Purchase Solution

Agent and principal utility

Not what you're looking for?

Ask Custom Question

The utility of the agent is given by U(w, a) = √w − a, where w is wage and a is effort. The reservation utility of the agent is 1. There are two profit levels, π;l = $0 and π;h = $100. The principal is risk-neutral. The wages are restricted to be non-negative, w ≥; 0. Suppose there are three levels of effort for the agent, a1 = 1, a2 = 2 and a3 = 4. The probabilities of high profit after respective actions are given by p1,h = 0.40, p2,h = 0.60 and p3,h = 0.85. The principal cannot observe agent's effort but observes profit. The principal offers the agent a contract (wl, wh), where wl is the wage paid after low profit and wh is the wage paid after high profit. The agent can accept or reject the contract. If the agent accepts the contract, the agent chooses effort. Agent's payoff is the expected utility and principal's payoff is the expected profit. If the agent rejects, agent's payoff is the reservation utility 1 and principal's payoff is 0.

(a) If the effort were observable, what is the optimal contract for the principal?

(b) Suppose now that effort is not observable. What is the minimal cost to induce a2?

(c) Find the minimal cost to induce a3 when effort is not observable.

(d) What effort does the principal want to induce when effort is not observable? What is the optimal contract for the principal?

Purchase this Solution
Solution Summary

This solution provides assistance with the problems related to the utility of the agent.

Solution Preview

Because the principal is risk-neutral, the principal's utility is given by h - w. This means that lw = 0. He will not want to have negative profits. The agent's utility tells us he is risk-adverse.

(a) There is no moral hazard problem here, because there is no hidden information. The principal wants to obtain the highest possible profit. The participation constraint requires:
w ≥; (1+a)^2
At a3,
wh = (1+a3)^2 = 25
Profit to principal is .85 (100) - 25= 60

Looking at it another way, the agent will choose to exert a=4 if and only if
√w1 - √w2 ≥; 4 + 1 ...

Purchase this Solution
Free BrainMass Quizzes
Economics, Basic Concepts, Demand-Supply-Equilibrium

The quiz tests the basic concepts of demand, supply, and equilibrium in a free market.

Basics of Economics

Quiz will help you to review some basics of microeconomics and macroeconomics which are often not understood.

Pricing Strategies

Discussion about various pricing techniques of profit-seeking firms.

Elementary Microeconomics

This quiz reviews the basic concept of supply and demand analysis.

Economic Issues and Concepts

This quiz provides a review of the basic microeconomic concepts. Students can test their understanding of major economic issues.

View More Free Quizzes
Related BrainMass Solutions

  • Moral Hazard Model

    Given s and b, the expected utility of working hard would be: On the other hand, the expected utility of shirking would be: Therefore, in order for the agent to work hard, the following constraint (the incentive constraint) must be satisfied

  • Principal-agent problem

    Agents have different functions than principle and these functions are known as utility functions (Principal-Agent Theory, 2008). Principle agent problem is based on designing an incentive scheme, which shows a theoretic summary of condition.

  • Agency and Liability

    Robbins as the principal to the purchase. Apparent authority is present when the principal does something to make a third party believe that the agent has authority to bind the principal. In this case, Dr.

  • von Neumann-Morgenstern utility function - risk averse agent

    V=(1-x)*v(y-pq)+x*v( y-T+(1-p)q) For maximizing the utility, we differentiate the utility curve by q and equate it to zero.

  • Business agency law relationships

    Intention of the agent to act on behalf of the principal. Duties of the Principal towards agent 1. To indemnify the agent against the consequences of all lawful acts and acts done in good faith. 2.

  • The principal and agent relationship

    407369 The principal and agent relationship is examined. Discuss the problems that could exist in the principal and agent relationship in aging services such as case manager and an nursing home.

  • agent to a principal: performance

    For instance, the agent must notify the principal if he represents more than one principal and he may represent the interests of the principal only after full disclosure and consent.

  • business law

    Also demonstrate your understanding of the relationship between the principal and the agent and the authority conferred upon the agent by the principal Since Al Agent is not merely an agent of Pete Principal, he is also an employee, Pete Principal

  • Agency Relationships

    199329 Agency Relationship: liability and third party In an agency relationship involving a principal, an agent and a third party, whether or not the agency relationship has been disclosed to the third party is a crucial issue.

View More Related Solutions