Chap012 - Chapter 12: Answers to Questions and Problems 1....

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Chapter 12: Answers to Questions and Problems 1. a. The expected value of option 1 is ( 29 ( 29 ( 29 ( 29 ( 29 300 100 16 1 200 16 4 500 16 6 200 16 4 100 16 1 = + + + + . The expected value of option 2 is ( 29 ( 29 ( 29 ( 29 ( 29 1 1 1 1 1 80 170 1,000 170 80 300 5 5 5 5 5 + + + + = . b. The variance of option 1 is ( 29 ( 29 ( 29 ( 29 ( 29 . 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. ( 29 ( 29 .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. 12-1
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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. d. Remain active until the price exceeds $75,000; then drop out.
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Chap012 - Chapter 12: Answers to Questions and Problems 1....

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