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- 1. A woman with current wealth X has the opportunity to bet an amount on the o ccurrence of an event that she knows will occur with probability P. If she wager s W, she will received 2W, if the event occur and if it does not. Assume that t he Bernoulli utility function takes the form u(x) = -e-TX with r> 0. How much should she wager? Does her utility function exhibit CARA, DARA, IARA?Becky is deciding whether to purchase an insurance for her home againtst burglary. the payoff for her is shown as follow: Net worth of her Net worth of her home: $ 20000 burglary(10%) Net worth of her Net worth of her home: $50000 burglary (90%) The insueance would cover all the loss from burlary and the insurance fee is $8000. Her utility funtion is given as u=w ^0.3 Should Beck purchase the insurance Explain.Please explain in detail about expected utility to get a positive upvote. An individual has a utility function U = W¼, where W is her total wealth. She has one safe asset worth Rs 5,000, and another risky asset whose value can be either Rs 5,000 or Rs 1,400 with equal probabilities. What is her expected utility? (a) Rs 11,400 (b) Rs 100 aw lo boeoqmoo vmonoos to on g cubire cou s o iva alagos ad a adWnooni lanou lo OAuti (c) Rs 2,580 (d) Rs 90
- 2- Who is risk aversion?Suppose there is a 50–50 chance that a risk-averse individual with a current wealth of $20,000 will contract a debilitating disease and suffer a loss of $10,000. a. Calculate the cost of actuarially fair insurance in this situation and use a utility-of-wealth graph (such as shown in Figure 7.1) to show that the individual will prefer fair insurance against this loss to accepting the gamble uninsured. b. Suppose two types of insurance policies were available: (1) a fair policy covering the complete loss; and (2) a fair policy covering only half of any loss incurred. Calculate the cost of the second type of policy and show that the individual will generally regard it as inferior to the first. Reference: Figure 7.1a. Suppose that you took part in a lottery that has a chance to increase, decrease or have no effect on your level of income. With probability 0.5, your income remains at it original level K500; with 0.2 probability, your income increases to K700; and with probability 0.3, your income decreases to K400. The utility function is.u(1) =I^0.7where I denote income leveli.Using the utility function show that the consumer's risk preference is averse. (2marks)ii.Calculate both the EU and EV of the income. (4marks)iii.Using the results in (il) above, indicate the attitude to risk of this consumer. (2marks)
- 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?When the second order derivative of a function is greater than zero than the agent is risk lover. question; Asses the risk attitude of an agent represented by the expected utility function u(x)= 2x2-5. However my course material writes that this agent is risk neutral because it is affine. My question is that whys is this so despite the fact that the second order derivative is '4' which is >0. Kindly explain this to me with complete steps.Economics Shawn's consumption is subject to risk. With probability 0.75 he will enjoy 10000 in consumption, but with probability 0.25 he will have only 3600. His utility function for consumption is given by v(c) = Vc. -What is the expected value of Shawn's consumption? -What is his expected utility? -What is his certainty equivalent of having 10000 with probability 0.75 and 3600 with probability 0.25?
- Clancy has $4800. He plans to bet on a boxing match betweenSullivan and Flanagan. He finds that he can buy coupons for $6 thatwill pay off $10 each if Sullivan wins. He also finds in another storesome coupons that will pay off $10 if Flanagan wins. The Flanagantickets cost $4 each. Clancy believes that the two fighters each have aprobability of ½ of winning. Clancy is a risk averter who tries tomaximize the expected value of the natural log of his wealth. Whichof the following strategies would maximize his expected utility? (a) Don’t Gamble (b) Buy 400 S tickets and 600 F tickets(c) Buy exactly as many F tickets and S tickets (d) Buy 200 S and 300 F(e) Buy 200 S and 600 FBob earn 60,000 a year and an accounting firm each year he receives Reyes Bob has determined that the probability that he receives a 10% raise is .7 the probability that he earns a 3% raise is .2 and the probability that he earns a 2% raise is .1 a competing company has offered Bob a similar position for 65,000 a year Bob wonders if he should take the new job or take his chances with his current job. a. Find the mathematical expectation of the dollar amount of his raise at his current job b.According to the Intern al Revenue Service, the mean tax refund for the year 2014 was $2800 Assu me the stan dard devlation I6 $450 an d that the amounts 1etunded follow a normal probability distribution. a. What percont of the refunde aro more th an $3,100? (Round the Intermediate velues to 2 decimal places. Round your answer to 2 decimal places) Percert 0.25 % b. What percent of the refun ds are more th an $3,100 but less th an $3.500? (Round the intermediete values to 2 dec imal places Round your ans wer to 2 decimal places) Peroert c. What percent of the retun ds are more th an $2,250 but less than $3.500? (Round the inter mediate val ues to 2 decimal places Round your answer to 2 decimal places) Peroart