Prices! Prices, prices, prices. They're all around us, in shop windows and on supermarket shelves, in advertisements on TV and the internet and newspapers, in private conversations. How many prices does the average person see, or learn about, or transact on, in the course of a typical week? Hundreds? Thousands? Of course some people deal with more prices than other people do. College students are sometimes completely isolated from them, getting prepaid meals in the dining hall and attending prepaid lectures, the bills going to mom and dad. At the other extreme are Wall Street traders who probably see and even transact on thousands of prices every day.

Where do prices come from? The proximate cause of a typical price is the decision of some seller; in auctions or when bargaining is allowed it's a bit more complex. But since a seller who sets prices in a capricious or arbitrary way is unlikely to stay in business for long, the proximate cause is not enough. There are two main ways of explaining prices in economic theory to which I would like to add a third.

*1. Mythical auctioneers*

What we may call the Econ 101 supply-and-demand model is represented by the following chart:

In this chart, D is demand, S is supply, and the point (P*, Q*) represents the equilibrium price and quantity. But why should we expect P* to obtain in this market? Where does the price come from? Textbooks tend to explain it something like this:

What will suppliers do if they cannot sell all of their output at a price [greater than P*]? Hold a sale! Each seller will reason that by pricing just a little bit below his or her competitors, he or she will be able to sell much more.

Competition will push prices down whenever there is a surplus.As competition pushes prices down, the quantity demanded will increase and the quantity supplied will decrease. Only at a price of [P*] will equilibrium be restored because only at that price does the quantity demanded... equal the quantity supplied.What if price is below the equilibrium price?... At a price [below P*] demanders want [more than suppliers are willing to sell], which creates an excess demand or

shortage. What will sellers do if they discover that at a price [below P*] they can easily sell all of their output and still have buyers asking for more? Raise prices! Buyers also have an incentive to offer higher prices when there is a shortage because when they can't buy as much as they want at the going price, they will try to outbid other buyers by offering sellers a higher price.Competition will push prices up whenever there is a shortage.As prices are pushed up, the quantity supplied increases and the quantity demand decreases until at a price of [P*] there is no longer an incentive for prices to rise and equilibrium is restored. (Cowen and Tabarrok, p. 34)

The quote is from Tyler Cowen and Alex Tabarrok's textbook *Modern Principles: Macroeconomics* (though the argument is more typically associated with the microeconomics curriculum) but it is representative of the genre. Now, this story is quite plausible and general, but it is not proper theory in a rigorous sense. Assumptions about the information, objectives, and behaviors of economic agents have not been fully specified. Nor have the institutional forms governing transactions been explained. To give a non-hand-waving answer to "Where do prices come from?" in the neoclassical model, we have to postulate an "auctioneer." Let buyers and sellers be assembled in a room. Each buyer has a demand curve (willingness-to-pay, by quantity), each seller a supply curve. Aggregate demand and aggregate supply, known to none *ex ante*, are the sums of these curves. The auctioneer calls out prices and buyers and sellers state quantities they are willing to buy/sell at each price. If total quantity demanded equals total quantity supplied, the auction is concluded and transactions are executed, otherwise, the auction continues.

The theoretical device of an auctioneer gets us to (P*, Q*) in the Econ 101 model (it is also used in the Cournot model of duopoly/oligopoly) but the auctioneer does not have any obvious real-world counterpart.

*2. Strategic equilibrium with perfect information*

The second major answer to "Where do prices come from?" in economic theory comes from game theory. First, economic situations are described as "games" with formal rules. The theorist then studies the optimal strategies for each player, depending on the strategies adopted by other players. The most commonly used solution concept in game theory is *Nash equilibrium*, defined as a case where each player's strategy is optimal given the strategies chosen by the other players.

Bertrand duopoly is an example of applying game theory to price theory. Two duopolists, each enjoying unlimited capacity, compete by price. If their prices differ, one captures the whole market. *Ergo, *price is driven down to unit cost. Each firm's strategy is rational given what the other does.

An odd thing about the Nash equilibrium solution concept is that it introduces, in effect, an assumption of perfect information that could not, by the first principles of the logic of causation, hold in reality. If, just prior to the play of a certain game, players A and B are in the process of choosing their strategies, it does not make sense to say that their information sets include knowledge of what the other will do. It violates the requirement that causation be one-directional in time, that effects cannot precede causes, and creates a causal infinite regress: *A will play High because B will play High because A will play High because...* This does not prevent us from analyzing games to find Nash equilibria, but it does make the interpretation of Nash equilibria difficult. It is far from unproblematic to say that the fact that outcome X is a Nash equilibrium of a game provides the basis for a prediction that X will occur.

Other solution concepts in game theory, such as *dominant strategy *equilibrium, are more compelling than Nash. An example of a game solvable with the dominant strategy equilibrium solution concept is the Bertrand duopoly model with the following modifications:

- Firms can charge only a High or a Low price;
- A firm which charges a Low price earns positive profit.
- If a firm's rival charges a High price, it will earn greater profits by playing Low than by playing High.

Thus reformulated, the Bertrand model has a dominant strategy equilibrium, namely: both play Low. But in the normal Bertrand model, with continuous prices, there is no dominant strategy equilibrium.

*3. Empiricist pricing*

There is, I think, some precedent in the economics literature for the answer to the question "Where do prices come from?" that I want to put forward, but it is not mainstream. What I propose is that prices are set by firms in an *attempt* to maximize profits, but subject to limited information. More specifically, they operate under conditions of *Knightian uncertainty:* while they have some relevant information, they don't know the demand curve, and they don't know any probability distribution of what the demand curve might turn out to be, either. Therefore, no mathematical optimization is possible. Instead, firms form beliefs about demand in the same way that econometricians form beliefs about the world using datasets. They run regressions.

I have implemented empiricist pricing in an agent-based simulation, and the chart below, taken from a draft of the first paper in my dissertation, shows how empiricist competition affects prices, as a function of the (exogenous) number of firms in an industry (I'll get to free entry in a future post):

What happens in the simulation is pretty close to the story told by Cowen and Tabarrok above. As more firms enter the industry, each firm observes a flatter demand curve for its own product. It therefore sets its price closer and closer to unit cost. Interestingly, convergence of price to marginal cost occurs much more quickly than in the Cournot model.

I hope to show not only that empiricist competition gives a more persuasive answer to the question "Where do prices come from?" than those represented by the mythical auctioneer or the Nash equilibrium, but also that empiricist competition is capable of greater generality of application.

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