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Q: utilit
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A has a utility of money function given by U(y) = y.
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All of A's wealth is in his land and his house; the total value is $1,000,000. With probability 0.4, the house will burn down within the year, and A's remaining wealth will be only the value of the land, which is $28,900. Using at least half page for your diagram, sketch A's indifference curve given the situation above. Put income in the bad state (loss occurs) on the horizontal axis. Identify the following in your diagram:
a. the expected value of the gamble Jackson faces
b, A's certainty equivalent of the gamble
c. the amount Jackson would be charged for actuarially fair full insurance.
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- Arielle is a risk-averse traveler who is planning a trip to Canada. She is planning on carrying $400 in her backpack. Walking the streets of Canada, however, can be dangerous and there is some chance that she will have her backpack stolen. If she is only carrying cash and her backpack is stolen, she will have no money ($0). The probability that her backpack is stolen is 1/5. Finally assume that her preferences over money can be represented by the utility function U(x)=(x)^0.5 Suppose that she has the option to buy traveler’s checks. If her backpack is stolen and she is carrying traveler’s checks then she can have those checks replaced at no cost. National Express charges a fee of $p per $1 traveler’s check. In other words, the price of a $1 traveler’s check is $(1+p). If the purchase of traveler’s checks is a fair bet, then we know that the purchase of traveler checks will not change her expected income. Show that if the purchase is a fair bet, then the price (1+p) = $1.25.Assume that your utility has a natural log function U(W)=ln(W), which is a concave function. Your car is worth $10,000 and your total wealth is $20,000 including the car. There is a 5% chance that a major accident occurs and you have a total loss of $10,000; a 10% chance that a minor accident occurs and you have a loss of $500; 85% chance you will not have any accident. Given these assumptions, how much are you willing to pay for an insurance that provides full coverage against car accidents? Thank you. Regards, Jim CarrollLeora has a monthly income of $20,736. Unfortunately, there is a chance that she will have an accident that will result in costs of $10,736. Thus leaving her an income of only $10,000. The probability of an accident is 0.5. Finally assume that her preferences over income can be represented by the utility function u(x) = 2ln(x).a) What is the expected income? What is Leora’s expected utility (you may leave in log form)? b) What is the certainty equivalent to her situation? What is the risk premium associated with her situation?c) What is the maximum that Leora would be willing to pay for a full insurance policy?d) Illustrate her expected utility, expected wealth, certainty equivalent, the risk premium and her willingness to pay for a full insurance policy in a diagram.
- 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=_____________ If the probability that her phone breaks is p=0.25, will Donna will prefer to buy or not buy the warranty?Suppose that consumers have utility function U(C) = log(C) where C is the consumption level and log is the natural logarithm. Consumers have initial consumptionlevels of 100 and are exposed to the following risk of loss: lose 10 with probability0.4 and lose 5 with probability 0.6. They are considering buying insurance to coverthese losses. What is the fair price for the insurance?
- how then can we find the total utility given q1=24, q2=30 and q3=15Dr. Gambles has a utility function given as U(w)=In(w). Due to the pandemic affecting his consulting business, Dr Gambles faces the prospect of having his wealth reduced to £2 or £75,000 or £100,000 with probabilities of 0.15, 0.25, and 0.60, respectively. Suppose insurance is available that will protect his wealth from this risk. How much would he be willing to pay for such insurance?A consumer has the following utility function u(x)= root x where x is the consumer’s total wealth. The consumer's total wealth is the consumer’s cash plus the value of her house. The consumer has $400 in cash (risk free) plus a house. The house is currently worth $756. With probability 70% nothing happens, and the value of the house stays the same. With probability 30%, high winds will cause $580 in damages to the house (in which case, the house value becomes $176). An insurance company offers to fully insure the house at an insurance premium p. What is the maximum insurance premium that the consumer is willing to pay? The consumer is willing to pay at most p=. The fair insurance premium is . In this example, the associated risk premium is .
- Assume that someone has inherited 2,000 bottles of wine from a rich uncle. He or she intends to drink these bottles over the next 40 years. Suppose that this person’s utility function for wine is given by u(c(t)) = (c(t))0.5, where c(t) is each instant t consumption of bottles. Assume also this person discounts future consumption at the rate δ = 0.05. Hence this person’s goal is to maximize 0ʃ40 e–0.05tu(c(t))dt = 0ʃ40 e–0.05t(c(t))0.5dt. Let x(t) represent the number of bottle of wine remaining at time t, constrained by x(0) = 2,000, x(40) = 0 and dx(t)/dt = – c(t): the stock of remaining bottles at each instant t is decreased by the consumption of bottles at instant t. The current value Hamiltonian expression yields: H = e–0.05t(c(t))0.5 + λ(– c(t)) + x(t)(dλ/dt). This person’s wine consumption decreases at a continuous rate of ??? percent per year. The number of bottles being consumed in the 30th year is approximately ???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?Lukas is a risk-averse farmer. He grows barley on his 1000 acre farm. In a typical year his farm yields 100 bushels of barley per acre. However, in a wet season, the farm only yields 40 bushels per acre. The probability of a typical season is 0.8 and of a wet season is 0.2. Regardless of the productivity of his farm, he expects to earn $3 per bushel (net of all costs of farming). Assume that Lukas has no other income. Write an expression for Lukas's expected utility.