Question

1. There are two auto producers in Karmania, F1 and F2. The cars they produce are essentially identical. The marker inverse demand curve is given by p = a - bQ, where p is the price (in thousands of dollars); Q market output (in thousands of units); and a and b are parameters. It is estimated that a = 25 and b = 0.1. Both F1 and F2 have a marginal cost of 10 thousand dollars per car. Competition in the Karmania auto market works as follows. At the beginning of each year, both firms simultaneously and independently decide how many cars to produce. Then the market price adjusts to so that supply equals demand.

(1) What is firm F1’s best response mapping? (a) q1 = 150 ? q2 (b) q1 = 150 + q2 (c) q1 = 75 ? 0.5q2 (d) q1 = 75 + 0.5q2

Hint: If firms F1’s profit is ?1 = ?0 + ?1q1 + ?2q 2 1 + ?3q1q2, where ?0, ?1, ?2, ?3 are parameters, q1 is firm F1’s quantity supplied, and q2 is firm F2’s quantity supplied. Then firm F1’s best response mapping is q1 = ? ?1 /2?2 ? ?3 2?2/ x q2.

(2) What is the equilibrium of the game played between F1 and F2? (a) p = 20, q1 = q2 = 25 (b) p = 15, q1 = q2 = 50 (c) p = 13, q1 = q2 = 60 (d) p = 5, q1 = q2 = 100 Hint: At equilibrium, the equilibrium output for firm F1 is the same as that for firm F2.

Answer 1