What Can Coase Teach Us About Paintings, Bank Notes, and Bitcoin?

On Durability and Monopoly

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Here at Economic Forces, we have some topics that are obviously our favorites. Among those favorite topics is how to think about a monopoly. Today, I want to revisit the topic of monopoly by discussing an interesting application that is often ignored in textbook analysis: the role of the durability of a particular good sold by a monopoly.

Although economists might not mention it explicitly, many of the examples that we talk about in class and in textbooks involve non-durable goods. We can think of non-durable goods as goods that are consumed over a short period of time or that cannot be reused. Think about a gallon of milk or a bag of oranges or a pack of notebook paper. Once I drink the milk or eat the orange or write on the paper, the good has been consumed.

One way to think about a durable good is that it really isn’t the good itself that is consumed. Instead, what is consumed is the flow of services that are provided by that good. An example might be something like a refrigerator or a car or a painting. You don’t consume the refrigerator. What you consume is the refrigeration provided by the refrigerator. You don’t consume a car. You consume the transportation that the car provides. You don’t consume a painting, you consume the enjoyment of looking at the painting and conversations you have with others about the painting.

This distinction is important for thinking about how one might value these different types of goods. When I am buying a gallon of milk, I am valuing the consumption I get from that gallon of milk. What I am willing to pay for a gallon of milk is determined by the marginal benefit that I get from drinking milk.

When I am buying a car, I am valuing the car for the flow of transportation services that I will get from owning the car. Thus, what I am willing to pay for a car is equal to the present discounted value of the flow of services I expect to get from the car over the life of the car.

Okay, so that outlines the role of durability in consumption, but what does this have to do with monopoly?

Let’s first consider what we know about a monopoly. The objective of a monopoly, like any firm, is to maximize its profit. What makes a monopoly distinct is that a monopoly sets its own price. Suppose the monopoly also sells its product to all consumers at the same price. We know two things about a monopoly that maximizes its profit and charges a uniform price. The first is that the monopoly produces a lower quantity of a good than a competitive market would produce. The second is that the monopoly will charge a price above the marginal cost of production (above the competitive price).

Now let’s think about the behavior of a monopolist in possession of a stock of a durable good. To be more specific, we can use a variation of an example about durability and monopoly first provided by Ronald Coase. Suppose the specific good being sold is uniform-quality land on an island owned by the monopolist. Also, assume the monopolist has no use for the land such that the marginal cost of selling the land is zero.

In a competitive market, since the quality of land is all the same, the price would adjust until all of the land was sold at the uniform price. However, what we know about a monopolist is that the monopolist will sell the land at a price above the competitive price and therefore will sell only a fraction of the land on the island.

But is this really possible?

Potential land buyers know that the monopolist is going to have land left over after selling at the monopoly price. Furthermore, potential land buyers know that after this initial quantity of land is sold, there will be land left over and that other buyers would be willing to pay a price below the monopoly price, but above the marginal cost. The seller therefore faces a commitment problem. After the initial amount of land is sold at the monopoly price, the monopolist can gain from trading with remaining buyers over the remaining land. Since potential buyers know this ahead of time, they can choose to wait to purchase the land until the initial round of buying at the monopoly price is complete. Yet, if everyone waits until the initial round of buying is complete, then no buyers actually participate in the initial round of buying. The monopolist will not be able to sell any land at the monopoly price. Instead, the monopoly will be forced to sell all the land at the competitive price. This is suboptimal since it means the monopolist will not be able to maximize its profit.

As Coase points out, one would therefore expect a monopolist to demonstrate a commitment not to sell the extra land. He provides several ways in which this could be achieved. One example is to promise to repurchase the land from the initial buyers at the original price. The monopoly seller would have no incentive to sell additional land below the monopoly price if it was forced to buy back the land it had already sold at the monopoly price. Another example would be some type of explicit commitment to only sell a particular quantity (the profit-maximizing quantity) of land. In this example, that might mean donating the remaining land to the state, government, or other entity for public use.

This all seems interesting, but it is not often that there is a monopolist selling land of uniform-quality at zero marginal cost on some island. One might therefore wonder about the practical relevance of this insight. Let’s think about some practical examples.

Consider a painting. An artist might sell an original painting as well as prints of the painting. The market for the painting itself and the market for the prints are really two different markets. Let’s focus on the market for prints. Assuming the artist owns the property rights to the art, the artist has a monopoly over the selling of prints. As a result, the artist will face the same commitment problem as the owner of the island. The artist faces a downward-sloping demand curve for prints in which the willingness to pay of each consumer is equal to the present discounted value to the consumer of hanging, displaying, and enjoying the print. The artist can maximize his or her profit from the prints by selling a quantity less than a competitive market would produce and charging a price above the marginal cost of producing the prints.

Potential consumers of the print, however, know that since the artist is selling prints above the marginal cost of printing, the artist might have an incentive to sell an initial profit-maximizing quantity at the monopoly price and then do a subsequent printing and sell the new prints above marginal cost, but at a lower price than the initial printing. Knowing that this is a possibility, consumers might choose not to purchase the initial prints at the monopoly price, preferring to wait until subsequent printings. If this happens, the price of the prints will fall to the competitive price and the artist will forgo monopoly profits.

To prevent the price from falling, the artist could commit to a single printing in which the quantity of prints is announced and each print is numbered. By doing so, the artist is signaling a commitment to a limited printing. Of course, one has to trust that the artist will not renege on that promise. An artist that intends to make a living from art has an incentive not to renege on this promise, otherwise he or she would lose the present discounted value of all future profits from prints of their artwork.

Another example where this might be relevant is in thinking about a competitively-supplied money. Imagine a world in which there are no restrictions on bank note issuance by private banks. In that world, banks could issue their own notes. Each bank would hold the property rights to its own unique brand of notes.

A bank note fits with this idea of durability in the sense that the value of the bank notes to a particular consumer is not in the note itself, but in the flow of services provided by the note. A bank note serves as a way of storing one’s wealth and as a medium of exchange for purchasing goods and services. The value to the consumer is therefore tied to the purchasing power (and the stability thereof) of the bank notes.

Here again, each bank has a monopoly over its brand of bank notes. As the monopoly issuer of a particular brand of bank note, the bank faces a similar commitment problem as the previous examples. The bank might promise to limit its note issuance to maintain the purchasing power of the bank notes. However, after people have started to hold and accept these notes, the bank might find it advantageous to expand note issuance if the purchasing power of new notes (albeit lower because of the increased supply) exceeds the marginal cost of production. Knowing that banks have an incentive to increase the supply of bank notes, people might refuse to hold and accept the bank notes in the first place.

As Earl Thompson pointed out, one solution to this problem is to promise to buy back the bank notes for a particular quantity of a particular good. This solves the commitment problem as long as the bank makes good on its promise. (Of course, it it fails to keep its promise, things can go wrong. To understand that, see my recent paper with Bryan Cutsinger.) Regardless, this is one way to rationalize the historical experience of redeemable paper money in which bank notes were redeemable for a fixed quantity of a commodity, such as gold or silver.

A different solution would be to commit to a particular supply of bank notes. Until recently, however, it is not clear how this would be done. If a bank promised to issue only a fixed quantity of bank notes, how would one verify this? The promise of a quantity restriction would rely on trusting the issuer to keep his or her promise. But whether the issuer had an incentive to keep his or her promise depends on financial incentives that might be hidden from the potential note holders. As Ben Klein’s model implies, reputation isn’t necessarily enough. An issuer might have an incentive to produce hyperinflation if the one-time transfer it generates to the issuer is greater than the present discounted value of future profits from limiting the supply.

In recent years, however, someone (or some group of people) named Satoshi Nakamoto invented Bitcoin. The people who run the Bitcoin software are the participants in the Bitcoin network. What makes this relevant is that the Bitcoin software explicitly limits the total supply of bitcoin, the cryptocurrency, to 21 million. In some sense, this resembles Milton Friedman’s recommendation to replace the central bank with a computer that would grow the money supply automatically at a rate of k-percent per year. In the case of Bitcoin, the software is programmed to increase the supply of bitcoin at a slower and slower rate until the supply reaches 21 million bitcoin. Furthermore, and unlike Milton Friedman’s k-percent rule, one needn’t rely on trustworthiness when it comes to the supply of bitcoin. Friedman’s proposed computer could always be replaced or have its “k” adjusted by Congress. In the case of Bitcoin, the total supply of bitcoin could only be changed if there was a change in the code and if the participants on the network chose to run the new version of the software with the new supply schedule. But participants on the network have no incentive to make such a change. Those who are participating in the Bitcoin network are more than likely holders of bitcoin themselves. An increase in the supply of bitcoin would dilute the value and the purchasing power of existing bitcoin. As a result, none of the users on the network would have an incentive to adopt such a change in the code because it would be against their financial interest to do so. Bitcoin is therefore an application of Coase’s insights into durability and monopoly. (That this solves the “Klein problem” is something that I long recognized on my own. That this was an application of Coase’s discussion of durability and monopoly was first pointed out to me by — I think — Larry White, who I should note, also discusses this in his recent book.) The fact that it solves this problem can help to explain why people are willing to hold it and participate in the network.

We can think about redeemable paper money and the Bitcoin software as two distinct solutions to the same problem.

Thus, it seems that examining the role of durability in monopoly is fruitful for a number of practical applications. The role of durability shifts our focus from thinking about flows to thinking about stocks. When thinking about a monopoly over a stock supply, there are a number of important issues that come to mind about the incentives and commitment of a monopoly that do not apply when one is thinking about flows. Coase’s insights into this distinction can help us understand the market for paintings, bank notes, bitcoin, and beyond.