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Calculate optimal profit of firm

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Consider a market for DRAM chips used in computer processors. The industry consists of only two firms. The market demand function is given by:

P = 172 - 2Q

Where Q = Q1 + Q2, is the industry output and P the price. Q1 and Q2 are the outputs of the two firms respectively.

The total cost functions for the two firms are given by:

TC1 = 16Q1 + 300

TC2 = Q2 2 + 4Q2 + 172

(a) Assume that the two firms behave as Cournot Duopolists. Explaining the concept of "best response" or "reaction" function, determine the best response function for each firm. Calculate the Nash-Cournot equilibrium output for each firm and the market price. Graphically show the NashCournot equilibrium. Calculate optimal profit of each firm.

(b) Assume that the two firms collude and form a cartel to maximize their joint profit. Calculate the optimal output and profit for each firm and the market price. Also, calculate the resulting profit of cartel. Determine whether firm 1 has any incentive to "cheat" the cartel by overproducing.

(c) Now, suppose that firm 1 acts as a Stackelberg leader and firm 2 acts as a follower. Calculate optimal outputs of the two firms and the market price. Also, calculate each firm's optimal profit.

(d) While collusion may be illegal but merger and acquisitions may not be. If firm 1 3 wants to buy firm 2 (and firm 2 ceases to exist after that) calculate the maximum price that firm 1 can offer.

Reference no: EM133125545

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