Problem 1: Oligopoly (30 points)
Suppose that there are only two copper-producing countries, China (country 1) and Chile
(country 2) with identical total cost functions $TC(y_1) = 6y_1$ and $TC(y_2) = 6y_2$, where $y_1$
denotes the amount of copper generated by country 1 and $y_2$ denotes the output level of
country 2 (in tons). Assume that the market demand for copper is given by the inverse
demand function $P(Q) = 30 - Y$, where prices are given in thousands of dollars and
$Y = y_1 + y_2$ denotes the total amount of copper traded.
(a) (10 points) Suppose that both countries make simultaneous decisions about the
amount of copper to be produced. What are their residual demands? What are the
marginal revenues? Find both countries' reaction functions and draw a graph with
reaction curves.
(b) (10 points) Given your results in (a), calculate the profit-maximizing output levels
of both countries, the market output and the market price. How is this equilibrium
result called in economic literature? Represent your findings graphically. Does this
market outcome result in a market failure? Using your graph, explain why or why
not.
(c) (10 points) Suppose that now both countries collude and maximize their joint prof-
its. What is their joint marginal revenue? Calculate the resulting joint output level
and the market price. Under the assumption that every member of the agreement
produces exactly one half of the total output, evaluate whether this collusive agree-
ment leads to higher profits for a country compared to the equilibrium in (b). Using
your results from (a) and (c), discuss whether this collusive agreement is likely to
be stable.
