Sophie is offered a performance based wage that will either be equal to $4,200 or to $3,600, each with a probability of 50%. Sophie says that getting $3,900 for certain would be as good as being offered that random wage. Which, of the following sentences, is true? options: Sophie is risk averse and her risk premium is zero. Sophie is risk neutral and her risk premium is zero. Sophie is risk averse and her risk premium is $300. Sophie is risk neutral and her risk premium is $300.

Sophie is offered a performance based wage that will either be equal to $4,200 or to $3,600, each with a probability of 50%. Sophie says that getting $3,900 for certain would be as good as being offered that random wage. Which, of the following sentences, is true? options: Sophie is risk averse and her risk premium is zero. Sophie is risk neutral and her risk premium is zero. Sophie is risk averse and her risk premium is $300. Sophie is risk neutral and her risk premium is $300.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.5P

See similar textbooks

Similar questions

Natasha has utility function u(I) = (10*I)0.5, where I is her annual income (in thousands). (a) Is she a risk loving, risk averse or risk neutral individual? She is [risk loving, risk adverse, risk neutral] , as her utility function is [concave, convex, linear] (b) Suppose that she is currently earning an income of $40,000 (I = 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. She should [take, not take] the new job because her expected utility of (approximately) [18.27,19.82,20,20.95,21.14] is [greater than, less than, equal to] her current utility of [18.27,19.85,20,20.95,21.14] .
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 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. a. b. c. d. Graph Jamal’s utility function. Is he risk averse? Explain. (2+2) Does A or B offer Jamal a higher expected prize? Explain your reasoning with appropriate calculations. (1) Does A or B offer Jamal a higher expected utility? Explain your reasoning with calculations. (2) 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?
2. Maria has $100. There is a 50% that she will lose all of it. Her utility as a functionof wealth is u(c) = √c. a. What is the maximum amount she would be willing to pay to fully insure againstthe 50% probability of the loss? b. Is she risk averse, risk loving, or risk neutral?
Suppose that Mira has a utility function given by U=2I+10√I. She is considering two job opportunities. The first job pays a salary of $40,000 for sure. The second job pays a base salary of $20,000 but offers the possibility of a $40,000 bonus on top of your base salary. She believes that there is a probability of p=0.50 that she will earn the bonus. What is the expected salary of the second job? Which offer gives Mira a higher expected utility? Based on this information, is Mira risk adverse, risk neutral, or risk-loving?
Consider the model of competitive insurance. Peter is a risk averse individual with the utility function u(w) = w0.5. His current wealth is $300 and with probability 1/2 he will incur a loss of D = $240, but with probability 1/2 he will incur no loss. Ann has the same utility u(w) = w0.5 and current wealth $300 as Peter, but a different probability of loss: she will incur a loss of D = $240 with probability 0.3, and no loss with probability 0.7. In the separating equilibrium Peter is offered actuarially fair full insurance contract, so his wealth is equal to $180, whether loss happens or not. What amount of insurance (approximately) will Ann be offered an insurance contract with?
David is an expected-utility maximizer that likes to drive fast (and reckless at times), so his probability of an accident is 2/3. David’s preferences over wealth are u(w) = √?. Suppose that David’s initial wealth is $100. If David has an accident, he incurs a $51 loss. How much is the risk premium David willing to pay to be as well off in case of accident or not?
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?
Abigail is a consumer whose utility is a function of her total wealth W. u(W ) = log W. Suppose that Abigail begins with initial wealth of A = 100 but will suffer a serious illness with probability π = 0.15 which will require extensive treatment costing L = 80. To hedge against this risk, Abigail considers buying a health insurance policy. She may buy as much insurance I as she wishes at a cost of p per dollar of coverage, so her payoffs in each state are Healthy Ill Probability 0.85 0.15 No Insurance 100 20 Claim 0 I Premium −pI −pI a) Show that Abigail is risk averse. b) Suppose that the insurance premiums are actuarially fair so that p = 0. Find Abigail’s expected wealth E[W ] and expected utility E[u(W )] as functions of how much insurance she buys I. c) How much insurance should Abigail buy?
Abigail is a consumer whose utility is a function of her total wealth W. u(W ) = log W. Suppose that Abigail begins with initial wealth of A = 100 but will suffer a serious illness with probability π = 0.15 which will require extensive treatment costing L = 80. To hedge against this risk, Abigail considers buying a health insurance policy. She may buy as much insurance I as she wishes at a cost of p per dollar of coverage, so her payoffs in each state are Healthy Ill Probability 0.85 0.15 No Insurance 100 20 Claim 0 I Premium −pI −pI a) Now suppose that the insurance company raises premiums to p = 0.2 so that they are no longer actuarially fair. Find Abigail’s expected wealth E[W ] and expected utility E[u(W )]. b) How much insurance should Abigail buy now?
Suppose you must choose between the two prospects, (40,000, 0.025) or (1,000): The prospect of winning 40,000 with a probability of 2.5% or winning 1,000 with certainty. Suppose, too, that the following three graphs represent your utility function (according to expected utility theory) and your weighting and value scales (according to prospect theory). Finally, suppose that your current wealth is 20,000. a. What is the expected utility for the two prospects? b. Based on expected utility theory, which prospect would you choose? Why? c. According to prospect theory, what are the values for each of the prospects? d. Based on prospect theory, which prospect would you choose? Why? e. Why is your decision different under the two theories? (Hint: what is one of the common human traits that prospect theory captures that expected utility theory cannot?)