If you’re an economics major--or just want to consider yourself an educated person--you should know what the Coase Conjecture is.
One of its key insights is that, under certain conditions, a monopolist must “compete against future versions of himself,” which in turn could cause him to set price equal to marginal cost—i.e. to act as if he is in a perfectly competitive market.
Alex Tabarrok (
@ATabarrok) and I have recently published a paper (
onlinelibrary.wiley.com/doi/…) on the topic. Our main conclusion is that, although a brilliant idea, it doesn’t seem to hold in practice. Stay tuned for a summary of the paper, which Alex will post on Marginal Revolution (
@MargRev).
Why doesn’t the Conjecture work in practice? A brilliant, yet under-appreciated, explanation is the “outside options” model of Simon Board and Marek Pycia. It can be illustrated with the following example.
Suppose a publisher wants to sell a particular book, which has marginal costs of $1.00. There are 300 potential customers, all of whom are willing to buy at most one copy. Customer 1 values the book at $1.10; customer 2 values the book at $1.20; and so on, such that customer 300 values the book at $31.00. For simplicity, suppose that if a customer is indifferent between buying and not buying—say, because the price exactly equals the amount she values the book—then she buys.
Next, let us add Board and Pycia's innovation to the model. This is that each customer has an “outside option.” As the authors explain, the outside option could be a substitute, say a different book. But it could also be something else, such as (i) borrowing the book from a library or a friend or (ii) engaging in another activity such as watching television. Let us assume that, if a customer chooses her outside option, then she exits the market—that is, she will never buy the book that the publisher is selling (Board and Pycia, however, consider other versions of their model in which they relax this assumption).
An implication of the Board-Pycia model is that, even if the customers value their outside option at an infinitesimally small degree, then this can overturn many classic Coase Conjecture conclusions. To illustrate, suppose customers value their outside option at just one penny.
Now suppose that the model has an equilibrium similar to the standard Coase-type model. (We show that this leads to a contradiction.) First, suppose that the seller adopts a “skimming” strategy in equilibrium—that is, in the first round it sets a relatively high price, then gradually lowers the price as more and more customers buy and leave the market. Second, suppose that the market clears in a finite number of rounds, T ; that is, in period T the seller sets price (just) small enough to make the lowest-valuing customer buy (and consequently no sales take place afterward). Third, suppose that T >= 2; that is, it takes at least two periods for the market to clear.
We now show that the last property, T >= 2, cannot hold in the Board-Pycia model. To see why, suppose that the game has reached period T, and the seller chooses a price to clear the market. If so, it optimizes by choosing a price that makes customer 1 indifferent between buying and not buying. This price equals $1.09. (Note that it gives the customer a surplus of one penny [= $1.10–$1.09], which equals the value of her outside option).
Now consider customer 1's decision in the first round. She foresees that her consumer surplus from buying the book will be at most one penny, and that this surplus would not be realized until a future period. Due to discounting, she prefers to take her outside option immediately, so she exits the market in the first round.
Since customer 1 has exited, customer 2 is now the lowest-valuing customer. This means that in period T the publisher's profit-maximizing strategy is now to set the price so that customer 2 is indifferent between buying and not. That price is $1.19.
But, like customer 1, customer 2 can foresee the publisher's strategy. She anticipates that her consumer surplus will be at most one penny and it will only come in round T. Accordingly, she realizes that she is best off exercising her outside option in the first round. By repeating this reasoning, one can show that in equilibrium no customer makes a purchase after the first round.
Thus, this reveals that the assumption that T >= 2 cannot be correct. Instead, as Board and Pycia show, the only equilibrium is one in which all trading takes place in the first round—that is T=1. In this equilibrium, the publisher chooses the static-monopoly price in the first round. Customers with valuations at or above this price purchase the book, while those with lower valuations choose their outside option and exit (Although no customers remain after the first round, in future rounds the publisher continues to set the price equal to the initial, static-monopoly price, thus justifying the lower-valuing customers deciding to exit the market in the first round).
Crucially, this equilibrium persists even as the discount factor approaches one. Thus, the model does not produce the Coase Outcome.
Importantly, Board and Pycia show that the Coase result is knife-edge. That is, even if customers’ preferences for their outside option are infinitesimally small, the Coase result still disappears.