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- Government provided social insurance is most beneficial in the cases where the probability of adverse events is _____ to calculate and the costs of the adverse events are _____. a.hard/low b.easy/high c.easy/low d.hard/highFind the values of Absolute Risk Aversion (ARA) and Relative Risk Aversion (RRA) for all the cases below. . U(C) = C0.5. . U(C) = C2. . U(C) = 5×C. . U(C) = -C-2. . U(C) = -C-7. . U(C) = -e-7C. . U(C) = [1/(1-a)]×C1-a , where a is a constant.Consider an individual with an expected utility function of the form u(w) = √wwhere wrep-resents this individual’s wealth. This individual currently has wealth of $100. This individualfaces a risk of losing $64 with a probability of (1/2). The maximum price that this individualwould pay for insurance that covers the entire $64 loss is?
- Calculate absolute and relative risk aversion for U(x)=ln(x) and U(x)=-e-x where wealth is (w)Exercise 3: Risky Investment Charlie has von Neumann-Morgenstern utility function u(x) = ln x and has wealth W = 250, 000. She is offered the opportunity to purchase a risky project for price P = 160, 000. 1 1 With probability p = 2 the project will be a success and return V > 160, 000. With probability 1 −p = 2 the project will fail and be worthless (i.e. it returns 0). For simplicity assume there is no interest between the time of the investment and the time of its return, that is r = 0 . How large must V be in order for Charlie to want to purchase the risky project? [Hint: What is Charlie’s expected utility is she does not purchase the project? What is Charlie’s expected utility is she purchases the project?]Match the term with its corresponding definition.___ Attributable risk___ Attributable risk percent___ Relative Risk___ Incidence rateA. Compares the incidence rate of the exposed to the incidence rate of theunexposed.B. The proportion of incidence cases among the exposed that are due to theexposure.C. The number of new cases of disease in a population divided by the total numberof persons in the population who were at risk for disease during a specified periodof time.D. The absolute difference in the incidence rate between the exposed and theunexposed.
- John wants to buy a used car. He knows that there are two types of car in the market, plums and lemons. Lemons are worse quality cars and are more likely to break down than plums. John is willing to pay £10, 000 for a plum and £2, 000 for a lemon. Unfortunately, however, he cannot distinguish between the two types. Sellers can offer a warranty that would cover the full cost of any repair needed by the car for y ∗ years. Considering the type and likelihood of problems their cars can have, owners of plums estimate that y years of guarantee would cost them 1000y, owners of lemons estimate that the cost would be 2000y. John knows these estimates and decides to offer £10, 000 if a car comes with y ∗ years of warranty, £2, 000 if a car comes without warranty. For which values of y ∗ is there a separating equilibrium where only owners of plums are willing to offer the y ∗ -years warranty? Clearly explain your reasoning.Clancy has $4800. He plans to bet on a boxing match betweenSullivan and Flanagan. He finds that he can buy coupons for $6 thatwill pay off $10 each if Sullivan wins. He also finds in another storesome coupons that will pay off $10 if Flanagan wins. The Flanagantickets cost $4 each. Clancy believes that the two fighters each have aprobability of ½ of winning. Clancy is a risk averter who tries tomaximize the expected value of the natural log of his wealth. Whichof the following strategies would maximize his expected utility? (a) Don’t Gamble (b) Buy 400 S tickets and 600 F tickets(c) Buy exactly as many F tickets and S tickets (d) Buy 200 S and 300 F(e) Buy 200 S and 600 FSuppose that Winnie the Pooh and Eeyore have the same value function: v(x) = x1/2 for gains and v(x) = -2(|x|)1/2 for losses. The two are also facing the same choice, between (S) $1 for sure and (G) a gamble with a 25% chance of winning $4 and a 75% chance of winning nothing. Winnie the Pooh and Eeyore both subjectively weight probabilities correctly. Winnie the Pooh codes all outcomes as gains; that is, he takes as his reference point winning nothing. For Pooh: What is the value of S? What is the value of G? Which would he choose? Eeyore codes all outcomes as losses; that is, he takes as his reference point winning $4. For Eeyore: What is the value of S? What is the value of G? Which would he choose?
- Farmer Brown faces a 25% chance of there being a year with prolongeddrought, with zero yields and zero profit, and he faces a 75% chance of a normal year, with good yields and$100,000 profit. These probabilities are well-known. Suppose that an insurance company offered a droughtinsurance policy that pays the farmer $100,000 if a prolonged drought occurs. Assume that the farmer’sutility function is u(c) = ln(c). He has initial wealth of $40,000. What is the economic intuition on why X > Y? Confine your answer to at most three sentences.Setup from Question 1) An expected utility maximiser owns a car worth £60000 and has a bank account with £20000. The money in the bank is safe, but there is a 50% probability that the car will be stolen. The utility of wealth for the agent is u(y)=ln(y) and they have no other assets. Setup from question 2)Consider the setup from Question 1. A risk-neutral insurance company is willing to insure the car at the premium of π=£2/3 for every one pound of coverage. Question 3:David is an expected-utility maximizer that likes to drive fast (and reckless at times), so his probability of an accident is 2/3. David’s preferences over wealth are u(w) = √?. Suppose that David’s initial wealth is $100. If David has an accident, he incurs a $51 loss. How much is the risk premium David willing to pay to be as well off in case of accident or not?