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- Calculate absolute and relative risk aversion for U(x)=ln(x) and U(x)=-e-x where wealth is (w)Find 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.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.
- The application which provides a way of revising conditional probabilities by using available information and provisions for revising conditional probabilities with other information that is useful for management decision making is called? Select one: a. Bayes’ theorem. b. overinvolvement ratios. c. probability rules. d. empirical formula.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?]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.
- The expected value of sample information (EVSI) is equal to A) EMV with perfect information EMV without information B) EMV with free information EMV without information C) EMV with posterior information EMV with prior information D) EMV with free perfect information EMV free information E) none of these choicesIn the CRRA utility family u(x) = x^(1−γ). If this individual has autility where γ = 0.01, would he prefer the payment of $320 or the gamble?Suppose that there are two types of workers: high and low. Employers cannot distinguish between different types during an interview. Employers value high type at $200,000 and low type at $100,000. Employers are in a competitive market (i.e. zero profit applies). High type workers have a reservation wage of 140,000 and low type workers have a reservation wage of 80,000. Suppose that 50% of all workers are high type. The productivities, reservation wages, and the probabilities are common knowledge). What wage would the employers offer? Please explain the solution!
- A risk averse individual will always choose the safe but less profitable activity instead of the riskier but more profitable activity. True or FalseDr. 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?Consider a gamble/lottery in which a coin is tossed rapidly until a tail comes up. 2m rupee is given if the tail comes up at the mth toss. Let the individual be risk neutral, having u(x) = x where x is the amount of winning. Find the expected utility from the lottery.
