incentives2-17-18 - The Principal-Agent model The...

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The Principal-Agent model The principal-agent model Firm owner ( principal ) hires a sales agent Agent’s sales ( z ) : z = e + x = gent’s effort e = agent’s effort x = random factors not controlled by the agent . E(x)=0 and Var(x)= σ 2 Effort has a cost for the agent: c(e)=(k/2)e 2 The agent’s best alternative gives him utility B.
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The Principal-Agent model Optimal effort ( e* ) for the principal? In general, not “maximum” effort Why? Effort is costly for the agent b if the agent is not a slave, the principal will have to compensate him for the effort b for high enough levels of effort, marginal cost of effort (which neads to be compensated) greater than marginal benefit (increased sales) b not optimal to induce agent to increase e .
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The Principal-Agent model
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Optimal compensation contracts Principal can observe sales z, but not e or x . To provide incentives to the agent b pay must depend on z. We will look at compensation contracts with: A fixed component: F A variable component, computed as a fraction of sales (z): pz (p = % commission on sales) I(z)=F+pz
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Optimal compensation contracts Optimal contract for the principal? Values of F and p that maximize the P’s expected profits.
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Optimal compensation contracts To determine optimal contract for principal: 1. Determine how A responds to each contract 2. Compute the P’s expected profit for each contract 3. Pick the contract that maximizes P’s expected profit
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Optimal compensation contracts To determine optimal contract for principal: 1. Determine how A responds to each contract 2. Compute the P’s expected profit for each contract 3. Pick the contract that maximizes P’s expected profit
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1. Agent’s response to compensation contract We will first assume that agent seeks to maximize his expected wealth net of his cost of effort (risk neutral): E(I(z))-c(e)
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1. Agent’s response to compensation contract For given contract (i.e., for given F,p ): I(z)=F+pz How does
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This note was uploaded on 02/03/2011 for the course ECON 302 taught by Professor Pablo during the Spring '11 term at Universidad Carlos III de Madrid.

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incentives2-17-18 - The Principal-Agent model The...

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