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Suppose that there are only two copper-producing countries, Chile (country 1) and Peru (country 2) with identical total cost functions TC(q1) = 2q1 and TC(q2) = 2q2, where q1 denotes the amount of copper generated by country 1 and q2 denotes the output level of country 2 (in tons)

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Suppose that there are only two copper-producing countries, Chile (country 1) and Peru (country 2) with identical total cost functions TC(q1) = 2q1 and TC(q2) = 2q2, where q1 denotes the amount of copper generated by country 1 and q2 denotes the output level of country 2 (in tons). Assume that the market demand for copper is given by the inverse demand function P (Q) = 30 − Q, where prices are given in thousands of dollars and Q = q1 + q2 denotes the total amount of copper traded.

(a) Suppose that both countries make sequential decisions about the amount of copper to be produced. Assume that Chile is the leader whereas Peru is the follower. What is the residual demand of the follower? What is the marginal revenues of the follower? Find Peru’s reaction function.

(b) What is the residual demand of Chile given its anticipation of Peru’s optimal reaction? Calculate the profit-maximizing output level of both countries, the market output and the market price. Does this market outcome result in a market failure? Explain why or why not.

(c) Now assume that a third country, China, that has the same cost function, enters the world market and makes a decision about its output given the observed decisions of Chile and Peru. Using the general concepts of sequential rationality and backward induction, discuss whether Chile and Peru can be expected to adjust (if yes, how to adjust) their output levels if they expect China to enter. Describe in words how you would proceed to calculate the profit-maximizing output level for China.