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Unformatted text preview: Industrial Organization: EC460 Spring 2009 Instructor: Thomas D. Jeitschko Notes on Price Competition Homogenous Goods and the Bertrand Paradox The Cournot model of oligopoly has some compelling insights, but it also has a conceptual drawback: We frequently think of firms deciding on an optimal price policy, rather than simply setting quantities and letting the market determine the equilibrium price. This criticism need not always have much bite, since there are industries in which production plans must be made well in advance and only after output decisions have been made are prices realized. This is, for example, plausible in the auto industry in which prices are adjusted more frequently than are production plans throughout the year. Also, if products are homogenous (i.e., perfect substitutes) then it is hard to imagine that there is more than one equilibrium price. Indeed, this latter supposition has been formalized and studied as a model of oligopoly competition. Consider two firms (a duopoly) producing a homogenous good at a constant marginal cost of MC = 1. Suppose demand for the good that the firms produce is given by P = 9- Q . We have studied this market when firms each independently choose a level of output, but now we want to consider the case where firms chose a price at which to sell their product. Specifically, we suppose that firm post a price and then have the flexibility to produce however many units consumers demand from the firm. For this we make the following assumption: since the goods are homogenous (i.e., identical from the consumers perspectives) we assume that consumers will always patronize the firm that posts the lower price. No-one will buy from the firm that is charging a higher price for what is essentially 1 the same good. Should both firms charge the same price, we assume that half of the market goes to each firm. What is the equilibrium? We approach the problem as we did the Cournot model, by letting one firm choose an arbitrary strategy (i.e., price) and then we determine the other firms best response to this price. Thus, suppose that Firm 1 chooses a price of P 1 . Clearly since charging a price below marginal cost is a dominated strategy (the firm makes losses when it sells below costs), we restrict attention to prices above MC = 1. Another useful benchmark is the monopoly price. It is easy to verify that if there is only one firm in the market (a monopoly) its optimal price is P m = 5 (check this). Therefore, if= 5 (check this)....
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This note was uploaded on 03/29/2009 for the course ECON 460 taught by Professor Boyer during the Spring '08 term at Michigan State University.
- Spring '08