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Moral Hazard and Optimal Contracting

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Moral HazardMoral Hazard in Insurance and Contracting
information asymmetry moral hazard principal-agent

Core Idea

Moral hazard arises when an agent's hidden actions (effort, risk-taking) are unobservable to a principal who bears the cost. The principal cannot condition payment on effort, so must use output-based contracts to incentivize. Optimal contracts balance incentive provision (high-powered) against risk imposition on risk-averse agents (low-powered). Insurance, employment, and debt contracts exemplify this tradeoff: full insurance eliminates incentive; no insurance removes the principal's control.

Explainer

From your prerequisite study of moral hazard, you know the core problem: a principal (employer, insurer, lender) wants an agent (employee, policyholder, borrower) to take a costly action — exert effort, drive carefully, run the business prudently — but cannot directly observe whether they do. The question now is: what contract should the principal offer? The answer is not obvious because there are two things the principal wants simultaneously, and they pull in opposite directions.

The first goal is risk sharing. If the agent is risk-averse and the principal is risk-neutral (or has better access to diversification), efficiency requires that the principal absorb the output variability. The agent should receive a fixed payment regardless of outcomes. A salaried employee is the clearest example: the employer takes the revenue risk, the worker gets a stable paycheck. But here is the problem: once the employee's income is fixed, they bear no personal cost from low output. The effort-supply incentive disappears entirely. This is the fundamental tension.

The second goal is incentive provision. To restore effort incentives, the contract must make the agent's pay depend on output. A commission salesperson earns more when they sell more — that creates incentive. But now the agent bears outcome risk that partly reflects luck, not just effort. A good salesperson can have a bad quarter because of macro conditions. Forcing them to bear that risk is inefficient from a pure insurance standpoint. The optimal contract navigates this tradeoff: it imposes just enough output-contingent pay to induce the desired effort level, and no more. The tradeoff is often called risk vs. incentives: high-powered contracts (large pay-for-performance) provide strong incentives but impose large risk; low-powered contracts (near-flat pay) impose little risk but provide weak incentives.

Applications across domains follow the same logic. Insurance: full coverage eliminates the policyholder's incentive to prevent loss (drive carefully, lock doors). Insurers respond with deductibles and co-pays — partial loss-bearing restores prevention incentives. Debt: once a firm is deeply insolvent, shareholders bear no additional downside but capture any upside, so they have incentive to take excessive risk ("gambling for resurrection"). Equity-based executive compensation aligns manager incentives with shareholders but forces executives to hold concentrated, undiversified wealth. In each case, the contract designer faces the same tradeoff and picks an interior solution that accepts some inefficiency on one dimension to reduce inefficiency on the other.

Practice Questions 5 questions

Prerequisite Chain

Understanding ZeroThe Number ZeroCounting to FiveCounting to 10Counting to 20Counting a Set of Objects Up to 20Cardinality: The Last Number CountedMatching Numerals to QuantitiesSubitizing Small QuantitiesAddition Within 10Number Bonds to 10Addition Within 20Doubles and Near DoublesDoubles Facts Within 10Near Doubles Facts Within 20Mental Math Strategies for AdditionMental Math: Adding and Subtracting TensAddition Within 100Repeated Addition as MultiplicationMultiplication as Equal GroupsMultiplication: ArraysBasic Multiplication Facts (0s, 1s, 2s, 5s, 10s)Multiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Multiplication and Division Fact FamiliesRelationship Between Multiplication and DivisionDivision Facts as Inverse of MultiplicationRemainders and Quotients in DivisionDivision Word ProblemsMulti-Step Word ProblemsSolving Multi-Step Word ProblemsMultiplication Word ProblemsDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueIntegers and the Number LineComparing and Ordering IntegersAbsolute ValueAdding IntegersSubtracting IntegersMultiplying IntegersDividing IntegersUnit RatesProportionsPercent ConceptConverting Between Fractions, Decimals, and PercentsOperations with Rational NumbersTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesLiteral EquationsSlope-Intercept FormPoint-Slope FormWriting Linear EquationsParallel and Perpendicular Line SlopesGraphing Linear EquationsPiecewise FunctionsOne-Sided LimitsContinuity DefinitionLimits and Continuity in Multiple VariablesFunctions of Several VariablesContinuity in Multiple VariablesPartial Derivatives: Definition and ComputationDifferentiability in Multiple VariablesDifferentiability in Multivariable FunctionsTotal Differential and Linear ApproximationChain Rule for Multivariable FunctionsImplicit DifferentiationRelated RatesOptimization ProblemsCritical Points of Multivariable FunctionsCritical Points and Classification of ExtremaSecond Partial Test for Local Extrema (Hessian)The Hessian Matrix and Second Derivative TestUnconstrained Optimization: Finding ExtremaOptimization in Multiple VariablesLagrange MultipliersConstrained Optimization and Lagrange MultipliersUtility and PreferencesMarginal Utility and Diminishing ReturnsProfit MaximizationPerfect CompetitionShutdown and Breakeven DecisionsMonopolyMonopolistic CompetitionOligopoly and Strategic BehaviorGame Theory BasicsNash EquilibriumBayesian Games (Games of Incomplete Information)Mechanism Design: Strategic ImplementationIndividual Rationality (Participation Constraint)Incentive Compatibility and Individual RationalityMoral HazardMoral Hazard and Optimal Contracting

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