Suppose that Jim has a von Neumann-Morgenstern utility function: U(c) = c². %3D Based on his utility function, we can tell that Jim is There is not enough information to determine his risk preference. risk averse. risk neutral. risk loving.
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- Suppose your wealth is 8 and you are considering a bet of a 50% chance of winning $4 and a 50% chance of losing $4. What is your risk premium given you have In utility ? Draw a diagram and label the relevant values.Joey has utility function 1+√x where x is the amount of money he has. He is... A) Cannot tell from the information provided B) Risk averse C) Risk Netutral D) Risk LovingThe value of a successful project is $420,000; the probabilities of success are 1/2 with good supervision and 1/4 without. The manager is risk neutral, not risk averse as in the text, so his expected utility equals his expected income minus his disutility of effort. He can get other jobs paying $90,000, and his disutility for exerting the extra effort for good supervision on your project is $100,000. (a) Show that inducing high effort would require the firm to offer a compensation scheme with a negative base salary; that is, if the project fails, the manager pays the firm an amount stipulated in the scheme. (b) How might a negative base salary be implemented in reality? (c) Show that if a negative base salary is not feasible, then the firm does better to settle for the low-pay, low-effort situation.
- Natalie entered a raffle recently and never checked her tickets. She has recently learned the exact number of the other unchecked tickets. Based on this information she knows that there is a 30% chance that she has won the raffle prize of $1,600. If she does not win the raffle her wealth will be zero. Natalie has a von Neumann- Morgenstern utility such that she wants to maximize the expected value of cvc, where cc is total wealth. What is the minimum price for which Natalie would sell her raffle tickets? $The von-Neumann Morgenstern utility function is of the form u(e) - In(e). There is a lottery over consumption outcomes: with probability 0.3, the consumption will be 1 and with probability 0.7 the consumption will be 3; Compute the risk premium (round to 2 decimals).Suppose Xavier has tickets to the Super Bowl, but is terribly ill with a noncontagious infection. How would a decision maker perform his economic calculation on whether to attend the game, based on the traditional model of risk behavior?
- Persons A and B are roommates. Person A smokes and Person B does not. The index s measures how smoky the room is. It varies from s=0, where there is no smoke in the room, to s=1, when the room is filled with smoke. Thus, 1-s measures how "clean" the air in the room is. Person A's utility function is UA(XA,S)=XA+In(1+s), where xA is the amount of money Person A owns. Person B's utility function is uB(XB,1s)%3D3XB+2(1-s), where Xg is the amount of money Person B owns. Each person starts with an endowment of 5 units of money. Persch B has the legal right to a smoke-free room and there is a market for "emission right." At the Walrasian equilibrium, what will be the (per unit of smoke index) price p of the emission rights if the price of money is 1? O a. None of the other answers. O b. p=2/3 O c. p=1 O d. p=3/2 О е. р31/6Which of the following utility functions exhibits constant absolute risk aversion? a. U(W) =W-0.5W² b. U(W) = -e-w c. U (W) = W d. U(W) = In WMicroeconomics 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)
- Persons A and B are roommates. Person A smokes and Person B does not. The index s measures how smoky the room is. It varies from s=0, when there is no smoke in the room, to s=1, when the room is filled with smoke. Thus, 1-s measures how "clean" the air in the room is. Person A's utility function is ua(XA,s)=Xa.S, where xA is the amount of money Person A owns. Person B's utility function is ug(xg, 1s)=Xg .(1-s)³, where xg is the amount of money Person B owns. Each person starts with an endowment of 5 units of money. Person A has the legal right to a fill up the room with smoke and there exists a market for smoke "abatements". At the Walrasian equilibrium, how much money will person B be left with? а. Хв31.25 ОБ. Хв32.25 O c. XB=0.25 O d. Xg=0.25 е. None of the other answers.Draw a utility function over income u(I) that describes a man who is a risk lover when his income is low but risk averse when his income is high. 1.) Using the 3-point curved line drawing tool, draw the low income portion of his utility function. Label it U₁. 2.) Using the 3-point curved line drawing tool, draw the high income portion of his utility function. Label it UH. Carefully follow the instructions above, and only draw the required objects. C 500- 450- 400- 350- 300- 250- 200- 150- 100- 50- 0 Utility 20,000 40,000 60,000 80,000 100,000 IncomeConsider the following game, with a risk-neutral principal with preferences π = q - w hiring an agent with preferences U = √w-e.. The agent's reservation utility is given by Ū = 2, and the agent can choose between an effort level of 0 or an effort level of 10. Output is either 0 or 400 and follows the following probability distribution, a function of effort level and some uncertain factor: e=0 e=10 Probability (q=0) Probability (q=400) 0.6 0.4 0.9 0.1 What would the contract look like if the principal tried to push the wages when q=0 to zero? Would the principal want to do this? Explain.