Problem 3
A firm sells in a domestic market and a foreign market. P1 and Q1 are domestic price and output. P2 and Q2 are foreign price and output. The demand functions are: P1 + Q1 = 500, 2P2 + 3Q2 = 720. The total cost function is: TC = 50,000 + 20Q, where Q = Q1 + Q2.
a. Set up the profit maximizing problem for this firm, state the first order conditions, and solve for the profit maximizing output in each market without price discrimination (2 pts).
b. Set up the profit maximizing problem for this firm, state the first order conditions, and solve for the profit maximizing output in each market with price discrimination (2 pts).
c. Formulate the Hessian for the price discrimination case, evaluate the principal minors, and demonstrate that you have found a maximum (2 pts).
d. Solve for the equilibrium prices under price discrimination and the equilibrium price without price discrimination (2 pts).
e. Calculate the elasticity of demand, under price discrimination, at the equilibrium price and quantity in each market. Verify that the more elastic market is charged a lower price (2 pts).