ECO 301 TEST BANK FOR CHAPTER 4 Uncertainty
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<strong>ECO</strong> <strong>301</strong> <strong>TEST</strong> <strong>BANK</strong> <strong>FOR</strong> <strong>CHAPTER</strong><br />
4 <strong>Uncertainty</strong><br />
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<strong>ECO</strong> <strong>301</strong> <strong>TEST</strong> <strong>BANK</strong> <strong>FOR</strong> <strong>CHAPTER</strong> 4 <strong>Uncertainty</strong><br />
1. Probability is sometimes defined as<br />
2. Expected value is defined as<br />
3. If a fair gamble is played many times, the combined monetary losses or gains will<br />
4. People who choose not to participate in fair gambles are called<br />
5. A gamble can be described as “fair” if the expected value of the gamble (including any costs of play)<br />
is<br />
6. Risk aversion is best explained by<br />
7. An individual will never buy complete insurance if<br />
8. With moral hazard, fair insurance contracts are not viable because<br />
9. Risk averse individuals will diversify their investments because this will<br />
10. Suppose a lottery ticket costs $1 and the probability that a holder will win nothing is 90%. What must<br />
the jackpot be for this to be a fair bet?<br />
11. Suppose a lottery ticket costs $1 and the probability that a holder will win nothing is 99%. What must<br />
the jackpot be for this to be a fair bet?<br />
12. Suppose a lottery ticket costs $1 and the probability that a holder will win nothing is 99.9%. What<br />
must the jackpot be for this to be a fair bet?<br />
13. Suppose a lottery ticket costs $1and has a jackpot of $1,000. What must the probability of winning<br />
nothing be if the bet is fair?<br />
14. Suppose a lottery ticket costs $1and has a jackpot of $1 million. What must the probability of winning<br />
nothing be if the bet is fair?<br />
15. Suppose a family has saved enough for a 10 day vacation (the only one they will be able to take for<br />
10 years) and has a utility function U = V 1/2 (where V is the number of healthy vacation days they experience).<br />
Suppose they are not a particularly healthy family and the probability that someone will have a vacation-ruining<br />
illness (V = 0) is 20%. What is the expected value of V?<br />
16. Continuing with the family from the preceding question, what is their expected utility?<br />
17. Continuing with the same family from the preceding question, what is the greatest (integer) number<br />
of vacation days the family would be willing to give up in order to guarantee a healthy vacation?<br />
18. Continuing with the same family from the preceding question, suppose a risk neutral insurance<br />
company exists to provide vacation insurance. Suppose further that each vacation day requires a constant<br />
expenditure, and this expenditure is standard across everybody. This allows us to simplify the problem by<br />
considering all payments to be in terms of vacation days. What is the least the insurance company would<br />
charge (in terms of vacation days)?<br />
19. Continuing with the same vacation-insurance company from the preceding question, what vacationday<br />
price(s) would be acceptable to both the family and the insurance company?<br />
20. Continuing with the same vacation-insurance company from the preceding question, is there any<br />
vacation-day price that would both strictly increase the family’s expected utility (compared to no insurance) and<br />
strictly increase the profits of the risk-neutral insurance company?
21. Suppose a family has saved enough for a 10 day vacation (the only one they will be able to take for<br />
10 years) and has a utility function U = V 1/2 (where V is the number of healthy vacation days they experience).<br />
Suppose they are not a particularly healthy family and the probability that someone will have a vacation ruining<br />
illness (V = 0) is 30%. What is the expected value of V?<br />
22. Continuing with the family from the preceding question, what is their expected utility?<br />
23. Continuing with the same family from the preceding question, what is the greatest (integer) number<br />
of vacation days the family would be willing to give up in order to guarantee a healthy vacation?<br />
24. Continuing with the same family from the preceding question, suppose a risk neutral insurance<br />
company exists to provide vacation insurance. Suppose further that each vacation day requires a constant<br />
expenditure, and this expenditure is standard across everybody. This allows us to simplify the problem by<br />
considering all payments to be in terms of vacation days. What is the least the insurance company would<br />
charge (in terms of vacation days)?<br />
25. Continuing with the same vacation-insurance company from the preceding question, what vacationday<br />
price(s) would be acceptable to both the family and the insurance company?<br />
26. Continuing with the same vacation-insurance company from the preceding question, is there any<br />
vacation-day price that would both strictly increase the family’s expected utility (compared to no insurance) and<br />
strictly increase the profits of the risk-neutral insurance company?<br />
27. Suppose a risk-neutral power plant needs 10,000 tons of coal for its operations next month. It is<br />
uncertain about the future price of coal. Today it sells for $60 a ton but next month it could be $50 or $70 (with<br />
equal probability). How much would the power plant be willing to pay today for an option to buy a ton of coal<br />
next month at today’s price? (Ignore discounting over the short period of a month.)<br />
28. Continuing with the power plant from the previous question, suppose instead the price of coal next<br />
month could be $54 or $66 (with equal probability). Now how much would it be willing to pay for an option to<br />
buy a ton of coal oil next month at today’s price?<br />
29. Continue with the power plant from the previous question, where again coal currently sells for $60 a<br />
ton but will sell for either $54 or $66 next month with equal probability. Now suppose coal can be stored for a<br />
month at the cost of $2 per ton. How would the new alternative of being able to buy coal at today’s prices and<br />
store it affect the amount the power plant would be willing to pay for an option to buy coal next month at today’s<br />
prices?
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