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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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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- Consider a game where there is a $2,520 prize if a player correctly guesses the outcome of a fair 7-sided die roll.Cindy will only play this game if there is a nonnegative expected value, even with the risk of losing the payment amount.What is the most Cindy would be willing to pay?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.Two employees witness fraud committed in their firm. Each has two pure strategies: to become a whistleblower and report a crime, or not to report a crime. Each employee gets a payoff of 1 if the crime is reported by someone (it does not matter if both or only one employee reports). However, reporting the crime is costly. An employee who reports has to pay the cost of reporting equal to 0.5-0.25*d, where d=1 if the other employee also reports, and d=0 otherwise. Suppose that employees simultaneously decide to report or not. There is a unique mixed strategy Nash equilibrium in this game where each employee reports with the same positive probability less than 1. What is the probability that the crime is reported by at least one employee in such an equilibrium? ________
- 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.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, $500For constants a and b, 0 < b, b 1, and expected profit E(p), the expected utility function of a person who is risk-neutral can be written as E(U) = Which one: a+b^p a + (E(p))^b. a - bE(p). a + bE(p). a + (E(p))^(-b).
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- Two 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?Consider the following game 1\2 Y Z A 10,2 3,9 B 8,5 6,1 Suppose Player 2 holds the following belief about Player 1: θ1 (A,B) = (1/3,2/3) What is the expected payoff from playing ‘Y’ ? What is the expected payoff from playing ‘Z’ ? Based on these beliefs, Player 2 should respond by playing ____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