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Question

consider a firm that uses consider a firm that uses consider a firm that uses consider a firm that uses 13. Two firms, Firm 1 and Firm 2, sell a homogeneous product in a single market. Firm 1 moves first and decides to produce q, units of output. After observing Firm I's decision, Firm 2 decides to produce q, units of output. Firm 1 produces output with zero marginal cost. Firm 2's cost function is c(%)-24-The inverse market demand function is given by p = l 0-Q, where Q = qtq. . What is the market price of the product in equilibrium? A) 5 B) 4 C) 6 D) 3 E) 2

Explanation / Answer

p = 10 - Q = 10 - (q1 + q2)

Revenue (firm 2) = pq2 = 10q2 - q1q2 -q22

MR (firm2) = dR2/dq2 = 10 - 2q2 -q1

Profit is maximized when MR = MC = 2:

2q2 + q1 = 8 (eq 1)

q2 = (8 - q1)/2

Firm 1:

Revenue (firm 1) = pq1 = 10q1 - q1q2 - q12

Replace q2 from the equation above:

R = 10q1 - 4q1 -q12/2

MR (firm 1) = 6 - q1

MC (firm 1) = 0

Profit is maximized when:

6 - q1 = 0 (eq 2)

Using the 2 equations, solve for q1 and q2:

q1 = 6 and q2 = 1

Price = 10 - (6 + 1) = 3 (Option D is correct)

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