Clearly answer the following questions,,,

1. Suppose a fair, two-sided coin is flipped. If it comes up heads you receive $5. If it comes up tails you lose $1. The expected value of this lottery is (a) $2 (b) $3 (c) $4 (d) $5 (e) None of the above

2. An individual has a vNM utility function over money of u(x) = p3 x , where x is final wealth. She currently has $8 and can choose among the following three lotteries. Which lottery will she choose? ? Lottery 1: Give up her $8 and face the gamble (0.1, 0.5, 0.4) over final wealth levels ($1, $8, $27). ? Lottery 2: Keep her $8. ? Lottery 3: Give up her $8 and face the gamble (0.2, 0.8,0.0) over final wealth levels ($1, $8, $27) (a) Lottery 1 (b) Lottery 2 (c) Lottery 3 (d) She is indifferent between the three lotteries.

3. An individual has a vNM utility function over money of u(x) = px, where x is final wealth. Assume the individual currently has $16. He is offered a lottery with three possible outcomes; he could gain an extra $9, lose $7, or not lose or gain anything. There is a 15% probability that he will win the extra $9. What probability, p, of losing $7 would make the individual indifferent between to play and to not play the lottery? (a) p = 0.15 (b) p = 1.08 (c) p = 0.415 (d) p = 0.05 (e) None of the above

4. Johnny owns a house that is worth $100,000. There is a 0.1% chance that the house will be completely destroyed by fire, leaving Johnny with $0. Johnny's utility function is u(x) = px, where x represents final wealth. Assuming that Johnny has no other wealth, what's the maximum amount that he would be willing to pay for an insurance policy that completely replaces his house if destroyed by fire? (a) $315.91 (b) $225.21 (c) $199.90 (d) $123.41

5. An individual has a vNM utility function over money of u(x) = px , where x is the amount of money won in the lottery. She faces two scenarios: Scenario 1: With a 50% probability she wins $36. With a 50% probability she wins $16. Scenario 2: With a 50% probability she wins $0. With a 50% probability she wins $x. For what value of x will the risk premia be identical in these two scenarios?

(a) 0

(b) 4

(c) 16 (d) For no values of x can the two risk premia be identical

6. A decision maker has a vNM utility function over money of u(x) = x2. This decision maker is

(a) risk-averse.

(b) risk-neutral.

(c) risk-loving.

(d) none of the above.

7. Consider two lotteries:

? Lottery 1:

The gamble (0.1, 0.6, 0.3) over the final wealth levels ($1, $2, $3). (The expected value of this lottery equals $2.2) ? Lottery 2: Get $2.2 for sure.

a) Any risk-averse individual will choose the first lottery.

b) Any risk-averse individual will choose the second lottery.

c) Any risk-averse individual will be indifferent between these two lotteries.

d) None of the above

For questions 8-10 assume that Rosa has a 10% chance of getting sick in the next year. If she gets sick, her medical bills will amount to $3600. She has a wealth of $10,000. Suppose she has the utility function u(x) = px, where x is her net wealth at the end of the year.

8. What is Rosa's risk premium?

(a) 0

(b) 16

(c) 36

(d) 56

(e) None of the above

9. What is the most that Rosa is willing to pay for an insurance policy that fully covers against her loss?

(a) 0

(b) 196

(c) 396

(d) 596

(e) None of the above

10. Some insurance policies have deductibles.

A deductible is an amount of a claim not covered by insurance. It's a fixed portion of the medical bills that the insured person must pay in order to make a claim to their insurer.

Suppose Rosa's insurance company provides two plans. Plan A has zero deductibles (good!) but charges a high premium (bad!). Specifically, Plan A charges $591 for full coverage.

Plan B has a deductible of $197, but charges a premium of just $199. Will Rosa purchase insurance and, if so, which plan?

(a) Rosa will not purchase any insurance

(b) Rosa will purchase plan A

(c) Rosa will purchase plan B

(d) Rosa is indifferent between plan A and plan B. She can purchase either of them.

(e) None of the above

1. An exchange economy has two dates t = 0, 1 and two states of nature s = 1,2 which will be revealed at date 1. Unlike the model in class, agents in this economy do have endowments, consume and trade in goods at t = 0. Use s = 0 to denote the date-event pair corresponding to date 0. There is one physical commodity, and two consumers i = 1, 2 whose endowments wis are as follows: 10 = 2, wn1 = 4,w12 = 3, w/20 = 4, w21 = 2, w2 = 3. Both share the von-Neumann-Moregenstern utility log co + logo, where a denotes date t consumption. Consumer 1 believes s = 1 will occur with probability ?, while consumer 2 believes s = 1 will occur with probability 2. At date 0, there is a spot commodity (i.e., for delivery at s = 0) market, besides two assets k = 1,2 whose date-1 returns fox are given by ru = 1, m12 = 2, 121 = 0, raz = 1. So consumers divide their date 0 wealth between consumption at t = 0 and purchasing assets that yield returns at t = 1. At date 1, agents realize their asset returns and trade in spot commodity markets after the state is revealed. (a) Derive the entire set of er ante Pareto optimal allocations in this economy. Are these allocations ex post Pareto optimal as well?1) Economists often make use of an exponential utility function for money: U(x) = 1 - e , ", where x is the payoff amount and R is a positive constant representing an individual's risk tolerance. Risk tolerance represents how likely an individual is to accept a lottery with a particular expected monetary value (EMV) versus some certain payoff. As R (which is measured in the same units as x) becomes larger, the individual becomes less risk-averse. a) Assume Mary has an exponential utility function with R = P500. Mary is given the choice between receiving P500 with certainty (probability 1) or participating in a lottery which has a 60% probability of winning P5000 and a 40% probability of winning nothing. Assuming Mary acts according to the maximum expected utility (MEU) principle, which option would she choose? b) Suppose a lottery has some expected utility. The certainty equivalent for this lottery is defined as the monetary amount that, if given with certainty (i.e., money given with 100% probability), gives the same utility (no longer expected due to the certainty) as the lottery. Consider a lottery that gives P1000 with probability 0.3, P500 with probability 0.5, and 0 otherwise. i) What is Mary's expected utility for this lottery (again with R = P500)? ii) What is Mary's certainty equivalent for this lottery? 2) Consider the joint probability distribution on the A B C P(A, B, C) right. False False False 0.10 i) What is P(A = false)? Show your work. False False True 0.13 False True False 0.15 i) What is P(A=true or B=true)? Explain. False True True 0.12 ili) What is P(A=true|C=false)? True False False 0.01 True False True 0.19 iv) Are A and C independent? Why? True True False 0.07 True True True 0.23 3) In the general population, 5 in every 100,000 people have the dreaded Dutertitis disease. Fortunately, there is a test (testD30) for this disease that is 99.9% accurate. That is, if one has the disease, 999 times out of 1000 testD30 will turn out positive; if one does not have the disease, 1 time out of 1000 the test will turn out positive. You take testD30 and the results come back true. Use Bayesian reasoning to calculate the probability that you actually have Dutertitis. That is, compute: Prob(haveDutertitis = true | testD30 = true). Show your solution. #4 on next page. 4) Consider the following Bayesian Network, where variables A to D are all Boolean-valued: B P(A=true) = 0.2 P(B=true) = 0.7 A B P(C =true | A, B) B C P(D=true | B.C) false false 0.1 false false 0.8 false true 0.5 false true 0.6 true false 0.4 true false 0.3 true true 0.9 true true 0.1 Show all solutions: What is the probability that a) all four of these Boolean variables are false? b) C is true, D is false, and B is true? c) C is true given that D is false and B is true?7) Assume that you can borrow or lend in the US for 2-years at a 4% (annual) rate, and assume that you can borrow or lend in Canada at a 6% (annual) rate. Further assume that the current exchange rate is .99 $/C$. What 2-year forward rate would you quote on the Canadian dollar? If UIP holds, what exchange rate do you expect in two years? If expected inflation is 2% annually in the US, what is expected inflation in Canada if PPP holds? On average, do you expect to get higher real returns if you hold US or Canadian dollars for the next two years? (2GD) Fud At - CIP ( it : )e ( I t r ) t