ECON 426 Lecture Notes - Lecture 21: Incentive Compatibility, Expected Utility Hypothesis, Institute For Operations Research And The Management Sciences
13 Jun 2018
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Crib sheet, 5 pages, double sided handwritten for the exam
Given a salary policy s(y), the agent will choose an effort level e* to maximize their expected utility
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Expected utility at the firms needs to exceed outside option
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The agent's problem?
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Induces a desired effort level e*
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Suffices to induce the agent to work at the firm
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The principal's problem is to set a salary policy s(y) that:
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The principal's problem?
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The Respective Problems
Given by (output - sharing rule): compensation/salary conditional on output
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Output here informs you of the effort of the individual
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The principal offers a contract, and their objective is to maximize their expected profit
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We're trying to solve the principal-agent problem
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This imposes the incentive compatibility constraint on the firm
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The problem to the firm: it doesn't see the action that the worker takes
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Therefore they must write down a contract that's self-fulfilling - i.e., that's self-enforcing
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This maximization is over the contract - the sharing rule - what the firm sees related to what the workers gets + the
effort the firm would like the worker to put in
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They wouldn't have to worry about whether this is still consistent with worker choices after signing the
contract
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Because the principal can't see effort, they have to worry about it
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If the firm could observe effort, then the firm could contract over effort and salary policy
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→the ethat would maximize the worker's expected utility
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When they write down the contract, they must make sure the ethat they choose is the one the worker would
themselves choose given the contract they face
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The only instrument the firm has is salary, because they can't observe effort
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When the firm offers a contract, they think - in terms of the contract I have offered the worker, will the worker
find it advantageous to choose the thing I want the worker to choose?
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Incentive Compatibility Constraint
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This is a function of the salary they receive and the effort they must put in given the contract they face
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Worker maximizes Utility
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Basic Structure of the Incentive Problem
The worker will take the contract if the value they achieve under the contract exceeds some outside
opportunity
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The firm must make sure that whatever contract they offer the worker, the worker must be willing to accept
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Participation Constraint
"Incentive Compatibility" constraint: e* maximizes worker problem
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"Participation Constraint": worker utility at least = to outside opportunity utility
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Maximize the expected profits of the firm w.r.t. salary policy s(y) and optimal effort e* subject to:
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How to Solve This Problem
Lecture 21 - Incentives
Monday, March 26, 2018
4:08 PM
ECON 426 Page 1
The inequality above is a weak inequality
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It won't be advantageous for the firm to offer something that makes the worker better off than the
outside opportunity
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The firm still wants to maximize profit - this means minimizing the left-hand side to the level where it is
strictly equal to outside opportunity
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In equilibrium, the contract the firm offers will make the PC a strict equality
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"Binding" Participation constraint: when the E(utility) = outside opportunity
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Separate preferences over consumption from the disutility of effort:
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Choose a simple relation between the signal, effort, and output
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Allow only linear salary policies:
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Simplifying Assumptions
If the principal could see e, then they could write a contract on e
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This contract would not need to solve the IC constraint - stipulate only that the individual gets paid if the
correct effort is chosen
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"First-Best Solution": What if the principal can contract on e?
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The solution to the First Best problem has a constant salary sand an optimal effort level
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All consumption risk remains with the principal
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Constant salary allows the risk-neutral Principal to absorb all the risk:
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Optimal effort level sets marginal cost = to the expected marginal product
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→effort needs to be observable
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First Best requires a lot of information!
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This is called the "First-Best"
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The worker will receive the outside opportunity
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In competitive labor markets, the firms will be willing to raise salaries until expected profits = 0
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Because of competition for workers, all surplus is paid to workers
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The First Best
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Risk neutral agents will have preferences that are linear in salaries s:
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Substituting the linear salary and output :
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Solution if the Agent is Risk Neutral
The Principal's Problem, 1
ECON 426 Page 2
Document Summary
Crib sheet, 5 pages, double sided handwritten for the exam. Given a salary policy s(y), the agent will choose an effort level e* to maximize their expected utility. Expected utility at the firms needs to exceed outside option. The principal"s problem is to set a salary policy s(y) that: Suffices to induce the agent to work at the firm. The principal offers a contract, and their objective is to maximize their expected profit. Given by (output - sharing rule): compensation/salary conditional on output. Output here informs you of the effort of the individual. This maximization is over the contract - the sharing rule - what the firm sees related to what the workers gets + the effort the firm would like the worker to put in. The problem to the firm: it doesn"t see the action that the worker takes. This imposes the incentive compatibility constraint on the firm.
