Q.No.4. If you are supposed to a 40/60 chance of gaining or losing Rs.400 and insurance that removes the risk costs Rs.150; at what level of wealth will you be indifferent relative to taking the gamble or paying the insurance? That is, what is your certainty equivalent wealth? Assuming your utility function is U(W)= In(W).
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- 5) A person with a current wealth of $100,000 who faces the prospect of 25 percent chance of losing his or her $20,000 automobile through theft during the next year. Suppose this person's utility function is U(Y) = InY. a). If this person takes no action, what is the expected utility? b). What is the actuarially fair premium? What is his expected utility if he purchase this insurance. c). Suppose that now the insurance company provides a new type of insurance. This insurance costs $4900 and requires the individual to incur the first $1000 of the loss from theft would yield. That is expected utility of this new insurance? Will the person choose the insurance in b) or c)?the video link is: https://www.youtube.com/watch?v=aqEz6kvXhc8please give me detailed solutions and calculations, thank you!Utility Theory You live in an area that has a possibility of incurring a massive earthquake, so you are considering buyingearthquake insurance on your home at an annual cost of $180. The probability of an earthquake damagingyour home during one year is 0.001. If this happens, you estimate that the cost of the damage (fully coveredby earthquake insurance) will be $160,000. Your total assets (including your home) are worth $250,000. A. Apply Bayes’ decision rule to determine which alternative (take the insurance or not) maximizes yourexpected assets after one year.
- help meeeeeeSeung’s utility function is given by U = ln(C), where C is consumption. She makes $30,000 per year and enjoy jumping out of airplanes. There's a 5% chance that in the next year, she will break both legs, incur medical costs of $15,000, and lose an additional $5,000 from missing work. (a) What is Seung’s expected utility without insurance? (b) Suppose Seung can buy insurance that will cover the medical expenses but not the forgone part of her salary. How much would an actuarially fair policy cost, and what is her expected utility if she buys it? (c) Suppose Seung can buy insurance that will cover her medical expenses and forgone salary. How much would such a policy cost if it's actuarially fair, and what is her expected utility if she buys it?19. An individual has initial wealth Wo = 3 and has the opportunity to invest some quantity of money x in an extremely risky corporate bond. With probability p= 1/4, the bond will be worth 10x at maturity. With probability 1 – p, it will be worth zero. The individual's utility function over final wealth is u(W) = W0.5. What is the level of investment x that maximizes expected utility? (а) 0 (b) 1 (c) 4/3 (d) V3 (e) 2
- Microeconomics 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)Assume that Rosemarie has the following utility function: U(W) = W1/2. She is selling her homeand believes that the house will sell for $250,000 with probability ¼ and $122,500 withprobability ¾.a. What is her expected utility?b. What is the risk premium (P) Rosemarie would pay to avoid bearing this risk?Do it correctly this time
- !# 4 Consider an individual with a utility function of the form u(w) = √w. The individual has an initial wealth of $4. He has two investments options available to him. He can eitffer keep his wealth in an interest-free account or he can take part in a particularly generous lottery that provides $12 with probability of 1/2 and $0 with probability 1/2. Assume that this person does not have to incur a cost if he decides to take part in the lottery. (a) Will this individual participate in the lottery? (b) Calculate this individual's certainty equivalent associated with the lottery. What is his risk premium?You live in an area that has a possibility of incurring a massive earthquake, so you are considering buyingearthquake insurance on your home at an annual cost of $180. The probability of an earthquake damagingyour home during one year is 0.001. If this happens, you estimate that the cost of the damage (fully coveredby earthquake insurance) will be $160,000. Your total assets (including your home) are worth $250,000.