Question

2. If times are bad, Dave’s consulting business earns a profit of $20,000 while if times are good his business earns a profit of $120,000. Dave’s total utility from a profit of $20,000 is 40 units and his total utility from a profit of $120,000 is 60 units.

a. If the probability of bad times is 50% and the probability of good times is 50%, what are Dave’s expected profit and his expected utility?
b. If the probability of bad times is 25% and the probability of good times is 75%, what are Dave’s expected profit and his expected utility?
c. If the probability of bad times is 10% and the probability of good times is 90%, what are Dave’s expected profit and his expected utility?

3. Suppose Scott is risk averse. If his current wealth is $60,000 and he loses $1,000 of wealth his total utility decreases by 20 units. If his current wealth is $60,000 and he gains $1,000 of wealth, by how much does his total utility rise? Relate your answer to the idea of diminishing marginal utility and risk aversion.

4. Figure 1 shows Alan’s utility of wealth curve. Alan has a car worth $50,000. It’s a fast car and so Alan runs the risk that he will be involved in an accident, in which case the car will be worth $0. Suppose the probability that Alan will be involved in an accident is 30%. (The car is really fast.)

a. What is Alan’s expected wealth if he has no insurance?
b. What is Alan’s expected utility if he has no insurance?
c. Presuming that its only cost is the cost of reimbursing its customers for an accident, how much will it cost an insurance to insure Alan for the full value of his car?
d. Will Alan be willing to buy insurance if the insurance market is competitive so that Alan is charged only the amount you answered for part c? Explain why Alan will be willing or unwilling to buy insurance at this price.

Answer 1