Consider two individuals, Bjorn and Angela. Bjorn has preferences over wealth represented by a utility function u (W) = In W and Angela has preferences over wealth represented by a utility function u4 (W) = 0.5/W. Using the Arrow-Pratt measure of risk aversion, what can you say (if anything) regarding the risk-aversion of these two individuals? O Bjorn is more risk-averse than Angela. O Angela is more risk-averse than Bjorn. O Both Bjorn and Angela are equally risk-averse. O You would require the levels of wealth to make a statement about the risk-aversion of these individuals.

Consider two individuals, Bjorn and Angela. Bjorn has preferences over wealth represented by a utility function u (W) = In W and Angela has preferences over wealth represented by a utility function u4 (W) = 0.5/W. Using the Arrow-Pratt measure of risk aversion, what can you say (if anything) regarding the risk-aversion of these two individuals? O Bjorn is more risk-averse than Angela. O Angela is more risk-averse than Bjorn. O Both Bjorn and Angela are equally risk-averse. O You would require the levels of wealth to make a statement about the risk-aversion of these individuals.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.2P

See similar textbooks

Similar questions

Suppose that Natasha's utility function is given by u(I) = √/10/, where I represents annual income in thousands of dollars. Is Natasha risk loving, risk neutral, or risk averse? Explain. A. She is risk averse because her utility function exhibits diminishing marginal utility. OB. She is risk loving because her utility function exhibits increasing marginal utility. OC. She is risk neutral because her utility function exhibits constant marginal utility. Suppose that Natasha is currently earning an income of $40,000 (1 = 40) and can earn that income next year with certainty. She is offered a chance to take a new job that offers a 0.6 probability of earning $44,000 and a 0.4 probability of earning $33,000. Should she take the new job? Natasha should not take the new job because her expected utility of 19.85 is less than her current utility. (Round expected utility to three decimal places.)
A risk-averse agent, Andy, has power utility of consumption with riskaversion coefficient γ = 0.5. While standing in line at the conveniencestore, Andy hears that the odds of winning the jackpot in a new statelottery game are 1 in 250. A lottery ticket costs $1. Assume his income isIt = $100. You can assume that there is only one jackpot prize awarded,and there is no chance it will be shared with another player. The lotterywill be drawn shortly after Andy buys the ticket, so you can ignore therole of discounting for time value. For simplicity, assume that ct+1 = 100even if Andy buys the ticket How large would the jackpot have to be in order for Andy to play thelottery? b) What is the fair (expected) value of the lottery with the jackpot youfound in (a)? What is the dollar amount of the risk premium that Andyrequires to play the lottery? Solve for the optimal number of lottery tickets that Andy would buyif the jackpot value were $10,000 (the ticket price, the odds of winning,and Andy’s…
1. 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 o if it does not. Assume that the Bernoulli utility function takes the form u(x) = -e-rx with r>0. How much should she wager? Does her utility function exhibit CARA, DARA, IARA?
Khalid has a utility function U = W1/2, where W is his wealth in millions of dollarsand U is the utility he obtains from the wealth. In a game show, the host offershim a choice between (A) $4 million for sure, or (B) a gamble that pays $1million with probability 0.6 and $9 million with probability 0.4.i. Graph Khalid’s utility function with the help of above utility function. Ishe risk lover? Explain. ii. Does A or B choice offer Khalid a higher expected prize? Explain yourreasoning with appropriate calculations. iii. Does A or B offer Khalid a higher expected utility? Again, show yourcalculations. iv. Should Jamal pick A or B choice? Why?
Jamal has a utility function 1/2 U W5 , where W is hiswealth in millions of dollars and U is the utility heobtains from that wealth. In the final stage of agame show, the host offers Jamal a choice between(A) $4 million for sure and (B) a gamble that pays$1 million with probability 0.6 and $9 million withprobability 0.4.a. Graph Jamal’s utility function. Is he risk averse?Explain.b. Does A or B offer Jamal the higher expectedprize? Explain your reasoning with appropriatecalculations. (Hint: The expected value of arandom variable is the weighted average of thepossible outcomes, where the probabilities arethe weights.)c. Does A or B offer Jamal the higher expectedutility? Again, show your calculations.d. Should Jamal pick A or B? Why?
Jamal has autility function U=W1/2,where W is his wealth in millions of dollars and U is the utitlity he obtains from that wealth.Inthe final stage of a game show,the host offers offers Jamal a choice(A)$4 million dollar for sure,or (B) a gamble that pays $1 million with probability 0.6 and $9million with probability 0.4. a.Graph Jamal's utitility function.Is he risk averse?Explain. b.Does A or B offers Jamal a higher expected price?Explain your reasoning with appropriate calculations. c.Does A or B offer Jamal a higher expected utility? d.Should Jamal pick A or B? Why?
Jamal has a utility function U= W1/2 where Wis his wealth in millions of 'dollars and Uis 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 $1million with a probability of 0.6 and $9 million with a probability of 0.4. a. Graph Jamal's utility function. Is he risk-averse? Explain. b. Does A or B offer, Jamal, a higher expected price? Explain your reasoning with appropriate calculations. (Hint: The expected value of a random variable is the weighted average of the possible outcomes, where the probabilities are the weights.) c. Does A or B offer Jamal a higher expected utility? Again, show your calculations. d. Should Jamal pick A or B? Why?
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
Jin's Utility Function Wealth Utility (Dollars) 60,000 4,000 61,000 4,110 62,000 4,209 63,000 4,288 Refer to Table 27-1. If Jin's current wealth is $61,000, then O his gain in utility from gaining $1,000 is less than his loss in utility from losing $1,000. Jin is not risk averse. O his gain in utility from gaining $1,000 is greater than his loss in utility from losing $1,000. Jin is not risk averse. O his gain in utility from gaining $1,000 is greater than his loss in utility from losing $1,000. Jin is risk averse. his gain in utility from gaining $1,000 is less than his loss in utility from losing $1,000. Jin is risk averse.
2. Suppose you asked the following question to Person A and Person B: "How much are you willing to pay to avoid the following fair gamble – win $100 with 50% chance and lose $100 with 50% chance (thus, Variance is equal to 10,000)?" A's answer- $2 B's answer-$10 Assuming that A and B have CARA utility function, a) compute their absolute risk aversion coefficients (approximately) and b) compute their risk premiums for avoiding the following new gamble - win $500 with 50% chance and lose $500 with 50% chance.
Let us return to the Texaco-Pennzoil example from Chapter 4 and think about Liedtke's risk attitude. Suppose that Liedtke's utility function is given by the utility function in Table 13.5. a Graph this utility function. Based on this graph, how would you classify Liedtke's at- titude toward risk'? b Use the utility function in conjunction with the decision tree sketched in Figure 4.2 to solve Liedtke's problem. With these utilities, what strategy should he pursue? Should he still counteroffer $5 billion? What if Texaco counteroffers $3 billion? Is your an- swer consistent with your response to part a? c Based on this utility function, what is the least amount (approximately) that Liedtke should agree to in a settlement? (Hint: Find a sure amount that gives him the same ex- pected utility that he gets for going to court.) What does this suggest regarding plau- sible counteroffers that Liedtke might make?
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.