ECON20120
Homework 2
Answer all questions.
All exercises refer to the following setup. There are two irms producing diferent but related products. The demand functions for the products of the two irms are:
D1(p1 , p2 ) = 10 - 2p1 + p2
D2(p1 , p2 ) = 10 - 2p2 + p1
where Di(p1 , p2) and pi i = 1, 2 are the corresponding quantity demanded and price respectively for the output of each irmi = 1, 2. Both irms operate with constant marginal costs c1 = c2 = 3.
Question 1 Suppose that both irms choose the price of their respective product (price com-petition). Find the equilibrium prices quantities and proits in this market.
Question 2 Suppose now that each irm chooses the quantity of the product that it produces and supplies to the market (quantity competition). Find the equilibrium prices quantities and proits in this market.
Question 3 Suppose now that irm 1 chooses the quantity it produces and supplies to the market but irm 2 chooses the price of its product. Find the equilibrium prices quantities and proits in this market.
Not for credit but as food for thought: having solved exercises 2 and 3 take a moment to relect on the following issue. In both cases irm 1 chooses its output. Suppose you were the owner of irm 2 and had to decide whether to choose your price or your quantity ahead of playing the game with irm 1. Can you formally model this situation and decide what would you do?