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.

Question

Areli Cabrera

Business

25 December, 02:45

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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Answers (1)

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Lucia Rios · Answer 1

Hi dear, the question you posted is not complete, but, not to worry I will be posting some important things for you to be able to solve this kind of question.

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.