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# chap012 - Chapter 12 Answers to Questions and Problems 1 a...

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Chapter 12: Answers to Questions and Problems 1. a. The expected value of option 1 is 300 100 16 1 200 16 4 500 16 6 200 16 4 100 16 1 . The expected value of option 2 is 1 1 1 1 1 80 170 1,000 170 80 300 5 5 5 5 5 . b. The variance of option 1 is . 000 , 25 300 100 16 1 300 200 16 4 300 500 16 6 300 200 16 4 300 100 16 1 2 2 2 2 2 Similarly, the variance of option 2 is 124,120. The standard deviation of option 1 is 158.11. The standard deviation of option 2 is 352.31. c. Option 2 is the most risky. 2. a. Risk loving. b. Risk averse. c. Risk neutral. 3. a. \$5. b. She will purchase, since your price is less than her reservation price. c. \$6. d. She will continue to search, since the price exceeds her reservation price. 4. a. .6 \$100 .4 \$200 \$140 Ep . b. Set Ep = MC to get 140 = 1 + 4 Q . Solve for Q to find your profit-maximizing output, Q = 34.75 units. c. Your expected profits are ( Ep)Q – C(Q) = \$140(34.75) – (34.75 + 2(34.75) 2 )=\$2,415.13. 5. a. The expected value, which is \$25. b. The maximum value, which is \$50. Managerial Economics and Business Strategy, 7e Page 1

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6. a. With only two bidders, n = 2. The lowest possible valuation is L = \$1,000, and your own valuation is v = \$2,500. Thus, your optimal sealed bid is \$2,500 \$1,000 \$2,500 \$1,750 2 v L b v n . b. With ten bidders, n =10 . The lowest possible valuation is L = \$1,000, and your own valuation is v = \$2,500. Thus, your optimal sealed bid is \$2,500 \$1,000 \$2,500 \$2,350 10 v L b v n . c. With one hundred bidders, n =100 . The lowest possible valuation is L = \$1,000, and your own valuation is v = \$2,500. Thus, your optimal sealed bid is \$2,500 \$1,000 \$2,500 \$2,485 100 v L b v n . 7. a. With 5 bidders, n = 5 . The lowest possible valuation is L = \$50,000, and your own valuation is v = \$75,000. Thus, your optimal sealed bid is \$75,000 \$50,000 \$75,000 \$70,000 5 v L b v n . b. A Dutch auction is strategically equivalent to a first-price sealed bid auction (see part (a)). Thus, you should let the auctioneer continue to lower the price until it reaches \$70,000, and then yell “Mine!” c. \$75,000, since it is a dominant strategy to bid your true valuation in a second- price, sealed-bid auction.
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