PROBLEM (3) (Regret Aversion, Gale's Roulette Wheels) Consider the regret utilityu(x, y) = {1 if x>y, 0 if x=y, and -1 if x

a) In order to determine the expected regret utilities, U(A/B), U(B/C), and U(C/A), we must first…

Answered: PROBLEM (3) (Regret Aversion, Gale's…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Sadija has a concave utility function of U(W) = In(W). She has inherited a ring from a relative, but she is unsure about its value. She believes that it is worth £6,000 with a probability of 1/3 and £3,000 with a probability of 2/3. a. Ahmed would like to buy the ring from her. Which price would he need to offer for Sadija' utility to remain unchanged after the sale? b. In fact, Ahmed offers £4,000 for the ring. What can you infer about Ahmed?
A buyer wants to purchase a house from a seller. Let v be the quality of this house. The quality v is known to the seller but unobservable to the buyer. The buyer thinks the chance that v=$1k is 20%, v=$10k is 40%, and v=$50k is 40%. The seller’s valuation of the house is v and the buyer’s valuation of the house is 2v a) Suppose both the buyer and the seller see the value of v . Also suppose the transaction price equals the value of v (i.e. if =10k, then the buyer pays 10k for the house). Calculate the buyer’s expected profit before seeing the value of b) Suppose only the seller sees v. Also suppose the buyer is allowed to make any offer to the seller and the seller accepts it if the offered price is above or equals to v. What is the buyer’s profit maximizing offer? What is the buyer’s maximum profit? c) Base on your answers from (a) and (b), what is the value of information (i.e. the benefits of seeing the value of ) to the buyer?
4. Kate has von Neumann-Morgenstern utility function U(x1,x2) = m7. She currently has $2025. a. Would she be willing to undertake a gamble that involves a gain $2875 with probability + and a loss of $1125 with probability ? Show your work and explain your answer. b. Would she be willing to undertake a gamble that involves a gain $2599 with probability and a loss of $800 with probability ? Show your work and explain your answer.
Let b(p,s,t) be the bet that pays out s with probability p and t with probability 1−p. We make the three following statements: S1: The CME for b is the value m such that u(m)=E[u(b(p,s,t))]. S2: A risk averse attitude corresponds to the case CME smaller than E[b(p,s,t))]. S3: A risk seeking attitude corresponds to a convex utility function. Are these statements true or false?
Lucy and Henry each have $1652. Each knows that with 0.1 probability, they will lose 85% of their wealth. They both have the option of buying a units of insurance, with each unit costing $0.1. Each unit of insurance pays out $1 in the event the loss occurs. The cost of the insurance policy is paid regardless of whether the loss is incurred. Lucy's utility is given by u²(x) = x, Henry's utility is given by u¹(x) = √√x. Answer the following: (If rounding is needed, only round at the end and write your answer to three decimal places.) a) Without insurance, what is the expected value of the loss? b) c) d). e) ( For Henry, facing the "lottery " above without any insurance is as bad as losing how many dollars for sure? Find Lucy's utility maximising choice of a. If more than 1 exist, enter the largest a. Now suppose insurance costs $0.2. Find Lucy's utility maximising choice of a. If more than 1 exist, enter the largest a. What is Henry's utility maximising choice of a with the new price of…
Y8
Choice under uncertainty. Consider a coin-toss game in which the player gets $30 if they win, and $5 if they lose. The probability of winning is 50%. (a) Alan is (just) willing to pay $15 to play this game. What is Alan’s attitude to risk? Show your work.(b) Assume a market with many identical Alans, who are all forced to pay $15 to play this coin-toss game. An insurer offers an insurance policy to protect the Alans from the risk. What would be the fair (zero profit) premium on this policy? i need help with question B please.
Firms A and B are contemplating whether or not to invest in R&D. Each has two options: “Invest” and “Abstain.” A firm that invests will invent product X with a probability of 0.5, whereas a firm that abstains is incapable of invention. Investment costs $6. If a firm doesn’t invent X, it makes $0 in revenue. If a firm invests and is the only one to invent X, it becomes a monopolist and generates $20 in revenue. If both firms invent X, each firm becomes a duopolist, and generates $8 in revenue. Revenues are gross figures (i.e. they are not net of investment costs), and there are no costs besides investments costs (i.e. no variable cost of production etc.). The firms are risk-neutral entities, and are uninformed of each other’s investment decisions. The “research and development” game is best analyzed as a simultaneous move game, because the parties lack information about each other’s investment decisions. Find the Nash Equilibria (or Equilibrium) of the “research and development”…
1 Q1. Jerry has wealth of $60 and derives utility from this according to the utility function U(w) = 1 - Where w is his wealth. Jerry now finds a lottery ticket (the drawing takes place the next day) that offers a 50% chance of winning $5. W a) What is the expected value of Jerry if he takes the lottery ticket? (pay attention, it's not jerry's wealth) b) What is the minimum amount for which Jerry would be willing-to-sell the ticket? (Hint: sets a price of p, and at the minimum amount, the expected utility of selling and not selling should be the same) c) Which is bigger, your answer to (a) or (b), and suggest whether Jerry is a risk averse person based on the previous conclusion? d) If he does not sell the ticket, what is Jerry's cost of risk? (The cost of risk is the difference between the expected wealth and the certainty equivalence)

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PROBLEM (3) (Regret Aversion, Gale's Roulette Wheels) Consider the regret utility u(x, y) = {1 if x>y, 0 if x=y, and -1 if x