Chap008 - Chapter 8 Answers to Questions and Problems 1 a b...

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Chapter 8: Answers to Questions and Problems 1. a. 7 units. b. $28. c. $224, since $32 x 7 = $224. d. $98, since $14 x 7 = $98. e. $126 (the difference between total cost and variable cost). f. It is earning a loss of $28, since ($28 -$32) x 7 = - $28. g. - $126, since its loss will equal its fixed costs. h. Shut down. 2. a. Set P = MC to get $80 = 8 + 4Q. Solve for Q to get Q = 18 units. b. $80. c. Revenues are R = ($80)(18) = $1440, costs are C = 40 + 8(18) + 2(18) 2 = $832, so profits are $608. d. Entry will occur, the market price will fall, and the firm should plan to reduce its output. In the long-run, economic profits will shrink to zero. 3. a. 7 units. b. $130. c. $140, since ($130 – 110) x 7 = $140. d. This firm’s demand will decrease over time as new firms enter the market. In the long-run, economic profits will shrink to zero. 4. a. MR = 200 – 4Q and MC = 6Q. Setting MR = MC yields 200 – 4Q = 6Q. Solving yields Q = 20 units. The profit-maximizing price is obtained by plugging this into the demand equation to get P = 200 - 2(20) = $160. b. Revenues are R = ($160)(20) = $3200 and costs are C = 2000 + 3(20) 2 = $3200, so the firm’s profits are zero. c. Elastic. d. TR is maximized when MR = 0. Setting MR = 0 yields 200 – 4Q = 0. Solving for Q yields Q = 50 units. The price at this output is P = 200 – 2(50) = $100. e. Using the results from part d, the firm’s maximum revenues are R = ($100) (50) = $5,000. f. Unit elastic. 8-1
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5. a. A perfectly competitive firm’s supply curve is its marginal cost curve above the minimum of its AVC curve. Here, 2 50 8 3 i i i MC q q = - + and 2 3 2 50 4 50 4 i i i i i i i q q q AVC q q q - + = = - + . Since MC and AVC are equal at the minimum point of AVC, set MC i = AVC i to get 2 2 50 8 3 50 4 i i i i q q q q - + = - + , or 2 i q = . Thus, AVC is minimized at an output of 2 units, and the corresponding AVC is ( 29 ( 29 2 50 4 2 2 46 i AVC = - + = . Thus the firm’s supply curve is described by the equation 2 3 8 50 i i q q MC + - = if $46 P ; otherwise, the firm produces zero units. b. A monopolist produces where MR = MC and thus does not have a supply curve. c. A monopolistically competitive firm produces where MR = MC and thus does not have a supply curve. 6. a. Q = 3 units; P = $70. b. Q = 4 units; P = $60.
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