D_PrincipalAgent&amp;Personnel

# D_PrincipalAgent&amp;Personnel - Introduction to...

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Introduction to Principal-Agent Theory, Personnel Economics, and Efficiency Wage Models 1. The Principal-Agent Problem In the basic Principal-Agent problem, the Agent chooses e (effort) to maximize: W = R ( q ( e )) – V ( e ) (1) Where V ( e ) is disutility of effort, q is the agent’s output, and R is the agent’s monetary reward. Note two important things: First, the utility function is linear in income, R . This means there are no income effects on effort supply. The usual justification for this is that the rewards we are thinking about are small relative to lifetime income. Second, for simplicity (1) ignores uncertainty in the relation between effort and results but the vast majority of actual treatments include it, for example in the form q = Q ( e , ε ), where ε is a random variable outside the agent’s and principal’s control. In that case, risk aversion matters. When risk aversion is considered in these models, it is pretty much always modelled by letting the the utility function be U [ R ( q ( e )) ] – V ( e ), where U ′ >0, U ″<0. This is still considerably simpler and more restrictive than the general case U ( R, e ), because U CL equals zero. The Principal , in turn, chooses R ( q ) (note this is a function ) to maximize expected profits: q R ( q ) (2) subject to two contraints: 1. The agent’s maximization as in (1) (“incentive compatibility”). Sometimes this is characterized by a first-order condition, but care must be taken if you do that…. . 2. The agent’s participation constraint, W W , where W is the agent’s alternative (or target) utility level. Thus, note that this is a “Stackelberg” type problem: The principal moves first, but chooses her actions anticipating how the agent will respond to R ( q ). To solve these problems, the economist proceeds backwards in time, solving (1) first, then using that information to solve (2). Also, note that the participation constraint ensures that the solution is (constrained) Pareto-Optimal, i.e. it maximizes one party’s utility (the principal’s) subject to a minimum level of the agent’s. Thus, by varying W , we can find not just the best

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solution for the principal that prevents the agent from quitting, but any Pareto-optimal reward schedule that satisfies the incentive-compatibility constraints. 2
2. Theoretical Predictions a) The most basic result in P/A theory is that, when there is no uncertainty (or, more importantly, when the agent is risk neutral), the optimal reward schedule takes the form: R ( q ) = q + k Note that this is linear and the coefficient on q is 1. In other words, this is a “100% piece rate”, where the agent receives every dollar of (net) revenue he generates for the principal. Note that, for the principal to make any profit under this arrangement,

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## This note was uploaded on 12/26/2011 for the course ECON 250A taught by Professor Kuhn during the Fall '09 term at UCSB.

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D_PrincipalAgent&amp;Personnel - Introduction to...

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