Consider the following game, with a risk-neutral principal with preferences = q - w hiring an agent with preferences U = √w-e.. The agent's reservation utility is given by U = 2, and the agent can choose between an effort level of 0 or an effort level of 10. Output is either 0 or 400 and follows the following probability distribution, a function of effort level and some uncertain factor: e=0 e=10 Probability (q=0) Probability (q=400) 0.4 0.9 0.6 0.1 What would the contract look like if the principal tried to push the wages when q=0 to zero? Would the principal want to do this? Explain.
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- Consider the following game, with a risk-neutral principal with preferences π = q - w hiring an agent 2, and the agent can = with preferences U = √w- - e.. The agent's reservation utility is given by U choose between an effort level of 0 or an effort level of 10. Output is either 0 or 400 and follows the following probability distribution, a function of effort level and some uncertain factor: Probability (q=0) Probability (q=400) 0.4 0.9 e=0 0.6 e-10 0.1 a) Illustrate this game of moral hazard using a fully labeled game tree with payouts.Consider the following game, with a risk-neutral principal with preferences π = q - w hiring an agent with preferences U = √w-e.. The agent's reservation utility is given by Ū = 2, and the agent can choose between an effort level of 0 or an effort level of 10. Output is either 0 or 400 and follows the following probability distribution, a function of effort level and some uncertain factor: Probability (q=0) Probability (q=400) e=0 0.6 e=10 0.1 0.4 0.9 Interpret those constraints in words - what are they imposing on the contract being designed by the principal?Consider the following game, with a risk-neutral principal with preferences π = q - w hiring an agent with preferences U = √w- 7-e.. The agent's reservation utility is given by U = 2, and the agent can choose between an effort level of 0 or an effort level of 10. Output is either 0 or 400 and follows the following probability distribution, a function of effort level and some uncertain factor: Probability (q=0) Probability (q=400) 0.4 0.9 e=0 0.6 e=10 0.1 a) Illustrate this game of moral hazard using a fully labeled game tree with payouts. b) Write out the agent's incentive compatibility (ICC) and participation constraints (PC).
- Consider the following game, with a risk-neutral principal with preferences π = q - w hiring an agent with preferences U = √w-e.. The agent's reservation utility is given by Ū = 2, and the agent can choose between an effort level of 0 or an effort level of 10. Output is either 0 or 400 and follows the following probability distribution, a function of effort level and some uncertain factor: Probability (q=0) Probability (q=400) 0.4 0.9 e=0 0.6 e=10 0.1 Find the optimal contract under the assumption that agents compete for principals. Begin by identifying which constraints will bind with equality!A driver's wealth $100,000 includes a car of $20,000. To install a car alarm costs the driver $1,750. The probability that the car is stolen is 0.2 when the car does not have an alarm and 0.1 when the car does have an alarm. Assume the driver's von Neumann- Morgenstern utility function is U(W) = In(W). Suppose the driver is deciding between the following three options: (a) purchase no car insurance, do not install car alarm; (b) purchase fair insurance to replace the car, do not install car alarm; and (c) purchase no car insurance, install car alarm. Of these three options, the driver prefers: A. option (a). B. option (b). C.option (c). D.options (a) and (b). E. options (a) and (c). F. options (b) and (c). G.all options equally. H.none of these options.Let U(x)= x^(beta/2) denote an agent's utility function, where Beta > 0 is a parameter that defines the agent's attitude towards risk. Consider a gamble that pays a prize X = 10 with probability 0.2, a price X = 50 with probability 0.4 and a price X = 100 with probability 0.4. Compute the agentís expected utility for such gamble and find the value of Beta such that the agentis risk neutral? Suppose B= 1, what is the certainty equivalent of the gamble described above? What is the Arrow-Pratt measure of absolute risk aversion?
- A driver's wealth $100,000 includes a car of $20,000. To install a car alarm costs the driver $1,750. The probability that the car is stolen is 0.2 when the car does not have an alarm and 0.1 when the car does have an alarm. Assume the driver's von Neumann-Morgenstern utility function is U(W) = ln(W). Suppose the driver is deciding between the following three options: (a) purchase no car insurance, do not install car alarm; (b) purchase fair insurance to replace the car, do not install car alarm; and (c) purchase no car insurance, install car alarm. Of these three options, the driver prefers: A. option (a). B. option (b). C. option (c). D. options (a) and (b). E. options (a) and (c). F. options (b) and (c). G. all options equally. H. none of these options.A client (the principal) is trying to determine the best possible contract to enter into with her favoring the client is x and the probability of winning is 8. lawyer (the agent). The principal makes the following assumptions: the dollar amount of a judgment The lawyer has offered to () work for a fixed fee of F. (i) pay the client a fixed fee of F and keep the remainder of the judgment, and (ii) work for a contingent fee or a share of the contract with t lawyer's share being a If the principal is highly risk-averse and is interested in production efficiency she will choose option i option i option iIf the utility function is U (W) = ((W0.75) / (0.75)), what is the absolute risk aversion coefficient?
- Leora has a monthly income of $20,736. Unfortunately, there is a chance that she will have an accident that will result in costs of $10,736. Thus leaving her an income of only $10,000. The probability of an accident is 0.5. Finally assume that her preferences over income can be represented by the utility function u(x) = 2ln(x).a) What is the expected income? What is Leora’s expected utility (you may leave in log form)? b) What is the certainty equivalent to her situation? What is the risk premium associated with her situation?c) What is the maximum that Leora would be willing to pay for a full insurance policy?d) Illustrate her expected utility, expected wealth, certainty equivalent, the risk premium and her willingness to pay for a full insurance policy in a diagram.Suppose that Mike, with utility function, u(x) = v x+5000, is offered a gamble where a coin is flipped twice, and if the coin comes up heads both times (probability - .25), he gets $40,000. Would he prefer this gamble or $7,500 for sure? What is his Certainty Equivalent?Suppose your utility over money (X) is given by u(x)3x-, where r=2/3. You are one of two bidders in a first price sealed bid auction. The other bidder places a bid randomly drawn from a uniform distribution between 0 and 10. 1. What is your optimal bid in this case? 2. Compare that number with what your optimal bid would be ifr were equal to 0. What is the explanation for this difference?