Question: A firm produces and sells a product in two separate markets. When the price in market A is p per ton, and the price in market B is q per ton, the demand in tons per week in the two markets are, respectively, QA = a - bp, QB = c - dq
The cost function is C(QA, QB) = α + β(QA + QB), and all constants are positive.
(a) Find the firm's profit π as a function of the prices p and q, and then find the pair (p∗, q∗) that maximizes profits.
(b) Suppose it becomes unlawful to discriminate by price, so that the firm must charge the same price in the two markets. What price pˆ will now maximize profits? (c) In the case β = 0, find the firm's loss or profit if it has to charge the same price in both markets. Comment.