Two firms sell an identical product in a market by setting prices simultaneously. Consumers buy from the firm that offers the lower price; if the prices are identical, the firms split the demand. If ? is the lowest price (in dollars), aggregate demand is ? = 250 − ?. Suppose prices can only be set in increments of 1 cent. (a) Suppose Firm 1 and Firm 2 have limited production capacities of 40 units each. The marginal cost of firm 1 is $35 and the marginal cost of firm 2 is $25. If Firm 1 believes that Firm 2 will set a price of $30, what price should Firm 1 set? Show your work. (Assume efficient rationing while calculating firm’s residual demand.) (b) Ignore the information in part (a). Suppose each firm has unlimited capacity, but that the marginal costs of Firm 1 and Firm 2 are $40 and $150 respectively. Do ?1 = 149.99 and ?2 = 150 satisfy the requirements of a Nash equilibrium? Explain why. You must explain why a strategy is a best response or not to the other strategy.
Two firms sell an identical product in a market by setting prices simultaneously. Consumers buy from the firm that offers the lower
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