4. The Cournot Model of Imperfect Competition:

Suppose there are two firms, Firm A and Firm B, in a market, selling an identical good. These firms choose a profit-maximizing level of output to produce, taking into account the level of production of their competitor, and also of course taking into account market demand.

Let market demand be P = 100 - (QA + QB)

Suppose these firms have identical, constant marginal cost such that MC=AC=10.

a. TotalrevenueforfirmA=P*QA =(100-(QA +QB))*QA =100QA -QA 2 -QA*QB. This means that marginal revenue for firm A is MRA = 100 - 2 QA - QB. Suppose Firm B chooses QB = 40. What level of output should Firm A choose in order to maximize its profit, given B's action? (5)

b. In the same way, we can derive an expression for the marginal revenue of Firm B: MRB =100-2QB -QA. Suppose Firm A chooses the level of output you calculated in part (a). What level of output should Firm B choose in response, in order to profit maximize, given this choice by A?(5)

c. Explain why the combination of the value of QA that you calculated in part (a) and QB =30 do not constitute a Cournot equilibrium. (5)

d. Find the equilibrium values of QA, QB , and price in this market. (10)