- Consider a lottery with three possible outcomes:
- $125 will be received with probability 0.2
- $100 will be received with probability 0.3
- $50 will be received with probability 0.5
a. What is the expected value of the lottery?
b. What is the variance of the outcomes?.
c. What would a risk-neutral person pay to play the lottery?
- Suppose you have invested in a new computer company whose profitability depends on two factors: (1) whether the U.S. Congress passes a tariff raising the cost of Japanese computers and (2) whether the U.S. economy grows slowly or quickly. What are the four mutually exclusive states of the world that you should be concerned about?
- Richard is deciding whether to buy a state lottery ticket. Each ticket costs $1, and the probability of winning payoffs is given as follows:
Probability Return
0.5 $0.0
0.25 $1.00
0.2 $2.00
0.05 $7.5
a. What is the expected value of Richard’s payoff if he buys a lottery ticket? What is the variance?
b. Richard’s nickname is “No-Risk Rick” because he is an extremely risk-averse individual. Would he buy the ticket?
c. Suppose Richard was offered insurance against losing any money. If he buys 1000 lottery tickets, how much would he be willing to pay to insure his gamble?
d. In the long run, given the price of the lottery tickets and the probability/return table, what do you think the state would do about the lottery?
- Suppose that Natasha’s utility function is given by , where I represents annual income in thousands of dollars.
a. Is Natasha risk loving, risk neutral, or risk averse? Explain.
b. Suppose that Natasha is currently earning an income of $40,000 (I 40) and can earn that income next year with certainty. She is offered a chance to take a new job that offers a 0.6 probability of earning $44,000 and a 0.4 probability of earning $33,000. Should she take the new job?
c. In (b), would Natasha be willing to buy insurance to protect against the variable income associated with the new job? If so, how much would she be willing to pay for that insurance? (Hint: What is the risk premium?) - As the owner of a family farm whose wealth is $250,000, you must choose between sitting this season out and investing last year’s earnings ($200,000) in a safe money market fund paying 5.0% or planting summer corn. Planting costs $200,000, with a six-month time to harvest. If there is rain, planting summer corn will yield $500,000 in revenues at harvest. If there is a drought, planting will yield $50,000 in revenues. As a third choice, you can purchase AgriCorp drought-resistant summer corn at a cost of $250,000 that will yield $500,000 in revenues at harvest if there is rain, and $350,000 in revenues if there is a drought. You are risk averse, and your preference for family wealth (W) is specified by the relationship . The probability of a summer drought is 0.30, while the probability of summer rain is 0.70. Which of the three options should you choose? Explain.
- Draw a utility function over income u(I) that describes a man who is a risk lover when his income is low but risk averse when his income is high. Can you explain why such a utility function might reasonably describe a person’s preferences?
- A city is considering how much to spend to hire people to monitor its parking meters. The following information is available to the city manager:
● Hiring each meter monitor costs $10,000 per year.
● With one monitoring person hired, the probability of a driver getting a ticket each time he or she parks illegally is equal to 0.25.
● With two monitors, the probability of getting a ticket is 0.5; with three monitors, the probability is 0.75; and with four, it’s equal to 1.
● With two monitors hired, the current fine for overtime parking is $20.
a. Assume first that all drivers are risk neutral. What parking fine would you levy, and how many meter monitors would you hire (1, 2, 3, or 4) to achieve the current level of deterrence against illegal parking at the minimum cost?
b. Now assume that drivers are highly risk averse. How would your answer to (a) change?
c. (For discussion) What if drivers could insure themselves against the risk of parking fines? Would it make good public policy to permit such insurance?
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