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- Suppose you have an exponential utility function given by U(x) =1- exp(-x/R) where, for you, R = 1000. Further, suppose you have an investment with a 50/50 chance of returning either 0 or 2000 dollars. Note U(0) = 0 and U(2000) = 0.865, so the utility of the lottery is 0.432. What is the certain equivalent of that investment?(a) Calculate the risk-premium on this portfolio and provide a brief interpretation of it (b) Calculate the minimum sale price of the capital assets for the average investor.(a) Given a utility function of an individual is U(x) = x² - 4x, determine his risk attitude. (b) With a utility function of U(x) = x - 3x², where x is the amount invested. (i) determine if this function satisfy the two properties of utility functions. (ii) compute the utility when the amount invested is 3 and 5 respectively.
- Thelma is indifferent between $100 and a bet with a 0.6 chance of no return and a 0.4 chance of $200. If U(0) = 20 and U(200) = 220, then U(100) = :Reactors `R’ Us operates a nuclear power plant in Potsdam.In the event of reactor failure, there would be major damages to the North Country. The company can reduce the probability of failure through proper maintenance of the facility. The marginal cost of maintenance is increasing in the amount of maintenance done (and thus decreasing in the probability of an accident). We can write this marginal cost curve as MAC=2-10p (where 0<p<1, and represents the probability of a failure over a 50 year period). The marginal expected damages are an increasing function of the probability of an accident so that MD=2.2+10p. Provide a graph or graphs to illustrate your analysis/answers to the following questions. A. What is the efficient probability of reactor failure? B. If “Reactors ‘R’ Us” thinks that, in the event of reactor failure, they will NOT be found liable for damages, what probability of failure will they choose? C. If “Reactors ‘R’ Us” thinks that, in the…B) A firm has the option to decide between two new technologies T1 and T2. The monetary payoffs and probabilities for each technology is given below X2 Probability under state X; Income ($) with TI under state X Income (S) with T2 under state Xi 0.3 0.4 0.3 8 18 6 16 The utility function for the firm is given by u = E(T) – 0 Var(1), where E(x) represents average income, Var(n) represents the variance of income, and 020 1) Show that the firms risk preferences exhibit constant absolute risk aversion (CARA) 2) When 0- 0.1 how does the firms risk premium change under the two technologies TI and T2?
- please very very urgent Given the utility function, U(X)=ln(X) where X > 0, with initial consumption C=30000. Calculate the risk premium for a fair game with a chance of loosing -20000 is 0.5? (Hint: Start with the "fair game" definition)An individual has a utility function U(W) = VW, where W is the level of wealth. They have been offered a gamble with a payout of £170 with a probability of 0.74 and a payout of £49.7 with a probability of 1-0.74. The Certainty Equivalent of this gamble is: Answer:(ii) A mixed strategy profile (p, q) is one in which p = (p,P2.... P) is the mixed strategy of player 1, and q- (g1, q2,..q4) is the mixed strategy of player 2. Show that if p, >0 in a Nash equilibrium profile (p*, q*), the player 2 must also play i with strictly positive probability q'; > 0. (State clearly any theorem you use to show this. You are not required to justify the theorem.) %3D
- Suppose 2 players play the following game infinite times in the future. What should be the minimum value of the time discount so that the equilibrium strategy is (Cooperate, Cooperate)? Player 2 Player 1 Cooperate Defect Cooperate (10, 10) Defect (2, 12) (4,4) (12, 2)Global Gas International offers to contract the Halidurton Heavy Construction Corporation to build an oil pipeline from Canada to New Orleans that will provide Halidurton $500 million in income. The probability that the oil pipeline will leak, causing environmental damage is 0. If so, the legal liability will be $2,500 million. If Halidurton is risk neutral and liable for the damages from a leak, what is the 0 such that it is indifferent between accepting and rejecting the contract? Halidurton is indifferent between accepting and rejecting the contract if 0 equals rounded to the nearest whole number.) percent. (Enter your responseThe decision tree below describes the game faced by firm H and firm T. The payoffs are profits in million of US$. The SPNE is(are): (Build large, Build large) (Build Small, Build Small) (Build Small, Build Large) (No build, Build Large) (Build Large, No Build)