A monopolist faces two geographically distinct markets, say market 1 is New York and market 2 is California. The inverse demand curves in each market are P1 = 300 – Q1 and P2 = 200 – Q2. The monopolist’s total cost function is C(Q) = 0.5Q^2 + 50Q and marginal cost function is MC(Q) = Q + 50, 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 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*.
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) = 0.5Q^2 + 50Q and marginal cost function is MC(Q) = Q + 50,
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 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.
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