a) Carefully express this monopolist’s profit maximization problem. b) State the two equations that characterize the profit-maximizing amounts of Q1 and Q2, given an interior solution with positive quantities sold in each market. c) Solve these two equations for Q1* and Q2*. d) Find the prices P1* and P2* that the monopolist should charge in each market. e) Calculate the monopolist’s (maximized) profit.
A monopolist faces two geographically distinct markets, say market 1 is New York and market
2 is California. The inverse demand
monopolist’s total cost function is C(Q) = 0.25Q^2 and marginal cost function is MC(Q) = 0.5Q, where Q =
Q1 + Q2 is the total quantity that it produces. Your job is to find out how much quantity to sell in each
market in order to maximize the monopolist’s profit.
a) Carefully express this monopolist’s profit maximization problem.
b) State the two equations that characterize the profit-maximizing amounts of Q1 and Q2, given an interior
solution with positive quantities sold in each market.
c) Solve these two equations for Q1* and Q2*.
d) Find the prices P1* and P2* that the monopolist should charge in each market.
e) Calculate the monopolist’s (maximized) profit.
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