Download presentation
Presentation is loading. Please wait.
Published byJodie McGee Modified over 9 years ago
1
Frank Cowell: Microeconomics Contract Design MICROECONOMICS Principles and Analysis Frank Cowell Almost essential Adverse selection Almost essential Adverse selection Prerequisites August 2006
2
Frank Cowell: Microeconomics Purpose of contract design A step in moving from how we would like to organise the economy… A step in moving from how we would like to organise the economy… …to what we can actually implement …to what we can actually implement Plenty of examples of this issue: Plenty of examples of this issue: hiring a lawyer employing a manager Purpose and nature of the design problem Purpose and nature of the design problem construct a menu of alternatives… …to induce appropriate choice of action Key: takes account of incomplete information Key: takes account of incomplete information
3
Frank Cowell: Microeconomics Informational issues Two key types of informational problem: Two key types of informational problem: each is relevant to design question each can be interpreted as a version of “Principal and Agent” Hidden action: Hidden action: The moral hazard problem concerned with unseen/unverifiable events… …and unseen effort Hidden information: Hidden information: the adverse selection problem concerned with unseen attributes… …and unseen effort Here focus on the hidden information problem Here focus on the hidden information problem How to design a payment system ex ante… …when the quality of the service/good cannot be verified ex ante Attack this in stages: Attack this in stages: outline a model examine full-information case then contrast this with asymmetric information
4
Frank Cowell: Microeconomics Overview... Design principles Model outline Full information Asymmetric information Contract design Roots in social choice and asymmetric information
5
Frank Cowell: Microeconomics The essence of the model The Principal employs the Agent to produce some output The Principal employs the Agent to produce some output But Agent may be of unknown type But Agent may be of unknown type type here describes Agent’s innate productivity …how much output per unit of effort The Principal designs a payment scheme The Principal designs a payment scheme takes into account that type is unknown… …and that one type of Agent might try to masquerade as another Provides an illustration of second best problem Provides an illustration of second best problem because of delegation under imperfect information may have to forgo some output … “Agency cost” Use a parable to explain how it works Use a parable to explain how it works
6
Frank Cowell: Microeconomics A parable: paying a manager An owner hires a manager An owner hires a manager It makes sense to pay the manager according to talent But how talented is the manager? A problem of hidden information A problem of hidden information Similar to adverse selection problem But here with a monopolist – the owner The nature of the design problem The nature of the design problem Owner acts as designer Wants to maximise expected profits Wants to ensure that manager acts in accordance with this aim “Mechanism” here is the design of contract (s)
7
Frank Cowell: Microeconomics The employment contract: information Perhaps talent shows Perhaps talent shows Ability can be observed or … …costlessly verified Full-information solution Perhaps it doesn’t Perhaps it doesn’t Ability cannot be observed in advance of the contract Will low ability applicants misrepresent themselves? Will high ability applicants misrepresent themselves? The approach The approach Examine full-information solution Get rules for contract design in this case Remodel the problem for the second-best case Modify contract rules
8
Frank Cowell: Microeconomics Overview... Design principles Model outline Full information Asymmetric information Contract design A simple owner- and-manager story
9
Frank Cowell: Microeconomics Model basics: owner Owner makes first move Owner makes first move designs payment schedule for the manager makes a take-it-or-leave-it offer Has market power Has market power Can act as a monopolist Appropriates the gains from trade Gets profit after payment to manager: Gets profit after payment to manager: utility (payoff) to owner is just the profit pq y p: price of output q: amount of output y : payment to manager
10
Frank Cowell: Microeconomics Model basics: manager A manager’s talent and effort determines output: A manager’s talent and effort determines output: q = z. q : output produced : the amount of talent z : the effort put in Manager’s preferences Manager’s preferences = z + y : utility level y : income received : decreasing, strictly concave, function equivalently: = q / + y. Manager has an outside option Manager has an outside option : reservation utility A closer look at manager’s utility
11
Frank Cowell: Microeconomics The utility function (1) increasing preference y 1– z Preferences over leisure and income Indifference curves = z + y z z < 0 Reservation utility ≥ ≥ ≥ ≥
12
Frank Cowell: Microeconomics The utility function (2) increasing preference y q Preferences over leisure and output Indifference curves = q/ + y z q/ < 0 Reservation utility ≥ ≥ ≥ ≥
13
Frank Cowell: Microeconomics Model basics: information There are different talent types j = 1,2,… There are different talent types j = 1,2,… Type j has talent j Probability of a manger being type j is j Probability distribution is common knowledge Owner may or may not know type j of a potential manager Profits (owner’s payoff) depend on talent: Profits (owner’s payoff) depend on talent: pq j y j. q j = j z j : the output produced by a type j manager z j : effort put in by a type j manager Managers’ preferences are common knowledge Managers’ preferences are common knowledge Utility function is known Also known that all managers have the same preferences, independent of type
14
Frank Cowell: Microeconomics Indifference curves: pattern Managers of all types have the same preferences Managers of all types have the same preferences j = z j + y j. j = q j j + y j. Function is common knowledge Function is common knowledge But utility level j of type j depends on effort z j and payment y j. Take indifference curves in (q, y) space Take indifference curves in (q, y) space = q j + y. Clearly slope of type j indifference curve depends on j. Indifference curves of different types cross once only
15
Frank Cowell: Microeconomics The single-crossing condition increasing preference y q j=b j=a Preferences over leisure and output High talent q a = a z a Low talent q b = b z b Those with different talent will have different sloped ICs in this diagram
16
Frank Cowell: Microeconomics Overview... Design principles Model outline Full information Asymmetric information Contract design Where talent is known to all…
17
Frank Cowell: Microeconomics Full information: setting Owner may be faced with a manager of any type j Owner may be faced with a manager of any type j But owner can observe the type (talent) j But owner can observe the type (talent) j Therefore can observe effort z j = q j / j So the contract can be conditioned on effort Offer manager of type j the deal ( y j, z j ) Owner prepares menu of such contracts in advance Owner prepares menu of such contracts in advance Aims to maximise expected profits Manager then chooses effort in response Manager then chooses effort in response Aims to maximise utility This choice is correctly foreseen by the owner designing the contract
18
Frank Cowell: Microeconomics Full information: problem Owner aims to maximise expected profits Owner aims to maximise expected profits Expectation is over distribution of types. Maximisation subject to (known) manager behaviour Participation constraint of type j. Choose y j, z j to Choose y j, z j to max j j [p j z j y j ] subject to y j + z j ≥ j. Solve this using standard methods for constrained maximum Solve this using standard methods for constrained maximum
19
Frank Cowell: Microeconomics Full information: solution Set up standard Lagrangean: Set up standard Lagrangean: Lagrange multiplier j for participation constraint on type j. Choose y j, z j, j to max j j [p j z j y j ] + j j [y j + z j − j ] First-order conditions: First-order conditions: j = j z z* j = p j y j + z* j = j Interpretation Interpretation “Price” of constraint is probability of a type j manager MRS = MRT Reservation utility constraint is binding
20
Frank Cowell: Microeconomics Full-information solution y q q *a q *b y *b y *a _ bb _ aa p a type’s reservation utility b type’s reservation utility a type’s contract b type’s contract Both types get contract where marginal disutility of effort equals marginal product of labour
21
Frank Cowell: Microeconomics Full information: conclusions “Price” of constraint is probability of getting a type-j manager “Price” of constraint is probability of getting a type-j manager The outcome is efficient: The outcome is efficient: MRS = MRT …for each type of manager Owner drives manager down to reservation utility Owner drives manager down to reservation utility complete exploitation owner gets all the surplus
22
Frank Cowell: Microeconomics Overview... Design principles Model outline Full information Asymmetric information Contract design Where talent is private information
23
Frank Cowell: Microeconomics Asymmetric information: approach Full-information contract is simple and efficient Full-information contract is simple and efficient However, this version is not very interesting. However, this version is not very interesting. Problem arises when contract has to be drawn up before talent is known Problem arises when contract has to be drawn up before talent is known Agent may have an incentive to misrepresent his talents this will impose a constraint on the design of the contract Re-examine the Full-information solution Re-examine the Full-information solution
24
Frank Cowell: Microeconomics Another look at the FI solution y q q *a q *b y *b y *a _ bb _ aa p a type’s reservation utility b type’s reservation utility a type’s contract b type’s contract a type’s utility with b type contract An a type would like to masquerade as a b type!
25
Frank Cowell: Microeconomics Asymmetric information again As we have seen a type would want to mimic a b type As we have seen a type would want to mimic a b type We can exploit a standard approach to the problem. We can exploit a standard approach to the problem. Assume that the distribution of talent is known. Assume that the distribution of talent is known. For simplicity take two talent levels For simplicity take two talent levels q a = a z a with probability q b = b z b with probability
26
Frank Cowell: Microeconomics The “second-best” model Participation constraint for the b type: Participation constraint for the b type: y b + z b ≥ b. Have to offer at least as much as available elsewhere Incentive-compatibility constraint for the a type: Incentive-compatibility constraint for the a type: y a + q a / a ≥ y b + q b / a . Must be no worse off than if took b contract Maximise expected profits Maximise expected profits [pq a y a ] + [1 ][pq b y b ]. Choose q a q b y a y b to max Choose q a q b y a y b to max [pq a y a ] + [1 ][pq b y b ] [pq a y a ] + [1 ][pq b y b ] + [y b + q b / b b ] + [y a + q a / a y b q b / a ]
27
Frank Cowell: Microeconomics Second-best: results Lagrangean is Lagrangean is [pq a y a ] + [1 ][pq b y b ] [pq a y a ] + [1 ][pq b y b ] + [y b + q b / b b ] + [y a + qk a / a y b q b / a ] FOC are: FOC are: z q a / a = p a z q b / b = p b + k [1 ] k := z q b / b [ b / a ] z q b / a Results imply Results imply MRS a = MRT a MRS b < MRT b
28
Frank Cowell: Microeconomics Two types of Agent: contract design y q q ~ a q ~ b y ~ a y ~ b a type’s reservation utility b type’s reservation utility b type’s contract incentive-compatibility constraint b type’s contract a contract schedule
29
Frank Cowell: Microeconomics Second-best: less ons a-types a-types for high-talent people… …marginal rate of substitution equals marginal rate of transformation no distortion at the top b-types b-types for low-talent people… …MRS is strictly less than MRT Principal Principal will make lower profits than in full-information case this is the Agency cost
30
Frank Cowell: Microeconomics Summary Contract design fundamental to economic relations Contract design fundamental to economic relations Asymmetric information raises deep issues: Asymmetric information raises deep issues: Principal cannot know the productivity of the agent beforehand Agent may have incentive to misrepresent information important not to have a manipulable contract Second-best approach builds these issues into the problem Second-best approach builds these issues into the problem known distribution of types incentive-compatibility constraint Solution Solution satisfies “no-distortion-at-the-top” principle gives no surplus to the lowest productivity type
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.