Ans_Quiz6

Ans_Quiz6 - Answer_Quiz6 13.13 a) Begin by inverting the...

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Answer_Quiz6 13.13 a) Begin by inverting the market demand curve: Q = 600 – 3P P = 200 – (1/3)Q. The marketing-clearing price if firm 1 produces Q 1 and firm 2 produces Q 2 is: P = 200 – (1/3)(Q 1 + Q 2 ). Let’s focus on firm 1 first. Firm 1’s residual demand curve has the equation P = [200 – (1/3)Q 2 ] – (1/3)Q 1 . The corresponding marginal revenue curve is thus: MR 1 = [200 – (1/3)Q 2 ] – (2/3)Q 1 . Equating firm 1’s marginal revenue to marginal cost and solving for Q 1 gives us: [200 – (1/3)Q 2 ] – (2/3)Q 1 = 80, or 120 – (1/3)Q 2 = (2/3)Q 1 Q 1 = 180 – ½ Q 2 . This is firm 1’s reaction function. Similar logic gives us firm 2’s reaction function: Q 2 = 180 – ½ Q 1 . Now, we have two equations (the two reaction functions) in two unknowns (Q 1 and Q 2 ). Solving this system of linear equations gives us: Q 1 = Q 2 = 120. The resulting market price is: P = 200 – (1/3)(120+120) = 120. Each firm’s profit is (P – M)Q i , for i = 1,2, or (120 – 80)(120) = $4,800 per month. Industry profit is thus:
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This note was uploaded on 01/30/2011 for the course 730 368 taught by Professor Bryant during the Spring '08 term at Rutgers.

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Ans_Quiz6 - Answer_Quiz6 13.13 a) Begin by inverting the...

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