solutionsps8f06 - Problem Set 8 Suggested Solutions 1...

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Problem Set 8 Suggested Solutions 1. Question 6, page 379 C=100+2Q 2 MC=4Q P=90-2Q MR=90-4Q a. Monopoly: MR=MC 90-4Q=4Q, 8Q=90 25 . 11 4 45 = = m Q Hence, 5 . 67 2 135 = = m P 125 . 353 375 . 759 25 . 11 ) 25 . 11 ( 2 100 ) 5 . 11 )( 5 . 67 ( ) 2 100 ( 2 2 - = = - - = + - = Π m m m m Q Q p Hence, 25 . 406 = Π m b. Perfect Competition: Marginal cost intercepts demand: 90-2Q=MC, 6Q=90, Q c =15. Hence P c =60, and Profit=$350 in the short run and zero in the long run. c. 2. Question 8, page 379
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You can assume that the information about marginal cost and marginal revenue are given. C 1 (Q 1 )=10Q 1 2 , MC 1 =20Q 1 C 2 (Q 2 )=20Q 2 2 , MC 1 =40Q 2 P=700-5Q, MR=700-10Q a. Only the total marginal cost is not given. Total marginal cost is the horizontal sum of the factories’ individual marginal cost. That is, you should add the quantities for a specific marginal cost. So, first solve the two MC equations for Q. Then add them to find an expression for Q T and MR. Finally solve this expression for MR. MC Q 20 1 1 = MC Q 40 1 2 = So, MC Q Q Q T 40 3 2 1 = = + .
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