Assume a firm wants to hire a worker. The firm knows that the worker is risk-neutral but does not know the disutility of effort at work, e. This could be of two types e² or 2e2, that is the worker of second type (Bad type) has a greater disutility of work than first type (Good type). The payoff function of worker can either be u(w. e) = w-e² or us (w. e) = w-2e² where w is wage received by the worker. The proportion of Good types is q. Both workers have reservation utility level U = 0. The firm values the effort of the worker as II(e) = ke, where k is sufficiently large so that the it wants to hire both agents, independent of their type. (a) If the firm had full information, what will be the effort levels demanded by the firm and the wages paid? (b) Now suppose that there is asymmetric information so that the firm does not know the workers' types and wants to find the separating contract. Explain which constraints will you expect to be binding/non-binding for each worker? Using this solve for the optimal separating contract and compare these to the full information contract

Assume a firm wants to hire a worker. The firm knows that the worker is risk-neutral but does not know the disutility of effort at work, e. This could be of two types e² or 2e2, that is the worker of second type (Bad type) has a greater disutility of work than first type (Good type). The payoff function of worker can either be u(w. e) = w-e² or us (w. e) = w-2e² where w is wage received by the worker. The proportion of Good types is q. Both workers have reservation utility level U = 0. The firm values the effort of the worker as II(e) = ke, where k is sufficiently large so that the it wants to hire both agents, independent of their type. (a) If the firm had full information, what will be the effort levels demanded by the firm and the wages paid? (b) Now suppose that there is asymmetric information so that the firm does not know the workers' types and wants to find the separating contract. Explain which constraints will you expect to be binding/non-binding for each worker? Using this solve for the optimal separating contract and compare these to the full information contract

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.11P

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3. A risk-neutral principal hires an agent to work on a project at wage w. The agent's utility function is: v(w)-g(e), where v(w)= Jw and g(e)=e/2 The agent can choose one of two possible effort levels, e¡ = 4 or e, = 6 . If the agent chooses effort level e, = 4 the project yields 100 with probability 1/4 and 0 with probability 3/4. If he chooses e, = 6 the project yields 100 with probability ½ and 0 with probability ½. The reservation utility of the agent is 0. (a) Suppose the effort level chosen by the agent is observable by the principal. Find the contract chosen by the principal. Show graphically in terms of contingent utilities v(w,00) and v(w.)
b)Rachel’s objective is to maximize the expected profit, subject to that Emma works for Racheland Emma puts effort. However, effort level is not observable. Hence, Rachel needs to writea contract based on the observables. Let’s say, Rachel pays Emma based on the outcome: xLwhen the profit is $0, xM when the profit is $2000, and xH when the profit is $3,000. ThenEmma has three options:(i) Not to work for Rachel(ii) Work for Rachel without effort(iii) Work for Rachel with effortFind Emma’s expected utility on each optionc)ssuming Rachel wants Emma to put effort, her objective essentially becomes to find thelowest contingent payment scheme that is just enough for Emma to work for Rachel, andgives an incentive for Emma to put effort. Formally, we can write this as:min 0.1xL + 0.3xM + 0.6xH ,subject to0.1√xL + 0.3√xM + 0.6√xH − 5 ≥ 15, (1)and0.1√xL + 0.3√xM + 0.6√xH − 5 ≥ 0.6√xL + 0.3√xM + 0.1√xH . (2)What is Constraint (1) called? What is Constraint (2) called?d) or your information, the…
advanced microeconomics, principal agent
Charles is participating in an experiment. His payoff in the experiment is tied to his effort e doing a mundane task. There is also some risk involved by design-there is a chance p that Charles is going to get a fixed payment L regardless of his effort. Charles' payoff is thus: with probability p w.e with probability 1- p Charles has to pay a cost C, which increases with his effort. First, let us assume that Charles' utility is the expected payoff net of this cost: U(e) = pL + (1 – p)we – c(e) Derive the first order condition with respect to e. b. How doesp affect Charles' effort e? c. How does L affect e?
2. Consider a cheap talk game in which Nature moves by choosing a sender's type, where the type space has four elements: −1, 1, 2, and 3, each occur- ring with equal probability of 1½. The sender learns his type and chooses one of three possible messages: bumpy, smooth, and slick. The receiver observes the sender's message and then chooses one of three actions: 0, 5, and 10. The sender's payoff equals his type multiplied by the receiver's action. The receiver's payoff equals the sender's type multiplied by twice the receiver's payoff. a. Find a separating perfect Bayes-Nash equilibrium. b. Find a semiseparating perfect Bayes-Nash equilibrium.
Suppose that Natasha's utility function is given by u(I) = √/10/, where I represents annual income in thousands of dollars. Is Natasha risk loving, risk neutral, or risk averse? Explain. A. She is risk averse because her utility function exhibits diminishing marginal utility. OB. She is risk loving because her utility function exhibits increasing marginal utility. OC. She is risk neutral because her utility function exhibits constant marginal utility. Suppose that Natasha is currently earning an income of $40,000 (1 = 40) and can earn that income next year with certainty. She is offered a chance to take a new job that offers a 0.6 probability of earning $44,000 and a 0.4 probability of earning $33,000. Should she take the new job? Natasha should not take the new job because her expected utility of 19.85 is less than her current utility. (Round expected utility to three decimal places.)
Consider the game below with a worker (W) and a firm (F). The worker initially can choose to acquire skills or not acquire skills. If the worker does acquire skills, the firm then gets to decide whether to compensate the worker or not. The extensive form of the game and the payoffs are below. Which of the following is true? W Acquirre Not Acquire There is no Nash equilibrium. C Compensate Not Compensate This game has a single Nash equilibrium. There are two Nash equilibria. None of the above. (0,0) Both players have a strictly dominant strategy. (10,10) (-5,20)
bottom is the question, top is a part to the solution one of he chegg tutors wrote down. In WHAT WORLD does 100/1000=0.01 IT DOESN'T. 100/1000 = 0.1 to the power of -2 is 100 NOT 1000 so CAN SOMEONE PLEASE PLEASE correctly solve this. This is my third time posting it like jesssusssss
QUESTION 12 Suppose that a worker value jobs by both the wage rate and the workplace collegiality. The woker's utility is strictly increasing in the wage rate but strictly decreasing in the chance of being bullied in the workplace. The utility function of the worker is U = wa (1- ), where a = 0.5, w is the wage rate and b is the probability that a worker is bullied in a workplace. Suppose for a typical job A, the chance of getting bullied is 0.01, and the wage rate is 100. Which of the following statements is correct? If job B offer w = 121 and b = 0.04, the worker would prefer job B to job A %3D If job B offer w = 144 and b = 0.09, the worker would prefer job B to job A %3D If job B offer w = 80 and b = 0, the worker would prefer job B to job A If job B has bullying probablity b = 0.04, the worker is indifferent between job A and job B. Then, the compensating wage differential of job B is at least 25. %3D If job B offer w = 80 and b = 0, the worker would be indifferent between job A…
1) Consider observable effort. Assume that if the Agent does not accept the wage the Principal offers his outside option gives him a net utility of v =2. The probability of high profit under e=1 is %, the probability of high profit under low effort is 1/4. Calculate the minimum wage that the agent will accept to work and supply the asked effort when the Principal asks him to supply e=0, and e=1. Let us call these wages wo and wi. Now, assume that instead of offering him a flat wage, the Principal is offering the agent a wage schedule (, w) where the agent receives when the (gross) profit is High and w when the (gross) profit is low. Calculate all the lowest cost wage schedules the agent will accept to supply e=1, and e=D0. Does the principal's expected net profit change when he pays the minimum cost wage schedule instead of the flat wage minimum cost wage? Explain the intuition for your answer.
Suppose that 20 risk neutral competitors participate in a rent seeking game with a fixed prize of $500. Each player may invest as much money as he wishes in the political contest. The probability of winning is directly proportional to the candidate's share of the total rent-seeking investment. 1. What is the expected net benefit of a player if all other players invest $20 each? Write the net benefit as a function of the player's investment. 2. Solve the maximization problem to arrive at the profit-maximizing investment. Round to the nearest cent.
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