Question

In: Economics

Consider a firm that sells a product in two isolated geographical areas. If it wants to,...

Consider a firm that sells a product in two isolated geographical areas. If it wants to, it can then charge different prices in the two different areas because what is sold in one area cannot easily be resold in the other. Suppose that the firm has also some monopoly power to influence the different prices it faces in the two separate markets by adjusting the quantity it sells in each. This is called a 'discriminating monopolist". The following are the demand functions it faces:

P1 = 200 – 2 Q1, P2 = 180 – 4 Q2

for market areas 1 and 2, respectively. Suppose, too, that the total cost is proportional to total production:

C(Q) = 20 (Q1 + Q2).

  1. Set up the firm's profit function and determine how much should be sold in the two markets to maximize profits. What are the corresponding prices?
  2. Check for second-order conditions.
  3. How much profit is lost if it becomes illegal to discriminate? (i.e. P1 = P2 = P, and Q = Q1 + Q2).

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