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
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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)
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- For each of the following scenarios, determine whether the decision maker is risk neutral, risk averse, or risk loving.a) A manager prefers a 10 percent chance of receiving $1,000 and a 90 percent chance of receiving $100 to receiving $190 for sure.b) A shareholder prefers receiving $775 with certainty to a 75 percent chance of receiving $1,000 and a 25 percent chance of receiving $100.c) A consumer is indifferent between receiving $550 for sure and a lottery that pays $1,000 half of the time and $100 half of the time.For each of the following scenarios, determine whether the decision maker is risk neutral, risk averse, or risk loving. a. A manager prefers a 20 percent chance of receiving $1,400 and an 80 percent chance of receiving $500 to receiving $680 for sure. b. A shareholder prefers receiving $920 with certainty to an 80 percent chance of receiving $1,100 and a 20 percent chance of receiving $200. c. A consumer is indifferent between receiving $1,360 for sure and a lottery that pays $2,000 with a 60 percent probability and $400 with a 40 percent probability.You are a bidder in an independent private values auction, and you value the object at $4,000. Each bidder perceives that valuations are uniformly distributed between $1,500 and $9,000. Determine your optimal bidding strategy in a first-price, sealed-bid auction when the total number of bidders (including you) is: a. 2. b. 10. c. 100
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- Assume that the effective security level is now determined by the highest (not the lowest) security measures chosen by airlines. Letting max{s1, . . . , sn} denote the highest of the airlines’ strategies, we find that airline i’s payoff is now 50 + 20 x max{s1, . . . , sn} -10 si.Assuming the same strategy sets, find all Nash equilibria.The preferences of agents A and B are representable by expected utility functions such that uA(x) = 5x^1/3 +30, and uB(x)= 1/5x - 20. Then, the following allocation of the expected returns of a risky joint investment of A and B as represented by lottery L = ((2/3);1500), (1/3);120)) is Pareto efficient: (a) xA = (500,100), xB = (1000,20) (b) xA = (100,100), xB= (1300,20) (c) xA= (80,80), xB = (1420,40) (d) xA = (750,60), xB= (750,60) (e) NOPACTwo firms, A and B, know that holder of a telecom license will make a profit of either £0 or £4m with equal probabilities. They bid simultaneously either £0 or £1m for this license. The highest bidder wins the license (with probability ½ if both bidders submit the same bid) and pays its bid. a) Represent the game in normal and extensive form. b) Solve the game with the relevant solution concept(s). c) Represent the game in normal and extensive form when, before bidding, firm A learns the actual profit (£0 or £4m) of the license holder. d) Solve the game in c) with the relevant solution concept(s). Does firm A benefit from learning the actual profit?
- Translate the following monetary payoffs into utilities for a decision maker whose utility function is described by an exponential function with R 5 250: 2$200, 2$100, $0, $100, $200, $300, $400, $500There are three bidders participating in a first-price auction for a painting. Each bidder has a private, independent value vi for such a painting that is drawn uniformly from [0,1] Assume that each bidder i has a linear bidding function bi=avi, where a>0. What is the bidding strategy of bidder i , namely bi in the Bayesian equilibrium?Consider a first-price, sealed-bid auction, and suppose there are only three feasible bids: A bidder can bid 1, 2, or 3. The payoff to a losing bidder is zero. The payoff to a winning bidder equals his valuation minus the price paid (which, by the rules of the auction, is his bid). What is private information to a bidder is how much the item is worth to him; hence, a bidder’s type is his valuation. Assume that there are only two valuations, which we’ll denote L and H, where H > 3 > L > 2. Assume also that each bidder has probability .75 of having a high valuation, H. The Bayesian game is then structured as follows: First, Nature chooses the two bidders’ valuations. Second, each bidder learns his valuation, but does not learn the valuation of the other bidder. Third, the two bidders simultaneously submit bids. A strategy for a bidder is a pair of actions: what to bid when he has a high valuation and what to bid when he has a low valuation. a. Derive the conditions on H and L…