incentives2-17-18

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

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