Suppose that left-handed people are more prone to injury than right-handed people. Lefties have an 80 percent chance of suffering an injury leading to a $1,000 loss (in terms of medical expenses and the monetary equivalent of pain and suffering) but righties have only a 20 percent chance of suffering such an injury. The population contains equal numbers of lefties and righties. Individuals all have logarithmic utility-of-wealth functions and initial wealth of $10,000. Insurance is provided by a monopoly company. a.Compute the “first best” for the monopoly insurer b.Try to characterize the “second best” contracts as well as you can (start from the profit maximization problem and write down the four relevant constraints, point out which constraints matter, which ones don’t, proceed as much as you can, etc.). In addition: assume perfectly competitive insurance market instead of monopoly, and find (i) the first best and (ii) the second-best contracts.

Suppose that left-handed people are more prone to injury than right-handed people. Lefties have an 80 percent chance of suffering an injury leading to a $1,000 loss (in terms of medical expenses and the monetary equivalent of pain and suffering) but righties have only a 20 percent chance of suffering such an injury. The population contains equal numbers of lefties and righties. Individuals all have logarithmic utility-of-wealth functions and initial wealth of $10,000. Insurance is provided by a monopoly company. a.Compute the “first best” for the monopoly insurer b.Try to characterize the “second best” contracts as well as you can (start from the profit maximization problem and write down the four relevant constraints, point out which constraints matter, which ones don’t, proceed as much as you can, etc.). In addition: assume perfectly competitive insurance market instead of monopoly, and find (i) the first best and (ii) the second-best contracts.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.2P

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Suppose that left-handed people are more prone to injury than right-handed people. Lefties have an 80 percent chance of suffering an injury leading to a $1,000 loss (in terms of medical expenses and the monetary equivalent of pain and suffering) but righties have only a 20 percent chance of suffering such an injury. The population contains equal numbers of lefties and righties. Individuals all have logarithmic utility-of-wealth functions and initial wealth of $10,000. Assume perfectly competitive insurance market and find (i) the first best and (ii) the second-best contracts.
Zac has a current wealth of £400. He gets an email offering him the chance to enter a prize draw that gives £500 prize with a 25% chance and £0 the rest of the time. Zac is an expected utility maximiser with a von Neumann-Morgenstern utility in wealth w of u (w) = Vw. What is the minimum price at which Zac will sell his rights to enter the draw? £106.25 £506.25 O E31.25 £22.5 £56.25
Jamal has a utility function U = W1/2, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 million for sure, or (B) a gamble that pays $1 million with probability 0.6 and $9 million with probability 0.4. (1) Does A or B offer Jamal a higher expected utility? Explain your reasoning with calculations. (2) Should Jamal pick A or B? Why? I would like help with the unanswered last parts of the questions.
Economists define the ‘certainty equivalent’ of a risky stream of income as the amount of guaranteed money an individual would accept instead of taking a risk. The certainty equivalent varies between individuals based on their risk preference. Consider a risky bet that involves a 25% chance of losing $5,000 or a 75% winning $5,000 for an individual with starting income of $50,000. Calculate the certainty equivalent income that provides the same utility as this bet for individuals with these different utility functions: 1. U(I) = I 2. U(I) = I–√ 3. U(I) = ln(I)where ln represents the natural logarithm function Type the numerical answers in the corresponding numbered boxes below. Round your answers to two decimal places. Do not use $ or , in your answers. (for example, enter 45223.45 or 46500.00) What can you conclude about the relative level of risk aversion for these three individuals? Explain.
Gary likes to gamble. Donna offers to bet him $31 on the outcome of a boat race. If Gary's boat wins, Donna would give him $31. If Gary's boat does not win, Gary would give her $31. Gary's utility function is p1x^21+p2x^22, where P₁ and p2 are the probabilities of events 1 and 2 and where x₁ and x₂ are his wealth if events 1 and 2 occur respectively. Gary's total wealth is currently only $80 and he believes that the probability that he will win the race is 0.3. Which of the following is correct? (please submit the number corresponding to the correct answer). 1. Taking the bet would reduce his expected utility. 2. Taking the bet would leave his expected utility unchanged. 3. Taking the bet would increase his expected utility. 4. There is not enough information to determine whether taking the bet would increase or decrease his expected utility. 5. The information given in the problem is self-contradictory.
Gary likes to gamble. Donna offers to bet him $31 on the outcome of a boat race. If Gary’s boat wins, Donna would give him $31. If Gary’s boat does not win, Gary would give her $31. Gary’s utility function is p1x^21+p2x^22, where p1 and p2 are the probabilities of events 1 and 2 and where x1 and x2 are his wealth if events 1 and 2 occur respectively. Gary’s total wealth is currently only $80 and he believes that the probability that he will win the race is 0.3. Which of the following is correct? (please submit the number corresponding to the correct answer). Taking the bet would reduce his expected utility. Taking the bet would leave his expected utility unchanged. Taking the bet would increase his expected utility. There is not enough information to determine whether taking the bet would increase or decrease his expected utility. The information given in the problem is self-contradictory.
Consider a person with the following utility function over wealth: u(w) = ew, where e is the exponential function (approximately equal to 2.7183) and w = wealth in hundreds of thousands of dollars. Suppose that this person has a 40% chance of wealth of $100,000 and a 60% chance of wealth of $2,000,000 as summarized by P(0.40, $100,000, $2,000,000). a. What is the expected value of wealth? b. Construct a graph of this utility function . c. Is this person risk averse, risk neutral, or a risk seeker? d. What is this person’s certainty equivalent for the prospect?
Let W0 represents an individual’s current wealth and U(W) is this individual’s von Neumann-Morgenstern utility index (or utility function) that reflects how s/he feels about various levels of wealth. Assume this individual marginal utility of wealth decreases a wealth increases. Which of the following statements is true? a. This individual will prefer to keep his or her current wealth rather than taking a fair gamble. b. For this individual, a 50-50 chance of winning or losing c dollars yields less expected utility than does refusing the bet. c. This individual is said to be risk averse. d. All of the above.
The Anderson family lives in the Arizona wilderness. Their property is at risk for being destroyed by a forest fire. It is estimated that each year the Anderson face a 5 percent probability of a $500,000 loss. The Anderson family has a utility function of U = W 0.7, where W is wealth and measured in dollars. Suppose their current wealth is $1 million. What is the family's expected loss from fire? What is the Anderson family's expected utility? What is the maximum value the Andersons will pay for insurance to completely protect their home? What is the risk premium?
Amy likes to go fast in her new Mustang GT. Their utility function over wealth is v(w) where w is wealth. If Amy goes fast she gets an increase in utility equal to F. But when Amy drives fast, she is more likely to crash: when she drives fast the probability of a crash is 10%, but when she obeys the speed limit, the probability of a crash is only 5%. Amy's car is worth $2000 unless she crashes, in which case it is worth $0. If Amy doesn't have insurance, driving fast isn't worth the risk, so she will alway obey the speed limit. If Amy is offered an insurance contract with full insurance for a premium P with the deductible D, which of the inequalites below is her incentive compatibility constraint that makes sure that she will still obey the speed limit even when she is fully insured? 0.05U(2000 – P – D) + 0.95U(2000 – P) > 0.05U(0 – P – D + 2000) + 0.95U(2000 – P) 0.05U(2000 – P – D) + 0.95U(2000 – P) > 0.1(U(2000 – P – D) + F) + 0.90(U(2000 – P) + F) 0.05U(2000 – P – D) + 0.95U(2000)…
Economists define the 'certainty equivalent' of a risky stream of income as the amount of guaranteed money an individual would accept instead of taking a risk. The certainty equivalent varies between individuals based on their risk preference. Consider a risky bet that involves a 50-50 chance of losing $5,000 or winning $5,000 for an individual with starting income of $50,000. Calculate the certainty equivalent income that provides the same utility as this bet for individuals with these different utility functions: a. U(1) Vi b. U(1) = In(1) where In represents the natural logarithm function C. U(I) = -1/1 d. What can you conclude about the relative level of risk aversion for these three individuals? e What would be the certainty equivalent income for this bet for a risk neutral individual? f. What is the likelihood that a profit maximizing risk neutral insurance company would be willing and able to purchase these bets from the individuals in a, b and c? Explain.
Microeconomics Wilfred’s expected utility function is px1^0.5+(1−p)x2^0.5, where p is the probability that he consumes x1 and 1 - p is the probability that he consumes x2. Wilfred is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2500 with probability p = 0.4 and $3700 with probability 1 - p. Wilfred will choose the sure payment if Z > CE and the lottery if Z < CE, where the value of CE is equal to ___ (please round your final answer to two decimal places if necessary)