WEEK 6 CYU

# Myisha coleman week 6 cyu b what is the total market

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Myisha Coleman Week 6 CYU b) What is the total market demand for polyglue at the price established by Alchem in Part (a)? How much of total demand do the follower firms supply? Part (a) Alchem's (L) profit-maximizing output occurs where: MR L = MC L MR L is found as follows: MR L = d(TR L )/dQ L TR L is given by the following expression: TR L = P  Q L Also, Q L is given by: Q L = Q T Q F Using the total demand function, one can solve for Q T : P = 20,000 4Q T or Q T = 5000 .25P In order to find Q F , one notes that Alchem lets the follower firms (F) sell as much polyglue as they wish at the given market price (P). Therefore, the follower firms are faced with a horizontal demand function and hence: MR F = P In order to maximize profits, the follower firms will operate where: MR F = MC F , or where: P = 2000 + 4Q F Solving for Q F yields: Q F = .25 P 500 Substituting Q F and Q T into the expression above for Q L gives: Q L = (5000 .25P) (.25P 500) = 5500 .50P Solving for P gives: P = 11,000 2Q L

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Myisha Coleman Week 6 CYU Substituting P into the TR L expression above gives: TR L = (11,000 2Q L )Q L = 11,000Q L 2Q L 2 MR L is therefore equal to: MR L = 11,000 4Q L Setting MR L = MC L gives: 11,000 4Q L = 5000 + 5Q L so Q L * = 666.7. Substituting this value into the expression for P gives: P* = 11,000 2(666.7) = \$9,666.70. Part (b) From the expression above for Q T , one obtains: Q T * = 5000 .25(9666.7) = 2,583.3. The followers supply the rest: Q F * = .25(9666.7) 500 = 1,916.7.
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• Fall '12
• Babb
• Myisha Coleman

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