Assignment 7

Price Discrimination

A monopolist sells the same good in 3 separate markets. The demand functions and cost function are given below:

Market 1:   P₁ = 80 - 4Q₁
Market 2:   P₂ = 100 - 5Q₂
Market 3:   P₃ = 70 - 6Q₃

Cost function: C = 20 + Q² - 4Q, where Q is total output, i.e., Q = Q₁ + Q₂ + Q₃.

1. Obtain the firm's profit function in terms of the three choice variables: Q₁, Q₂ and Q₃.
2. Using FOCs, find the optimal values of output in each market.
3. Obtain the Hessian. Do the SOCs correspond to a maximum?
4. What are the prices charged by the firm in each market?
5. Find the firm's maximum profit.
6. Compute the elasticity of demand (e) in each market at the optimal P-Q combination.
7. In which market does the firm charge the highest price--the market with the highest elasticity of demand, or the one with the lowest? Explain.