Problem 5 (Watson 10.2 a-c). Consider a more general Bertrand model than the one presented in this chapter. Suppose there are n firms that simultaneously and inde- pendently select their prices, P1, P2, ..., Pn in a market. These prices are greater than or equal to zero. The lowest price offered in the market is defined as p = min{P1, P2, ,Pn}. Consumers observe these prices and purchase only from the firm (or firms) charging p, according to the demand curve Q: =a- - p. That is, the firm with lowest price gets all of the sales. If the lowest prices is offered by more than one firm, then these firms equally share the quantity demanded. Assume that firms must supply the quantities demanded of them and that production takes at a cost of c per unit. That is, a firm producing di units pays a cost cqi. Assume a > c> 0. (a) Represent this game in the normal form by describing the strategy spaces and payoff (profit) functions.

Problem 5 (Watson 10.2 a-c). Consider a more general Bertrand model than the one presented in this chapter. Suppose there are n firms that simultaneously and inde- pendently select their prices, P1, P2, ..., Pn in a market. These prices are greater than or equal to zero. The lowest price offered in the market is defined as p = min{P1, P2, ,Pn}. Consumers observe these prices and purchase only from the firm (or firms) charging p, according to the demand curve Q: =a- - p. That is, the firm with lowest price gets all of the sales. If the lowest prices is offered by more than one firm, then these firms equally share the quantity demanded. Assume that firms must supply the quantities demanded of them and that production takes at a cost of c per unit. That is, a firm producing di units pays a cost cqi. Assume a > c> 0. (a) Represent this game in the normal form by describing the strategy spaces and payoff (profit) functions.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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