Question

Consider a Bertrand-type price competition in a situation where Q (p) of demand is composed of smart buyers (buying at a lower price) and x shares of silly buyers (buying at a random price). Two companies are simultaneously choosing the prices. What is the profit for a company from (a) smart consumers and (b) stupid consumers? Show that there is no balance in the game with pure strategies. Tip: Try different pricing options and show that at least one company should always deviate from any pure balance. Consider the reasons why some consumers behave "smartly" / "foolishly".

Answer 1

An economy is an interdependent system. In the process of solving it we have deliberately pushed that interdependency into the background. The individual, both as consumer and producer, is a small part of the market and can therefore take everyone else's behavior as given; he does not have to worry about how what he does will affect what they do. The rest of the world consists for him of a set of prices--prices at which he can sell what he produces and buy what he wants.

The monopolist of Chapter 10 is big enough to affect the entire market, but he is dealing with a multitude of individual consumers. Each consumer knows that what he does will not affect the monopolist's behavior. Each consumer therefore reacts passively to the monopolist, buying the quantity that maximizes the consumer's welfare at the price the monopolist decides to charge. From the standpoint of the monopolist, the customer is not a person at all; he is simply a demand curve.