Strategic Economics

The Principal-agent Problem and the Optimal Contract

Get the actual formula for how steep a pay plan should be — and discover that the answer is driven almost entirely by how noisy your measure is, which is why most incentive schemes are set at a level the mathematics does not support.

  • Advanced
  • 14 min total
  • 14 chapters

What decision this helps you make: What share of someone's pay should depend on results, which measure it should depend on, and whether a variable plan is worth having at all for this particular role.

What this topic is

A principal-agent problem exists whenever one party acts on behalf of another, their interests are not identical, and the first party cannot fully observe what the second one does or knows. Owner and manager, client and agency, board and chief executive, insurer and insured, buyer and contractor. The optimal contract is the answer to a constrained problem: maximise the principal's payoff, subject to the agent being willing to sign, and subject to the behaviour you want being the behaviour the agent picks for themselves.

Why it matters

This frame produces one of the few genuinely quantitative results in management: an explicit formula for how much pay should be at risk. It says the right answer depends on the agent's risk tolerance, on how responsive output is to effort, and — dominantly — on how noisy the measure is. Plug in real numbers and you find that a variable share appropriate for a salesperson with attributable revenue is wildly wrong for a manager measured on divisional profit, and close to meaningless for anyone measured on the whole firm.

Who should learn it

Owners deciding how to pay a manager they cannot supervise, boards setting executive compensation, anyone structuring an agency or outsourcing relationship, and operators who have watched three consecutive bonus schemes fail to change anything.

What you will understand

  • The two constraints that define any contract, and which one sets level versus slope
  • The optimal pay-performance slope formula, and why measurement noise dominates every other input
  • The exact share of achievable surplus a second-best contract captures — and why it equals the slope
  • How to read a compensation document and find the clause that quietly flattens the whole plan

Prerequisites

Common misconception

"Align incentives and the problem goes away." Alignment is not free and it is not fully achievable. Every dollar of pay you make contingent hands the agent risk they cannot control, and they charge you for carrying it. The optimal contract is therefore a deliberate compromise that leaves some misalignment in place on purpose, and the amount left in place is set by the noise in your measure. A second misconception is that a low variable share signals weak management. On a very noisy measure it is the mathematically correct answer, which is one reading of why executive pay-performance sensitivity has always looked so small.