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- 3. Assume W(F)=F². Probability of sun is 2/3 and hurricane, 1/3. Plot the IC that runs through Fs, Fh=(400, 400). Plot the constant expected consumption line that run through the same point. Is this person risk neutral or risk averse?Uncertainty and willingness to pay for insurance. Utility = (Wealth)1/3 Prob(flood) = .04 Prob(no flood) = .96 Total wealth if flood = $100,000. Total Wealth if no flood = $800,000. Find: (i) expected value, (ii) expected utility, (iii) certainty equivalent, and (iv) maximum willingness to pay for a policy that provides 100% flood insurance coverage. Draw the utility function and include all solved values on the diagram. What is the average gross profit per insurance customer, if each customer is charged his own maximum willingness to pay?Q1. A farmer believes there is a 50-50 chance that the next growing season will be abnormally rainy. His expected utility function has the form Expected utility = 0.5lnYNR + 0.5lnYR Where and represent the farmers income in the state of ‘normal rain’ and ‘rainy’ respectively. Suppose the farmer must choose between two crops that promise the following income prospects Crop YNR YR Wheat $83,000 $10,000 Maize $83,000 $15000 What mix of wheat and maize would provide maximum expected utility to this farmer?
- A lottery system has balls numbered 1 to 65 and randomly selects 6 of the lottery balls. There is only one prize of $ 10,000,000.00 which is awarded only it a lottery player selects the correct set of 6 lottery balls. a) If a lottery ticket costs $ 5.00, what is a lottery player's expected value? b) How much would the lottery prize have to be worth if it was to be a fair game? (Note: Include dollar signs in your answer)Seung’s utility function is given by U = ln(C), where C is consumption. She makes $30,000 per year and enjoy jumping out of airplanes. There's a 5% chance that in the next year, she will break both legs, incur medical costs of $15,000, and lose an additional $5,000 from missing work. (a) What is Seung’s expected utility without insurance? (b) Suppose Seung can buy insurance that will cover the medical expenses but not the forgone part of her salary. How much would an actuarially fair policy cost, and what is her expected utility if she buys it? (c) Suppose Seung can buy insurance that will cover her medical expenses and forgone salary. How much would such a policy cost if it's actuarially fair, and what is her expected utility if she buys it?Mr Usu has an expected utility function with u(x) = x0.5. He is analyzing an investment opportunity that promises to pay out $1,160 with prob. 0.6 and $2,800 with prob. 0.4. What is the expected utility of this opportunity?
- A person's utility function is U = C1/2 . C is the amount of consumption they have in a given period. Their income is $40,000/year and there is a 2% chance that they'll be involved in a catastrophic accident that will cost them $30,000 next year. a. Calculate the actuarially fair insurance premium. What would your expected utility be if you were to purchase the actuarially fair insurance premium? b. What is the most you would be willing to pay for insurance, given your utility function?Seung's utility function is given by U - C^(1/2), where C is consumption and C^(1/2) is the square root of consumption. She makes $50,625 per year and enjoys jumping out of airplanes. There's a 5% chance that in the next year, she will break both legs, incur medical costs of $30,000, and lose an additional $5,000 from missing work. a. What is Seung's expected utility without insurance? b. Suppose Seung can buy insurance that will cover the medical expenses but not the forgone part of her salary. How much would an actuarially fair policy cost, and what is the expected utility if she buys it? Policy cost: $___ Expected utility: ___ c. Suppose Seung can buy insurance that will cover her medical expenses and foregone salary. How much would such a policy cost if it's actuarially fair, and what is her expected utility if she buys it? Policy cost: $___ Expected Utility: ___B. Richard's nickname is "No-Risk Rick" because he is an extremely risk-averse individual. His utility function is given by U(W) = √W. where W represents his current wealth in dollars. He currently has $100 worth of property, but there is a 50% chance that all of it will be stolen. What is Richard's expect wealth and expected utility of wealth? An insurance company offers to reimburse Richard for his loss if the money is stolen. What is the most that Richard would pay for such a policy? Explain. Please solve this with in 1 hour
- a. Consider the Oakdale Furniture Company described in the given problem. Under what circumstances might the major portion of the usage of the glue be predictable?b. If the demand were predictable, would you want to use a probability law todescribe it? Under what circumstances might the use of a probability model of demand be justified even if the demand could be predicted exactly?Suppose that the probability of low demand is 0.75. (a) What is the maximum Expected Monetary Value (EMV)? (show calculation steps) (b) What is the Expected Value of Perfect Information (EVPI)? Hint: EVPI=EVwPI-maximum EMV.Suppose Grace and Lisa are to go to dinner. Lisa is visiting Grace from outof town, and they are to meet at a local restaurant. When Lisa lived in town,they had two favorite restaurants: Bel Loc Diner and the Corner Stable. Ofcourse, Lisa’s information is out of date, but Grace knows which is betterthese days. Assume that the probability that the Bel Loc Diner is better isp > 1/2 and the probability that the Corner Stable is better is 1 - p. Naturedetermines which restaurant Grace thinks is better. Grace then sends amessage to Lisa, either “Let’s go to the Bel Loc Diner,” “Let’s go to theCorner Stable,” or “I don’t know [which is better].” Lisa receives the message, and then Grace and Lisa simultaneously decide which restaurant to go to. Payoffs are such that Grace and Lisa want to go to the same restaurant, but they prefer it to be the one that Grace thinks is better. More specifically, if, in fact, the Bel Loc Diner is better, then the payoffs from theiractions are as shown in the…