Suppose a person chooses to play a gamble that is free to play. In this gamble, they have a 10% chance of $100.00, and a 90% chance of nothing. Their utility function is represented in the following equation: U=W 1/2 where W is equal to the amount of "winnings" (or the income). Suppose now Brown Insurance Company offers the person the option of purchasing insurance to insure they will win the $100. What is the minimum amount Brown Insurance would charge you to insure your win? 0.90 0.99 01 O 10

Suppose a person chooses to play a gamble that is free to play. In this gamble, they have a 10% chance of $100.00, and a 90% chance of nothing. Their utility function is represented in the following equation: U=W 1/2 where W is equal to the amount of "winnings" (or the income). Suppose now Brown Insurance Company offers the person the option of purchasing insurance to insure they will win the $100. What is the minimum amount Brown Insurance would charge you to insure your win? 0.90 0.99 01 O 10

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.5P

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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.
Victoria founded a start-up several years ago, together with her Macedonian friends. At first, she was fairly poor and therefore very afraid of taking risks. Any negative shock could send the company into bankruptcy. Nowadays her business is thriving, stretching across several markets from Europe to Asia. Victoria no longer worries about taking monetary risks. In fact she enjoys a good gamble over horse races from time to time. How would you draw Victoria's utility function in a way that describes her changing taste for risk as her wealth increased? Please draw a graph and comment. Please do fast ASAP fast
Consider two individuals whose utility function over wealth I is ?(?) = √?. Both people face a 10 percent chance of getting sick, and foreach the total cost of illness equals $50,000. Suppose person A has a total net worth of $100,000, and person B has a total net worth of $1,000,000. Both people have the option to buy an actuarially fair insurance contract that would fully insure them against the cost of the illness. a. Using expected utility calculations, show that person A would certainly buy full, actuarially fair insurance. b. Suppose an insurance company wants to maximize profits and wants to charge each customer the maximum price they are willing to pay. How much should the insurance company charge each client so that both buy the contract? c. What is surprising about your result in part b? What does this tell you about how insurance companies may be pricing health insurance contracts in the real world?
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?
A woman with current wealth X has the opportunity to bet an amount on the occurrence of an event that she knows will occur with probability P. If she wagers W, she will received 2W, if the event occur and if it does not. Assume that the Bernoulli utility function takes the form u(x) = with r > 0. How much should she wager? Does her utility function exhibit CARA, DARA, IARA? Alex plays football for a local club in Kumasi. If he does not suffer any injury by the end of the season, he will get a professional contract with Kotoko, which is worth $10,000. If he is injured though, he will get a contract as a fitness coach worth $100. The probability of the injury is 10%. Describe the lottery What is the expected value of this lottery? What is the expected utility of this lottery if u(x) = Assume he could buy insurance at price P that could pay $9,900 in case of injury. What is the highest value of P that makes it worthwhile for Alex to purchase insurance? What is the certainty…
Consider the following claim: “If a decision maker prefers one given lottery that yields $x with probability 1 over another given lottery whose expected return is $x, then we can fully characterize the agent's risk attitude. That is, this information comparing two given lotteries is enough to determine if the decision maker is risk averse, risk loving or risk neutral.” If this claim is TRUE, then provide a proof. If it is FALSE, then prove your argument by providing an explanation.
. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain.
Let U(x)= x^(beta/2) denote an agent's utility function, where Beta > 0 is a parameter that defines the agent's attitude towards risk. Consider a gamble that pays a prize X = 10 with probability 0.2, a price X = 50 with probability 0.4 and a price X = 100 with probability 0.4. Compute the agentís expected utility for such gamble and find the value of Beta such that the agentis risk neutral? Suppose B= 1, what is the certainty equivalent of the gamble described above? What is the Arrow-Pratt measure of absolute risk aversion?
An agent makes decisions using U(ct) = (ct−χct−1)1−γ 1−γ . Answer the following: (a) Suppose χ = 0. Derive an expression for the coefficient of relative risk aversion RR(ct)? (b) Suppose 0 < χ ≤ 1. Derive an expression for the coefficient of relative risk aversion RR(ct)?
Arielle is a risk-averse traveler who is planning a trip to Canada. She is planning on carrying $400 in her backpack. Walking the streets of Canada, however, can be dangerous and there is some chance that she will have her backpack stolen. If she is only carrying cash and her backpack is stolen, she will have no money ($0). The probability that her backpack is stolen is 1/5. Finally assume that her preferences over money can be represented by the utility function U(x)=(x)^0.5 Suppose that she has the option to buy traveler’s checks. If her backpack is stolen and she is carrying traveler’s checks then she can have those checks replaced at no cost. National Express charges a fee of $p per $1 traveler’s check. In other words, the price of a $1 traveler’s check is $(1+p). If the purchase of traveler’s checks is a fair bet, then we know that the purchase of traveler checks will not change her expected income. Show that if the purchase is a fair bet, then the price (1+p) = $1.25.
Consider the St. Petersburg Paradox problem first discussed by Daniel Bernoulli in 1738. The game consists of tossing a coin. The player gets a payoff of 2^n where n is the number of times the coin is tossed to get the first head. So, if the sequence of tosses yields TTTH, you get a payoff of 2^4 this payoff occurs with probability (1/2^4). Compute the expected value of playing this game. Next, assume that utility U is a function of wealth X given by U = X.5 and that X = $1,000,000. In this part of the question, assume that the game ends if the first head has not occurred after 40 tosses of the coin. In that case, the payoff is 240 and the game is over. What is the expected payout of this game? Finally, what is the most you would pay to play the game if you require that your expected utility after playing the game must be equal to your utility before playing the game? Use the Goal Seek function (found in Data, What-If Analysis) in Excel.
. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index u(x) √x . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain.