Prove rigourously, "Constant relative risk aversion (CRRA) implies decreasing absolute risk aversion (DARA), but the converse is not necessarily true."

3. In the second example, we will consider the case where the insurance contract involves a deductible this is an amount which is deducted from the final pay-out of the insurance firm in the case of a loss. In other words, the consumer bears this part of the loss herself. For this problem, assume a risk-averse, expected utility maximizing consumer with initial wealth wo who faces a potential loss of size L which will occur with probability p. Her utility-of-final-wealth function is denoted by u(.). Suppose that the consumer can purchase insurance coverage of C > 0 units of wealth from a perfectly competitive insurance firm at a premium of 7 per unit of coverage, but that the firm charges an additive deductible: if C units of insurance is purchased, the insurance firm pays out (C – d) if the loss occurs, where d 20 is a fixed amount independent of C. (a). For this problem, state the consumer's expected utility function. (b). Set up the consumer's utility maximization problem and find…

4) Luke is planning an around-the-world trip on which he plans to spend $10,000. The utility from the trip is a function of how much she spends on it (Y ), given by U(Y) = InY a). If there is a 25 percent probability that Luke will lose $1000 of his cash on the trip, what is the trip's expected utility. b). Suppose that Luke can buy insurance to fully against losing the $1,000 with a actuarially fair insurance. What is his expected utility if he purchase this insurance. Will he purchase the insurance? c). Now suppose utility function is U(Y) = Y/1000 What is his expected utility if he purchase the insurance in b). Will he purchase the insurance?

Using a scale of 1 to 10, where 10 is the most painful and 1 is least painful; when John's wealth is $100,000 he rates a $1,000 loss as being a 3. When John's wealth is $1,000,000 he rates the loss of $1,000 as a 6. This would be an example of: O A. none of the answers listed here. B. Increasing Relative Risk Aversion O C. Increasing Absolute Risk Aversion O D. Decreasing Absolute Risk Aversion

7. Consider an individual whose utility function over money is u(w) = 1+2w. (a) Is the individual risk-averse, risk-neutral, or risk-loving? Does it depend on w? (b) Suppose the individual has initial wealth ¥W and faces the possible loss of Y. The probability that the loss will occur is . Suppose insurance is available at price p, where p is not necessarily the fair price. Find the optimal amount of insurance the individual should buy. You may assume that the solution is interior. (c) Is there a price at which the individual will not want to buy any insurance? If so, find it. If no, explain.

Consider a game between player A with a choice between moves d₁ and d₂, and player B with a choice between 81 and 82, and the pay-offs given by: 3₁ Consider a zero-sum game with the following payoff matrix for player 1: 61 62 d₁ (4,6) (7,2) d₂ (2,8) (5,4) Is that game separable? a. Separable with r₁(d₁) = 5, r₁(d₂) = 2, 72(81) = 1, 72(82) = 4, (s₁ (d₁) = 2, 8₁ (d₂) = 4,82 (81) = 4, 82 (82) = 0 b. Separable with a different solution that the ones proposed c. Separable with r₁(d₁) = 3, r1(d₂) = 3,(61) = 0, 72(82) = 1, (81 (d₁) = 1, 81 (d₂) = 4, 82 (81) = 5, 82 (82) = 2 No, not separable. d. e. Separable with ri (d₁) = 4, r₁(d₂) = 1, r2(81) = -1, 72(82) = 2, (81 (d₁) = 1, 81 (d₂) = 4, 82 (81) = 6, 82 (8₂) = 1 f. Separable with r₁(d₁) = 4, r₁(d₂) = 2, 7₂(81) = 0,72(8₂) = 3, (s₁ (d₁) = 1, 8₁ (d₂) = 3, 82 (81) = 5, 82 (8₂) = 1 Consider the payoff matrix M for a zero-sum game as defined below: 81 82 d₁0-2 d₂-2-1 M1 M₂ M3 M4 M5 d₁ 0 1 5 6 8 d₂ 10 6 5 2 3 O a. r* = (1/2, 1/2), y* = (1/2, 1/2),…

4. Consider the situation in which player 1 knows what game is played (the first or the second). But player 2 only knows that the first game is played with probability 1/3 and the second game is played with probability 2/3. Player 1 Player 1 Player 2 S B S 1,1 0,0 B 0,0 0,0 Player 2 S B S 0,0 0,0 B 0,0 2,2 (a) Describe the game as a Bayesian game. (b) Find the Bayesian Nash equilibria.

please  only do: if you can teach explain steps of how to solve each part what is the optimizatio  formula that was use for foc?  please solve   each part

(d) Suppose Antonio has utility function over wealth given by Va (y) = Vy and suppose Dillon has the following utility function over wealth: va (y) = In %3D Who is more risk aversc, Antonio or Dillon? Show this using two approachcs. (e) Who is more risk averse, Chelsca or Dillon'? Explain.

those determinations. Respond to the following questions in a minimum of 175 words: . Consider a situation that you might need to use your understanding of probability to make an informed decision. • What sorts of information would you collect? • How might you use what you have learned about probability to determine a course of action? What are the possible benefits and limitations of this approach? Due Monday Reply to at least 2 of your classmates. Be constructive and professional in your responses. Copyright 2020 by University of Phoenix. All rights reserved. New Group 1 17 Responses 33 Replies