# 15 since credit card companies must charge the same

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15. Since credit-card companies must charge the same interest rate to all borrowers, they attract more low- than high-quality borrowers (i.e., more borrowers who either do not repay their debts or repay their debts late). This leads to an adverse selection problem and forces up the interest rate charged, which increases even more the proportion of low- quality borrowers, until interest rates would have to be so high that it would not pay even for low-quality borrowers to borrow. Credit-card companies reduce the adverse selection problem that they face by sharing the credit histories of borrowers with other credit-card companies. The sharing of borrowers' credit histories by credit-card companies in order to reduce the adverse selection problem that they face gives rise to complaints of invasion of privacy. This is true, but without sharing credit histories, credit-card companies would have to charge much higher credit rates, which might be unacceptable to most borrowers.

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b. Problems: Spreadsheet problems 1. The expected value of investment A is (\$4,000)(0.2) + (\$5,000)(0.3) + (\$6,000)(0.3) + (\$7,000)(0.2) = \$800 + \$1,500 + \$1,800 + \$1,400 = \$5,500. The expected value of investment B is (\$4,000)(0.3) + (\$6,000)(0.4) + (\$8,000)(0.3) = \$1,200 + \$2,400 + \$2,400 = \$6,000. ( a ) The standard deviation of investment A is \$1,024.70. The standard deviation of investment B is \$1,549.19. ( b ) Investment A is less risky than investment B because its standard deviation is smaller, but it also provides a lower expected income. ( c ) It is not clear, therefore, from the information given which investment is best. It depends on whether the lower expected income from investment A is more than balanced by its lower risk. This depends on the attitude of the individual toward risk. 2. ( a ) From the spreadsheet, the expected value of project A of 2.8 is higher than 2.7 for project B, so it is preferred. ( b ) Project B has a higher expected utility of 2.315, however, so it is preferred under this criterion. ( c ) The individual is risk averse because the utility function of profit increases at a decreasing rate or faces down so that the marginal utility of profit diminishes Froeb and McCann’s chapter 17: a. Individual problems: 17-3 Boat Insurance = \$2,150 Payment Probability \$25,000 1 – (0.6+0.25+.12) = 0.03 \$5,000 0.12 \$0 0.25 \$0 0.6 Expected payment = 0.03*25,000 + 0.12*5,000 + 0.25*0 + 0.6*0 = \$1,350 Expected payment + \$200 profit = \$1,550
17-4 Hotdog Uncertainty Compute expected payoffs: Enter: 0.35(50,000)+.65(0)=\$17,500 Do not enter: \$15,000 You should enter the market.

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