Firm A and firm B compete in the same market by simultaneous quantity competition. Firms can choose any quantity Q ≥ 0. The inverse market demand curve is P (Q) = 40−2Q. Both firms have cost functions C (Q) = 2Q2 , implying a marginal cost function of MC (Q) = 4Q.

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Explanation:

From the question, we are given that; inverse market demand curve is P (Q) = 40−2Q and the two (Both) firms have cost functions C (Q) = 2Q2. Also, marginal cost function of MC (Q) = 4Q.

The kind of questions that one can expect to be asked are;

(1). The maximization problem for both firms and determine the optimal price and quantity products produced.

The solution is;

P(q) q − C (q) = (40 − 2q) q − 2q2.

Therefore, we have;

40 − 2q∗ − 4 =0

or

q∗ = 36/4.

Given q∗ = 7/4, the two firms charge price will be;

p∗ = 40 − q∗ = 44/4 = 11.

(2). How much profit does the two firms make?

=> 11 × 7/4= 77/4.