ECON90034 Chap.9 Moral Hazard and Optimal Contracts
Moral Hazard and Optimal Contracts
Topic 6a studies contracts when one party cannot see what the other does. A risk-neutral principal hires a risk-averse agent whose effort raises the chance of a good outcome but costs the agent utility. When effort is observable, the first best pays a constant wage that just meets the agent's reservation utility, and the principal picks the effort with the highest net profit.
When effort is hidden, pay must depend on output: the participation and incentive constraints both bind, the agent bears some risk, and the principal pays a risk premium or settles for lower effort. The review lecture expects you to find both contracts with two or three effort levels, compare them and calculate the welfare loss.
What this chapter covers
- 01
Hidden action versus hidden information
- 02
The principal and agent model: who bears risk
- 03
Participation (IR) and incentive compatibility (IC) constraints
- 04
The first-best contract when effort is observable
- 05
The optimal contract under moral hazard with two effort levels
- 06
Three effort levels: which incentive constraint binds
- 07
Welfare loss: higher wage bill or inefficient effort
- 08
Multitasking, teams and relative performance
Worked example · free
First best and second best with two effort levels
- 1Expected output: high effort 0.8 × 64 + 0.2 × 16 = 54.4; low effort 0.4 × 64 + 0.6 × 16 = 35.2.
- 1First best: √w = 4 gives w = 16 for high effort, profit 38.4; √w = 3 gives w = 9 for low effort, profit 26.2. High effort at a constant 16.
- 2Moral hazard: IR 0.8sG + 0.2sB = 4 and IC 0.4(sG − sB) = 1, so sG − sB = 2.5, giving sG = 4.5 and sB = 2.
- 1Wages 20.25 after 64 and 4 after 16; expected wage 0.8 × 20.25 + 0.2 × 4 = 17, profit 37.4, still above 26.2.
- 1Welfare loss = 38.4 − 37.4 = 1, the extra expected wage needed to compensate the agent for risk.
Key terms
- Principal
- The party who designs and offers the contract and receives the output, assumed risk neutral in the subject's model.
- Participation constraint
- The requirement that the agent's expected utility from the contract is at least the reservation utility available elsewhere.
- Incentive compatibility
- The requirement that the agent prefers the effort the principal wants to any other effort, given the contract offered.
- Efficient risk sharing
- An allocation in which the risk-neutral party carries every bit of the uncertainty and the risk-averse party receives a certain payment.
Moral Hazard and Optimal Contracts FAQ
Why is the first-best wage constant?
When effort can be observed, it can be written into the contract directly, so pay need not depend on output. A risk-neutral principal can then carry all the risk, and a constant wage is the cheapest way to meet the agent's reservation utility.
Which constraints bind under moral hazard?
To implement high effort with two effort levels, both the participation constraint and the incentive constraint bind. To implement the lowest effort, only participation matters and the first-best constant wage is used.
What is the welfare loss from moral hazard?
The principal's profit under the first best minus the profit under the optimal moral hazard contract; the agent gets the reservation utility in both cases, so all of the loss shows up in the principal's profit.
Is there a welfare loss with a risk-neutral agent?
No. A risk-neutral agent needs no compensation for bearing risk, so making pay depend on output costs nothing extra and the first-best outcome can be reached even though effort is hidden.
What happens with three effort levels?
For any effort above the lowest, participation binds and one incentive constraint binds. For a middle effort, one constraint sets a lower bound on the pay gap and the other an upper bound; if they conflict, that effort cannot be implemented.
Exam move
Learn one template and run it on every past question: list expected outputs, solve the first best for each effort, then write IR and every IC in square roots, solve, square, compute the expected wage and compare profits. Finish each problem by naming the source of any welfare loss. Practise at least one three-effort problem to the end, checking feasibility of the middle effort, and keep fractions exact.
In the final week, redo the lecture-style three-effort problem without notes and time it against the twenty points a Part B question carries.
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