Suppose that Mira has a utility function given by U=2I+10√I. She is considering two job opportunities. The first job pays a salary of $40,000 for sure. The second job pays a base salary of $20,000 but offers the possibility of a $40,000 bonus on top of your base salary. She believes that there is a probability of p=0.50 that she will earn the bonus. What is the expected salary of the second job? Which offer gives Mira a higher expected utility? Based on this information, is Mira risk adverse, risk neutral, or risk-loving?
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Suppose that Mira has a utility function given by U=2I+10√I. She is considering two job opportunities. The first job pays a salary of $40,000 for sure. The second job pays a base salary of $20,000 but offers the possibility of a $40,000 bonus on top of your base salary. She believes that there is a probability of p=0.50 that she will earn the bonus.
What is the expected salary of the second job?
Which offer gives Mira a higher expected utility?
Based on this information, is Mira risk adverse, risk neutral, or risk-loving?
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- Your Utility function of U = 5, where I is income. You receive an income of 1600 each week from your laundry delivery service in which you face a 50% chance each week of an accident that costs you $700. Calculate your expected income and expected utility.Suppose your utility function for money is a square-root function of its value in US dollars. So, for instance, $400 is worth 20 utils for you, $961 is worth 31 utils for you, and $62.5K is worth 250 utils for you. Now, let’s say your annual salary is $90K, although there is a small risk (p = 0.05) that something catastrophic will happen and reduce your income for the year to $14.4K. An insurance company comes along and offers to insure you against the loss of your salary. The cost of the insurance is $4,736. If you buy the policy and catastrophe strikes, the insurance company will pay out the $75,600 that you would otherwise have lost. From the standpoint of maximizing expected utility, would buying this insurance be a good deal for you? What would be the insurance company’s expected monetary value of selling you the policy?Answer all questions. Imagine you are a person with a chronic disease. If the disease flares up, you will have to take substantial leave from work. The probability of the flare-up is 0.2 (or 20%). If you do not need to take leave from work, your income is $6400. If you take leave from work, your income is $1600. What is the expected value of your income? Expected utility E [= (U(1)] = pU (IS) + (1-p) U (IH) 1600 x 0.2 + 0.8 x 6400 = 5540 Assume that your utility function . What is the expected utility of your income? 0.8 √ 6400 + 0.2 √1600 = 72 utils Suppose a company is offering insurance where your premium is $500 and your payout is $2000. What is your expected utility from taking on this insurance? (Hint: you need to calculate your adjusted earnings in both states)
- 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)…AsapYou are trying to decide between rescuing a puppy or an older dog. You decide to try to assign some numbers to your preferences so you can compare options. You estimate that your utility for a dog that will chew your furniture is 0.1 and your utility for a dog that can go on hikes with you is 0.8. You expect that a puppy will have an 70% chance of chewing your belongings and a 90% chance of going on hikes. What is your expected utility for getting the puppy?
- Stewart will have a total wealth of $12,000 this year, if he stays healthy. Suppose Stewart has a 50% chance of staying healthy and a 50% chance of getting sick. If Stewart gets sick, then he will have to pay $8,000 for medical bills, leaving him $4,000 of total wealth. Under these conditions, Stewarts expected wealth (a.k.a. expected value of wealth) is $8,000. Based on the graph shown below, what level of wealth with certainty (i.e., wealth that Stewart is certain to have) would make Stewart equally as happy as he is when facing the 50% chance of being sick?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…
- Donna just paid $800 for a new iPhone. Apple offers a two year extended warranty for $200 and Donna is considering purchasing it. She has utility given by U(X)=√X. Without the extended warranty, the iPhone becomes worthless if it breaks. What is the minimum probability, p, that the iPhone breaks in the next two years that will cause Donna to prefer to purchase the extended warranty? p= ✓the warranty. If the probability that her phone breaks is p=0.25, Donna will prefer toMicroeconomics 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)Adam is considering what skills to study in online school. Her utility function is based on the income she earns, and is defined by U(I) = I0.8. If she learns the skill of SPSS, she will earn $145,000 per year with probability 1. If she learns the skill of Tableau, she will earn $300,000 per year with probability 0.6 (assuming that she gets the certificate) and $30,000 with probability 0.4 (if she learns without earning a certificate and she has to find a waiter job). a. Is she risk averse, risk neutral, or risk loving? Explain.b. Write out the equation for her expected utility for each skill. c.Which skill will she learn? Show your work. d.Suppose someone offers her insurance for the possibility that she does not get a Tableau certificate. This insurance will provide her an amount of income in addition to the waiter job wages that makes her indifferent between learning SPSS and Tableau. What is this amount, and what is the cost of the insurance? (note: many possible answers)