Firm A and Firm B are the only two firms in the housing market. beth these firms

Question

Firm A and Firm B are the only two firms in the housing market. beth these firms produce the same type of houses. They face the following market demand curve: Q = 28- 1/5P where Q = Q_A + Q_B Marginal cost (MC) for beth firms is equal to $20. When maximizing profits, beth these firms take their rival's output as given (i.e., the firms behave as Cournot oligopolists). a. Suppose these firms produce competitively witheut taking the other firm's quantity into consideration. How much will each firm produce now? What will be the total output produced by the two firms? WThat will be each firm's total profit? b. Draw the reaction curves of beth these firms and show the Cournot equilibrium. On your graph also show the collusive equilibrium and the competitive equilibrium. Compare these three equilibriums.

Explanation / Answer

a) If both the firms produce competitively without taking other firm's quantity into consideration:

We have Q = 28 - 1/2P or P = 56 - 2Q

MR = dTR/dQ

TR = P*Q = (56-2Q)Q = 56Q - 2Q2

MR = 56 - 4Q

equating MR with firm 1 's MC

56-4Q = 20

Q = 9

and P = 56 - 2(9)= $38

Similarly firm 2 will produce 9 units at price of $38 per unit.

Thus industry output is 9+9 = 18.

b) When firms compete in cournot oligopoly

Firm 1 respone function : Profit = PQ1 - CQ1 = 36Q1 - 2Q12 - 2Q1Q2

Firm 2 response function : Profit = PQ2 - CQ2 = 36Q2 - 2Q22 - 2Q1Q2

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