The Impossible Perfect Contract

Lesson 4 left you standing on a hilltop. We showed that the optimal contract sits at an interior optimum — not zero incentive, not full incentive, but a sweet spot somewhere in the middle — and that whatever you do, a stubborn residual loss refuses to disappear. You could shrink monitoring costs, sharpen bonding, tune the incentive dial all day, and the gap between “what your agent does” and “what a perfectly aligned clone of yourself would do” never quite hits zero.

That was the claim. This lesson is the proof. And like the best results in mechanism-design, it is a proof of impossibility — a demonstration that no clever contract, however ingenious, can wring out the last drop of loss. The reason isn’t that contract designers aren’t trying hard enough. It’s that three separate forces each guarantee a residual, and you cannot switch off all three at once. Meet the three impossibilities: the risk–incentive trade-off, the incompleteness of contracts, and the multitasking problem. Any one of them alone would keep the perfect contract out of reach. Together, they nail the door shut.

The risk–incentive trade-off

The analogy. Imagine paying a fisherman purely by the day’s catch. On a calm, fish-rich morning that rewards his skill beautifully. But the catch also depends on weather, currents, and where the shoals happened to swim — things he cannot control. Pay him only on the catch and you’ve made him gamble his rent on the ocean’s mood. A cautious fisherman will only accept that gamble if you sweeten the average payout enough to compensate for the sleepless nights. That sweetener is money you spend not on effort, but on fear.

The precise statement. To sharpen an agent’s incentives you must tie their pay to outcomes — because outcomes are what you actually care about, and the agent’s hidden effort is what moves them. But outcomes are noisy: they equal effort plus a large random shock (luck). So the very act of loading pay onto outcomes loads risk onto the agent. A risk-averse agent — one who prefers a sure thing to a fair gamble of equal average value — dislikes that risk and will only accept it in exchange for a risk premium: extra expected pay that compensates for the uncertainty. Write the intuition as words, not symbols: pay equals base plus rate times outcome, and outcome equals effort plus luck. Crank the “rate” up and you buy more effort — but you also force the agent to swallow more luck, and they bill you a premium for the privilege. The optimal contract balances the effort you gain against the risk premium you pay. That balance point is interior. That is why the hilltop in lesson 4 had a peak in the middle.

A worked example. Meet Dana, a salesperson. Her measured result each quarter is effort plus a big random shock. Suppose:

• Under a flat salary, she coasts, producing €80,000 of sales; you pay her €20,000; no risk sits on her.
• Under 100% commission (say she keeps 30% of sales, no base), the sharper incentive lifts her true effort so her average sales rise to €120,000 — genuinely more effort, genuinely more value to you. But the luck shock is huge: her quarterly sales swing by ±€60,000 for reasons she can’t touch. Being risk-averse, Dana treats that wild, uncontrollable swing as a real cost. To accept the gamble at all, she demands the average commission be padded by a €15,000 risk premium over what a risk-neutral person would accept.

Now tally it up from your side, focusing on your net (value created minus what you pay):

Full commission does raise average sales the most — but look closer at what happens if the luck shock is even bigger or Dana is even more risk-averse: the premium balloons. Push the premium from €15,000 to, say, €30,000 and full commission nets you €69,000, below the balanced contract’s €79,000 and barely above the flat salary. The lesson: the noisier the measure and the more risk-averse the agent, the more the premium eats the gains — until a lower-powered, flatter contract nets more. The 100% dial isn’t just imperfect; past a point it’s actively worse.

The corollary — noisier measure, flatter contract. This gives you a design rule you can carry anywhere: the noisier the measure of the agent’s contribution, the flatter the optimal contract should be. When output barely reflects effort — swamped by luck — put more weight on salary and less on the outcome, because high-powered pay would mostly be buying you an expensive risk premium for very little effort signal. When output tightly tracks effort (little luck), you can afford steeper incentives, because you’re paying for effort, not fear. Piece-rate factory work (clean signal) can be high-powered; a startup founder betting on a wildly uncertain market (filthy signal) often takes mostly equity precisely because they choose to bear that risk, but a hired manager under the same noise gets a flatter deal.

Incomplete contracts

The analogy. You hire a builder to renovate a bathroom and you write the tightest contract you can: tiles here, this fixture there, finish by June. Then they open the wall and find rotten joists, a mystery pipe, and asbestos nobody knew about. Your contract said nothing about any of it — because you couldn’t have known. No document, however long, could have enumerated every gremlin behind that wall. So now what happens is decided not by the contract, but by whoever holds the leverage in the argument that follows.

The precise statement. A complete contract would specify, in advance, exactly what each party does in every possible future state of the world. Such a contract is impossible to write. The world has effectively unlimited future states; many are unforeseeable; even the foreseeable ones are too costly to describe, verify, and enforce. So real contracts are necessarily incomplete — they leave gaps. And whatever the contract doesn’t nail down gets decided by whoever holds the residual control rights: the default right to decide in situations the contract didn’t cover. This is the core of the incomplete-contracts theory of Oliver Hart, Bengt Holmström, and Grossman–Hart–Moore — Nobel-recognised work — and it explains why ownership and bargaining power matter at all. If contracts could be complete, who “owned” the leftover decision rights wouldn’t matter, because nothing would be left over.

A worked example — the renovation, and then the job. Return to that bathroom. The contract couldn’t foresee the rotten joists, so when they appear you and the builder must renegotiate mid-project. He now holds a strong card: your bathroom is a hole in the floor, you can’t easily swap builders halfway, and he knows it. He can extract a higher price for the extra work than he’d have quoted up front. That extra price you overpay is a slice of the agency gap leaking through a hole the contract couldn’t have closed. Now scale it up. An employment contract is the purest case of incompleteness: no job description lists every task. Instead you sign up for something open-ended — “I’ll do the reasonable things my manager asks, within limits.” That vagueness is not sloppiness; it’s the only workable design, because the future tasks are unknowable on day one. But it means the exact boundary of the agent’s duties is forever unsettled, and misalignment seeps through the unwritten gaps every day.

The implication. Because you can’t specify everything, some misalignment always leaks through the unwritten gaps. Even if you magically solved the risk–incentive trade-off, incompleteness alone would leave a residual. The perfect contract would have to be complete — and complete contracts don’t exist.

The multitasking problem

The analogy. Give a teenager €5 for every dish they wash, and nothing for anything else. You will get sparkling dishes — and a kitchen where the floor is never swept, the bins overflow, and the milk sits out, because those don’t pay. You didn’t make them lazy. You made them rational. They poured their effort exactly where the reward pointed and abandoned everything you forgot to price. That is multitasking in one sentence: you get what you pay for, and only what you pay for.

The precise statement. The multitasking problem (Bengt Holmström and Paul Milgrom) arises when a job has several dimensions but you can only measure some of them. Attach strong incentives to the measurable dimensions and the agent, optimising rationally, shifts effort toward the measured tasks and away from the unmeasured ones — even when the unmeasured ones matter more. The stronger the incentive on the measurable part, the harder the unmeasurable part gets starved. This is the deep engine behind Goodhart’s Law from incentives: when a measure becomes a target, it ceases to be a good measure — because the agent optimises the number, not the thing the number was supposed to stand for.

Worked examples. The pattern repeats everywhere a job is broad and only part of it is countable:

In every row the agent isn’t cheating in any narrow sense — they’re doing exactly what the incentive rewards. The failure is in the measure, which captured one dimension and silently taxed the rest.

The sharp corollary. Here is the counter-intuitive punchline that ties the whole lesson together. When a job has competing tasks and some are unmeasurable, the optimal incentive on the measurable ones is deliberately weak — sometimes a flat salary is best, precisely because high-powered pay would distort the agent’s effort allocation toward the measurable and away from the more important unmeasurable. This is why professionals in broad, judgment-heavy roles — teachers, judges, academic researchers, doctors — are so often paid fixed salaries rather than piece rates. It is not that we forgot to incentivise them. It’s that any sharp incentive we could write would reward the countable sliver of their job and quietly gut the rest. Under multitasking, the least-distorting contract can be the one with no incentive power at all.

Putting it together: the residual loss is structural

Now stack the three impossibilities and watch the perfect contract die three deaths.

• Risk–incentive trade-off: to sharpen incentives you load risk onto a risk-averse agent, who charges a premium — so you can’t push incentive power to the max without overpaying. A residual gap survives.
• Incomplete contracts: you can’t specify every future state, so misalignment leaks through the unwritten gaps no matter how carefully you draft. A residual gap survives.
• Multitasking: when only some dimensions are measurable, strong incentives distort effort away from the unmeasured ones, so you must deliberately keep incentives weak — leaving the measured slice under-incentivised on purpose. A residual gap survives.

Each force, alone, would keep you off the peak. To reach a perfect contract you’d need to switch off all three at once — a world where outcomes carry no luck, contracts foresee every state, and every dimension of every job is cheaply measurable. That world does not exist. So the honest goal is never the perfect contract; it’s a good-enough contract — one that shrinks agency costs as far as the three trade-offs allow and then accepts the irreducible remainder.

Recap

• The residual loss is structural, not a sign of sloppy design. Three separate forces each guarantee it, and you cannot switch off all three at once.
• Risk–incentive trade-off: sharpening incentives means tying pay to noisy outcomes, which loads risk onto a risk-averse agent, who demands a risk premium. That premium buys no effort — it’s the price of a shaky measure. Corollary: the noisier the measure, the flatter the optimal contract.
• Incomplete contracts (Hart, Holmström, Grossman–Hart–Moore): you can’t specify every future state, so gaps are inevitable and get filled by whoever holds residual control / bargaining power. Misalignment always leaks through.
• Multitasking problem (Holmström & Milgrom): reward only the measurable dimensions and the agent drops the unmeasured ones (Goodhart). Sharp corollary: when tasks compete and some are unmeasurable, the optimal incentive is deliberately weak — sometimes a flat salary is best.
• The perfect contract is impossible. The mature goal is a good-enough contract — echoing mechanism-design’s impossibility results.

Next up — Where the Model Lies: the limits of the principal–agent lens itself, and the cases where treating everything as a contract to optimise quietly leads you astray.