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You hire someone whose effort you cannot watch. Pay a flat salary and they coast. Tie pay to results and they work, but results are noisy, so you end up paying for luck as well as effort. There is no contract that gets you the effort for free.

Contract theory and moral hazard

Moral hazard is a hidden-action problem: the agent chooses effort you cannot see, and only a noisy outcome is observable. To motivate effort you must make pay depend on the outcome, which hands the agent a reward for good luck. That extra pay, the rent, is the price of not being able to watch.

From earlier lessons

Two quick ones before we start.

Adverse selection is about hidden types; moral hazard is about hidden...

A risk-neutral agent evaluates a contract by its...

Predict, then play

Output is High (100) or Low (0). Effort costs the agent 15 and lifts the chance of High output from 40% to 80%. You cannot observe the effort, only the output. Design the pay: a base plus a bonus for high output.

Why did that happen?

Take a guess, then reveal the reason

Because effort is hidden, a flat wage gives the agent no reason to bear the cost of working, so they shirk. The only lever you have is the outcome, so pay must rise with high output. But output is noisy: a hard worker sometimes gets Low and a shirker sometimes gets High. To make effort the agent’s best choice, the bonus has to be big enough that the extra chance of the bonus outweighs the effort cost, and that same bonus overpays the agent on average, leaving them a rent. You cannot separate rewarding effort from rewarding luck.

The math

Output is $100$ (High) or $0$ (Low). Effort $e \in \{0,1\}$ costs $15$ when $e=1$ ; $\Pr(\text{High}\mid 1) = 0.8$ and $\Pr(\text{High}\mid 0) = 0.4$ . The agent is risk-neutral with limited liability (wages $\ge 0$ ) and reservation utility $0$ . Write the contract as a base $w_L$ and a high-output wage $w_H$ .

Incentive compatibility. The agent picks $e=1$ over $e=0$ iff

0.8\,w_H + 0.2\,w_L - 15 \ \ge\ 0.4\,w_H + 0.6\,w_L,

which simplifies to $w_H - w_L \ge 37.5$ . The bonus, not the base, drives effort.

Strict incentive contract. With limited liability set $w_L = 0$ . The cutoff is $w_H=37.5$ , where the agent is indifferent between effort and shirking. To avoid assuming a favourable tie-break, use $w_H=38$ . The agent’s expected utility is $0.8(38)-15=15.4$ , and the principal’s profit is $0.8(100)-0.8(38)=49.6$ , above the $40$ from paying nothing and letting the agent shirk.

Definition, moral hazard and the rent

When actions are hidden, pay must be tied to observable output to satisfy incentive compatibility, which exposes a risk-averse or limited-liability agent to outcome risk and generally leaves them a rent. With observable effort (the first best) the principal would pay just the effort cost $15$ and keep $65$ . Under the strict $38$ bonus, the hidden-action loss is $65-49.6=15.4$ , equal to the agent’s rent in this risk-neutral example.

Work it out

Find the profit-maximising contract

Start with incentive compatibility. Effort raises the chance of High by $0.8 - 0.4 = 0.4$ , so the expected gain from effort is $0.4(w_H - w_L)$ , and the agent works only if this covers the cost: $0.4(w_H - w_L) \ge 15$ , i.e., $w_H - w_L \ge 37.5$ .

Under limited liability, set $w_L=0$ . The mathematical cutoff is $w_H=37.5$ , but equality leaves the agent indifferent. On the game’s half-unit grid, $w_H=38$ is the smallest strict incentive contract. Expected pay is $0.8(38)=30.4$ , so the agent’s payoff is $15.4$ and the principal’s profit is $80-30.4=49.6$ . That still beats the no-effort profit of $40$ .

Key idea

Hidden effort forces you to pay for output, not effort, which rewards luck and leaves the agent a rent. A flat salary kills incentives; a bonus strictly above the incentive cutoff makes effort worthwhile.

Check yourself

Check yourselfapply

Why can a generous flat salary not solve the moral-hazard problem?

Check yourselfanalyse

The optimal contract leaves the agent a rent of 15. What does that rent represent?

Check yourselfbrings back: adverse selection

How does moral hazard differ from the adverse selection of the last unit?

Sources

Holmström, B. (1979). Moral hazard and observability. Bell Journal of Economics, 10(1), 74-91.
Grossman, S. J., and Hart, O. D. (1983). An analysis of the principal-agent problem. Econometrica, 51(1), 7-45.