation there too.

TABARROK: There is some famous stories of building these nuclear reactors and then they have to stop, and they literally forgot how to do it.

COWEN: That’s right.

TABARROK: They had to go back and recreate what the hell they did to get it right the first time.

COWEN: We’ll see if the same is true with the bombs as well.

TABARROK: Yes. Maybe ideas depreciate a little bit, but not as much as capital.

COWEN: I don’t know. There’s plenty I’ve forgotten in my life.

TABARROK: In any case, for a simple model, it is a workhorse model in economics, and you can apply it in different ways. I think one of the things we’re learning from this conversation is that models matter not just when they’re right, but also when they’re wrong, because they point you in a direction you might not have previously thought about.

COWEN: To close, I’ll point out on YouTube, Alex has a fantastic video on the Solow model. It’s literally one of the best economics videos ever made.

TABARROK: Thank you.

COWEN: Seriously, yes.

TABARROK: Thank you very much for that, Tyler. The Solow model also features in our textbook, so we have a little bit of advertising as well.

COWEN: Thank you, Alex.

TABARROK: Thank you, Tyler.