Gary likes to gamble. Donna offers to bet him $31 on the outcome of a boat race. If Gary's boat wins, Donna would give him $31. If Gary's boat does not win, Gary would give her $31. Gary's utility function is p1x^21+p2x^22, where P₁ and p2 are the probabilities of events 1 and 2 and where x₁ and x2 are his wealth if events 1 and 2 occur respectively. Gary's total wealth is currently only $80 and he believes that the probability that he will win the race is 0.3. Which of the following is correct? (please submit the number corresponding to the correct answer). 1. Taking the bet would reduce his expected utility. 2. Taking the bet would leave his expected utility unchanged. 3. Taking the bet would increase his expected utility. 4. There is not enough information to determine whether taking the bet would increase or decrease his expected utility. 5. The information given in the problem is self-contradictory.
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- Gary likes to gamble. Donna offers to bet him $31 on the outcome of a boat race. If Gary’s boat wins, Donna would give him $31. If Gary’s boat does not win, Gary would give her $31. Gary’s utility function is p1x^21+p2x^22, where p1 and p2 are the probabilities of events 1 and 2 and where x1 and x2 are his wealth if events 1 and 2 occur respectively. Gary’s total wealth is currently only $80 and he believes that the probability that he will win the race is 0.3. Which of the following is correct? (please submit the number corresponding to the correct answer). Taking the bet would reduce his expected utility. Taking the bet would leave his expected utility unchanged. Taking the bet would increase his expected utility. There is not enough information to determine whether taking the bet would increase or decrease his expected utility. The information given in the problem is self-contradictory.To go from Location 1 to Location 2, you can either take a car or take transit. Your utility function is: U= -1Xminutes -5Xdollars +0.13Xcar (i.e. 0.13 is the car constant) Car= 15 minutes and $8 Transit= 40 minutes and $4 What is your probability of taking transit given the conditions above? What is your probability of taking transit if the number of buses on the route were doubled, meaning the headways are halved? Remember to include units.John is a farmer with $225 of wealth. He can either plant corn or beans. If he plants corn, John earns an income of $675 if the weather is GOOD and $0 if the weather is BAD. If he plants beans, John earns an income of $451 under both GOOD and BAD weather. The probability of GOOD weather is 0.7. The probability of BAD weather is 0.3. John's utility function is u(C) = 5VC , where C is the value of consumption. Use this information to fill out the table below. (Don't forget to include the value of wealth when you compute consumption!). The PDF will round all typed numbers to two decimals; However, you should use all decimals when computing your answers. %3D Plant Corn Plant Beans Expected value of consumption Expected value of utility Certainty Equivalent Risk Premium 9. What type of risk preferences does John have? Mae owns an insurance company in a nearby town and has decided to offer conventional crop insurance to corn farmers in the area. Assume that Mae has perfect information and…
- John is a farmer with $225 of wealth. He can either plant corn or beans. If he plants corn, John earns an income of $675 if the weather is GOOD and $0 if the weather is BAD. If he plants beans, John earns an income of $451 under both GOOD and BAD weather. The probability of GOOD weather is 0.7. The probability of BAD weather is 0.3. John’s utility function is U(c) = 5√c , where c is the value of consumption. Mae owns an insurance company in a nearby town and has decided to offer conventional crop insurance to corn farmers in the area. Assume that Mae has perfect information and can write and enforce an insurance contract that requires the farmer to plant corn. Here’s how the insurance contract works. At the beginning of the year, the corn farmer pays an insurance premium of $202.5. If the weather is GOOD, Mae makes no payment to the farmer. If the weather is BAD, Mae makes an indemnity payment of $675 to the farmer. a. If a farmer buys this insurance contract,what is Mae’s expected…Max is thinking of starting a pinball palace near a large Melbourne university. His utility is given by u(W) = 1 - (5,000/W), where W is his wealth. Max's total wealth is $15,000. With probability p = 0.7 the palace will succeed and Max's wealth will grow from $15,000 to $x. With probability 1 - p the palace will be a failure and he’ll lose $10,000, so that his wealth will be just $5,000. What is the smallest value of x that would be sufficient to make Max want to invest in the pinball palace rather than have a wealth of $15,000 with certainty? (Please round your final answer to the whole dollar, if necessary)Microeconomics Wilfred’s expected utility function is px1^0.5+(1−p)x2^0.5, where p is the probability that he consumes x1 and 1 - p is the probability that he consumes x2. Wilfred is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2500 with probability p = 0.4 and $3700 with probability 1 - p. Wilfred will choose the sure payment if Z > CE and the lottery if Z < CE, where the value of CE is equal to ___ (please round your final answer to two decimal places if necessary)
- Your utility function is given by M1/2. You have $100 and are planning to invest in a venture where you can win or lose 50 with equal probability. Will you accept the venture? What is the minimum gain you need to make in the good scenario such that you will invest in the venture?Sadija has a concave utility function of U(W) = In(W). She has inherited a ring from a relative, but she is unsure about its value. She believes that it is worth £6,000 with a probability of 1/3 and £3,000 with a probability of 2/3. a. Ahmed would like to buy the ring from her. Which price would he need to offer for Sadija' utility to remain unchanged after the sale? b. In fact, Ahmed offers £4,000 for the ring. What can you infer about Ahmed?Amy likes to go fast in her new Mustang GT. Their utility function over wealth is v(w) where w is wealth. If Amy goes fast she gets an increase in utility equal to F. But when Amy drives fast, she is more likely to crash: when she drives fast the probability of a crash is 10%, but when she obeys the speed limit, the probability of a crash is only 5%. Amy's car is worth $2000 unless she crashes, in which case it is worth $0. If Amy doesn't have insurance, driving fast isn't worth the risk, so she will alway obey the speed limit. If Amy is offered an insurance contract with full insurance for a premium P with the deductible D, which of the inequalites below is her incentive compatibility constraint that makes sure that she will still obey the speed limit even when she is fully insured? 0.05U(2000 – P – D) + 0.95U(2000 – P) > 0.05U(0 – P – D + 2000) + 0.95U(2000 – P) 0.05U(2000 – P – D) + 0.95U(2000 – P) > 0.1(U(2000 – P – D) + F) + 0.90(U(2000 – P) + F) 0.05U(2000 – P – D) + 0.95U(2000)…
- Jamal has a utility function U = W1/2, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 million for sure, or (B) a gamble that pays $1 million with probability 0.6 and $9 million with probability 0.4. a. b. c. d. Graph Jamal’s utility function. Is he risk averse? Explain. (2+2) Does A or B offer Jamal a higher expected prize? Explain your reasoning with appropriate calculations. (1) Does A or B offer Jamal a higher expected utility? Explain your reasoning with calculations. (2) Should Jamal pick A or B? Why?You are considering two options for your next family vacation. You can visit Disney World or Chicago. Your utility from Disney World is 100 if the weather is clear, and 0 if it rains. Chicago is worth a utility of 70 if the weather is clear and a utility of 40 if the weather is rainy. Also assume that the chance of rain at Disney World is going to be 50% and the chance of rain in Chicago is 40%. As a utility maximizer, should you plan to go to Disney World or Chicago? (Explain using relevant equations)1. Now, imagine that Port Chester decides to crack down on motorists who park illegally by increasing the number of officers issuing parking tickets (thus, raising the probability of a ticket). If the cost of a ticket is $100, and the opportunity cost for the average driver of searching for parking is $12, which of the following probabilities would make the average person stop parking illegally? Assume that people will not park illegally if the expected value of doing so is negative. Check all that apply. A. 9% B. 18% C. 17% D. 10% 2. Alternatively, the city could hold the number of officers constant and discourage parking violations by raising the fine for illegal parking. Suppose the average probability of getting caught for parking illegally is currently 10% citywide, and the average opportunity cost of parking is, again, $12. The fine that would make the average person indifferent between searching for parking and parking illegally is ____ , assuming that people will not…