Question

Exercise 4 Suppose that cheese and ham are perfect substitutes and that they are produced by two independent producers which we can call Ola and Svein. Demand is given by the inverse demand function P = A - X where A is a constant and X = x1 + x2 is the total production of cheese and ham. Suppose further that Ola has cost function C1 (x1) = 10x1, while Svein has cost function C2 (x2) = 20x2. Fast costs we disregard.

a) Suppose that A equals 90. Determine the market price, the quantity of cheese and ham traded, and the profit to Ola and Svein if they compete with quantity as a strategic variable (Cournot competition).

b) What will be the answers to the questions under (a) if A equals 60?

c) The constant A can be regarded as an (imprecise) indicator of market size. Know the answers (a) and (b) tell us something about the importance of market size for efficiency and welfare when it comes is imperfect competition in the markets? Explain.

Answer 1

a. Firm 1's problem:

Solving:

Firm 1's best response function is:

Firm 2's problem:

Solving:

Firm 2's best response function is:

Solving the two best response function:

For A = 90,

Market price at these quantities is 40
Each firm's profit is:

b. For A = 60:

Market price at these quantities is 30.
Each firm's profit is:

c. As the market size (A) increases, both firms' profit increases. Therefore, as market size increases, welfare of the producers increases in imperfect competition.