MICROECONOMIC ANALYSIS OF LAW September 19, 2006

MICROECONOMIC ANALYSIS OF LAWSeptember 19, 2006

CLEA ConferenceFriday, September 29 to Saturday, September 30

• Posted at:

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• Answers to End of Chapter - Problems

Lecture II Bilateral Agency

BILATERAL AGENCY

Bilateral Agency

Bilateral Contracts

Principal Agency

Principal Agency Contracts

Double Moral Hazard

Moral Hazard

Adverse Selection

BILATERAL AGENCY

The models that follow are simply models.

The models simulate behaviour that occurs across the legal system – not what judges actually say or do in a court.

BILATERAL AGENCY

. Bilateral Agency

Implicit Bilateral AgencyStrategicPrimarily marketExample – Cournot Duopoly

Explicit Bilateral AgencyStrategic, relationalPrimarily non-marketExample – Joint Venture

BILATERAL AGENCY - IMPLICIT

• Implicit Bilateral Agency»Relationship is strategic in nature

• Examples: Duopoly – substitutes

• Duopoly – complements

In many economic contexts implied agencies arise.

These agencies involve non-legally binding strategic interaction between two or more agents.

BILATERAL AGENCY - IMPLICIT COURNOT DUOPOLY

The most well known is the Cournot duopoly, but there many other cases.

• Agents operate economically similar firms – sole proprietorships:

a1 = input of Agent 1

y1 = F(a1) = output of Agent 1

y2 = F(a2) = output of Agent 2

• Agents have “linear utility” in the profits they make. What does this mean?

U(1) = 1 = utility of Agent 1

• Agents are indifferent to risk - risk neutral

• These agents have the following profit functions

1(a1,a2) = (p-c)y1 = (1-y1-y2-c)y1

= y1-y1y1-y1y2-cy1

2(a1,a2) = (p-c)y2 = (1-y1-y2-c)y2

= y2-y2y1-y2y2-cy2

• These agents act in their own self - interest (reaction curves)

d1(a1,a2)/da1 = 0

d2(a1,a2)/da2 = 0

F1(a1) – 2F(a1)F1(a1) - F1(a1)y2-cF1(a1) = 0

F2(a2) – 2F(a2)F2(a1) - F2(a2)y2-cF2(a2) = 0

Set of Cost Minimizers

Set of Profit Maximizers

BILATERAL AGENCY - IMPLICIT COURNOT DUOPOLY – NASH EQUILIBRIUM

• The principle or axiom of self-interest

is (reflected in reaction curves)

F(a1) = (1/2)(1 - F(a2) - c)

F(a2) = (1/2)(1 - F(a1) - c)

• Equilibrium occurs where these “self-interested” actions intersect – Nash Equilibrium

a*1 = a*2 = F-1[(1/3)(1–c)]

• John Forbes Nash, 1928 -

AGENT 1 producing a1

a1 = ½(1- a2 -c)

AGENT 2 producing a2

a2 = ½(1- a2 – c)

E[(1/3)(1-c), (1/3)(1-c)]

• If F (a) = a, the agents have the following Nash equilibrium:

a*1 = a*2 = (1/3)(1 – c)

*1 = *2 = (1/9)(1 – c)(1 – c)

p* = 1 - (2/3)(1 – c) = (1/3)(1 + 2c)

• If F (a) = a, the agents have the following iso-profit functions :

*1 = a1-a1a1-a1a2-ca1

a2 = - a1 - /a1 + (1-c) - Agent 1

*2 = a2-a2a2-a2a1-ca2

a1 = - a2 - /a2 + (1-c) – Agent 2

E[1/3(1-c), 1/3(1-c)]

Iso-Profit Curve For Agent 1

• Professor Cooter both defines Nash equilibrium and distinguishes it from Pareto efficiency – (4th ed., 2004, c. 2., VII, p. 41)

Economic Measures

BILATERAL AGENCY - IMPLICITMarket Efficiency

• Efficiency

• An allocation of resources is efficient when no further increases to production can be made.

BILATERAL AGENCY - IMPLICITMarket Efficiency

• Perfect Competition • Duopoly

Consumer Demand

[(1-c), c]

Producer Supply

[1,0] [1,0]

[(2/3)(1-c), (1/3)(1+2c)]

P = 1-xP = 1-x

Consumer Demand

DECREASE in EFFICIENCY

BILATERAL AGENCY - IMPLICITMarket Competitiveness

• Competitiveness

• An allocation of resources is competitive when no further decreases to price can be made.

BILATERAL AGENCY - IMPLICIT Market Competitiveness

Consumer Demand

[(1-c), c]

Producer Supply

[1,0] [1,0]

[(2/3)(1-c), (1/3)(1+2c)]

P = 1-xP = 1-x

Consumer Demand

DECREASE in Competitiveness

BILATERAL AGENCY - IMPLICITMarket Optimality

• Professor Cooter explains Kaldor-Hicks “efficiency” – (4th ed., 2004, c. 2., IX, p. 48)

• Mr. Justice Posner also uses the word “efficiency” in reference to “market optimality”

• Pareto efficiency or Pareto optimality.• Maximizes social surplus making at

least one individual better off, without making any other individual worse off.

• An allocation of resources is Pareto optimal or Pareto efficient when no further improvements to social surplus can be made.

• Mr. Justice Posner offers a criticism of the Pareto criterion as being too narrow for policy formation. He uses the argument first raised by John Stuart Mill.

• “Every person should be entitled to the maximum liberty consistent with not infringing anyone else's liberty”.

• Because of the existence of interpersonal utility preferences, Mill's idea would contradict the strict application of the Pareto criterion to every case (6th ed., 2004, c. 1, pp. 12-13)

Consumer Surplus

[(1-c), c]

Producer Surplus

[1,0] [1,0]Duopolists’ Surplus

P = 1-xP = 1-x

Consumer Surplus

DECREASE in Social Surplus

• Kaldor-Hicks efficiency occurs when the economic value of social surplus is maximized.

• Under Kaldor-Hicks efficiency, a more optimal outcome can leave some people worse off.

• An outcome is more “optimal” or more “efficient” if those that are made better off could in theory compensate those that are made worse off.

• As Mr. Justice Richard Posner quite rightly points out, the Kaldor-Hicks criterion – has limitations:

• It does not answer the distributive issues. • Much of what economists call surplus is

hypothetical » what consumers would pay for certain goods » not what is actually paid. » (6th ed., 2004, c. 1, p. 16)

Kaldor-Hicks CriterionPareto

Criterion

Recall that these models simulate behaviour that occurs across the legal system.

Exception: Antitrust cases. As a matter of evidence, economic experts may testify as to how social surplus is effected by a merger or takeover

Recently, the Federal Court of Appeal in Canada ruled on the appropriateness of using “social surplus” as a criterion for evaluating a “friendly” merger between ICG Propane and Superior Propane.

. Implicit Bilateral AgencyStrategicPrimarily marketExample – Cournot Duopoly

Horizontal Implicit Agency

Example – Cournot Duopoly

Vertical Implicit Agency

Example – Stackelberg Duopoly

• Cournot Duopoly • Stackelberg Duopoly

AGENT 1 AGENT 2 PRINCIPAL

BILATERAL AGENCY - IMPLICIT STACKELBERG DUOPOLY

• The primary feature of the Stackelberg duopoly is that the “lead agent” takes into account not simply the existence of the rival agent (Cournot game) but as well its profit maximizing motivation.

• The Stackelberg game lies behind many of the vertical relationships to be examined.

• Heinrich von Stackelberg, 1905-1946

• Recall that the principle or axiom of self-interest for the Cournot duopoly

F(a1) = (1/2)(1 - F(a2) - c)

F(a2) = (1/2)(1 - F(a1) - c)

reflecting a “game” of simultaneous moves

• The principle or axiom of self-interest for the Stackelberg duopoly is

F(a1) = (1/2)(1 – [(1/2)(1 - F(a1) - c)] - c)reflecting a “game” of sequential moves with the “lead agent” making the “first move” by optimizing its profits by taking the profit of the follower into account.

• Duopoly • Stackelberg Duopoly

Agent I

Agent II

[(1/3)(1-c), (1/3)(1-c)]

[0,(1-c)]

[0,(1/2)(1-c)]

[(1/2)(1-c), 0][(1-c), 0]

[(1/2)(1-c), (1/4)(1-c)]

Agent I

Agent II

[(1/2)(1-c), 0]

[0,(1/2)(1-c)]

Isoprofit Curve of Firm II

Isoprofit Curve of Firm I

• Equilibrium occurs, not where the “self-interested” actions of simultaneously moving players intersect, but where the profits of the “lead agent” are maximized:

a*1 = F-1[(1/2)(1 – c)]

a*2 = F-1[(1/4)(1 – c)]

[(1/3)(1-c), 0] [(2/3)(1-c), 0] [1,0] [(1-c)/2,0] [(3/4)(1-c), 0] [1,0]

P = 1- a1 - a2 P = 1- a1 - a2

• Nash Equilibrium• Simultaneous Solution

a1 = a2 = (1/3)(1-c)

• Nash Equilibrium• Sequential Solution

a1 = (1/2)(1-c)

a2 = (1/4)(1-c)

[0,(1/3)(1+2c)]

[(1/3)(1-c), 0] [(2/3)(1-c), 0] [1,0] [(1-c)/2,0] [(3/4)(1-c), 0] [1,0]

[0,(1/4)(1+ 3c)]

P = 1- a1 - a2 P = 1- a1 - a2

• If F (a) = a, the agents have the following Nash equilibrium:

a*1 = (1/2)(1 – c)

a*2 = (1/4)(1 – c)

*1 = (1/8)(1 – c)(1 – c)

*2 = (1/16)(1 – c)(1 – c)

p* = 1 - (3/4)(1 – c) = (1/4)(1 + 3c)

• Cournot Benchmarks• Efficiencya1 + a2 = (2/3)(1-c)

• Competitivenessp = (1/3)(1 + 2c)

• Producers SurplusPS = (2/9)(1-c)(1-c)

• Social SurplusSS = (4/9)(1-c)(1-c)

• Stackelberg Benchmarks• Efficiencya1 + a2 = (3/4)(1-c)

• Competitivenessp = (1/4)(1 + 3c)

• Producers SurplusPS = (3/16)(1-c)(1-c)

• Social SurplusSS = (15/32)(1-c)(1-c)

Collusive Duopoly

•With no property rules - can contracts still exist?

BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY

New Nash Equilibrium

New Iso-Profit Curve For Firm X

New Iso-Profit Curve For Firm Y

•Yes. The collusive contract is more optimal for both parties, but is unstable. Either party has a “short-term” incentive to “defect” to the Nash equilibrium

• Perfect Competition • Collusive Duopoly

Consumer Demand

[(1-c), c]

Producer Supply

[1,0] [1,0]

[(1/2)(1-c), (1/2)(1+c)]

P = 1-xP = 1-x

Consumer Demand

BIGGER DECREASE in EFFICIENCY

Consumer Demand

[(1-c), c]

Producer Supply

[1,0] [1,0]

[(1/2)(1-c), (1/2)(1+c)]]

P = 1-xP = 1-x

Consumer Demand

BIGGER DECREASE in Competitiveness

Consumer Surplus

[(1-c), c]

Producer Surplus

[1,0] [1,0]

Duopolists’ Surplus

P = 1-xP = 1-x

Consumer Surplus

BIGGER DECREASE in Social Surplus

OPTIMAL LAW

• Recall Smith’s argument that “optimal” rules should make society better off economically

The “central problem” for “lawmakers” is to maximize social surplus

• Which alternative maximizes social surplus?

• Outcome 1: A law or a rule that would “prohibit” collusive contracts!

• Outcome 2: A law or a rule here that would “ignore” collusive contracts, but choose not to enforce them should they be breached!

• Outcome 3: A law or a rule that would “enforce” collusive contracts!

• The “Legal” Problem• “Hypothetical” social planner – Dictator• - Judge

• Maximize social surplus• Subject to the requirement that Agent 1 maximizes

its profits (Agent 1 is rational)• Subject to the requirement that Agent 2 maximizes

its profits (Agent 1 is rational)

. Social Planner

AGENT 1 AGENT 2

• Note the “Stackelberg” nature of the “legal problem”?

• Coincidence or are there any worthwhile analogies?

• Maximize SS• Subject to F1(a1) – 2F(a1)F1(a1) - F1(a1)y2-cF1(a1) =

0• Subject to F2(a2) – 2F(a2)F2(a1) - F2(a2)y2-cF2(a2) =

• Simple case F(a) = a:

• Maximize SS• Subject to 1 – 2F(a1) - F(a2) – c = 0• Subject to 1 – 2F(a2) - F(a1) – c = 0

• L = SS(a1,a2) + 1 (1 – 2F(a1) - F(a2) – c)

+ 2 (1 – 2F(a2) - F(a1) – c)

• The “legal problem” adds these first order conditions to the “duopoly problem”:

dL(a1,a2)/da1 = 0

dL(a1,a2)/da2 = 0

• Note the “self-interest” of each duopolistic agent still “applies” or is “binding”:

d1(a1,a2)/da1 = 0d2(a1,a2)/da2 = 0

• So this means:

1 ≠ 02 ≠ 0

• Best satisfies the “legal problem”

• This closely approximates the common law as it existed in Canada until 1889

• What happened?

• In 1889 after complaints about a Toronto coal cartel, fire insurance cartel, etc, the government “criminalized” collusive agreements – 1889 to 1990

• Some argue that Canada’s first antitrust legislation was designed to ward off the effects of monopoly due to Sir John A. Macdonald’s National Policy

• After 1990 – collusive agreements were decriminalized and are now subject to an elaborate administrative process supervised by the Competition Bureau

• Closer in some cases to • Outcome 1: A law or a rule that would “prohibit”

collusive contracts!

• This would suggest a “sub-optimal” choice by the “social planner”. Why?

• There is another key issue here.

• Note that a rule that does not enforce the “collusive contract” is a “complement” to the Prisoner’s dilemna

• A form of “strategic complementarity”

• Return to this specific issue under “Firms”

• This issue and related “antitrust” issues are studied in

• ECO310Y5 • Industrial Organization and Public Policy

DEFECTION

BILATERAL AGENCY - IMPLICIT PRISONERS DILEMNA

• Cooter explains the Prisoner's dilemna – (4th ed., 2004, c. 2., VII, p. 39)

• Outcome 2 involves the operation of the Nash equilibrium that motivates a Prisoners dilemna outcome

• So a law, rule or policy, as was the common law, that does not enforce the contract “complements” the Prisoner dilemna outcome

• What exactly happens?• Agent 1 decides to “defect” from the agreed upon

quota by increasing its profits at the “monopoly” price that resulted when the agents decided to collude:

» Output of each agent = (1/4)(1-c)» Market Price = (1/2)(1 + c)» Adjusted Output of Agent 1

= (3/8)(1 - c)

Collusive New Iso-Profit Curve For Firm X

Collusive Iso-Profit Curve For Firm Y

• In the first “round” Agent 1 has increased its production by 50%

• Agent 2 “reacts” to the defection from the quota by expanding its production to meet the falling market price:

» Total Output of Agents = (5/8)(1-c)» Market Price falls to = (1/8)(3 – 5c)» Adjusted Output of Agent 2

= (5/16)(1 - c)

• In the second “round” Agent 2 has increased its production by 25%

• Agent 1 “reacts” to Agent 2 expanding its production to meet the falling market price:

» Re-adjusted Output of Agent 1

= (11/32)(1 - c)

• In each successive “round” the agents readjust their outputs in response to each other until the original production Nash equilibrium is reached

Output of each agent = (1/3)(1-c)

E[1/3(1-c), 1/3(1-c)]

Is there a way to make the collusive contract more stable?

What happens if Agent 1 cannot observe the effort of Agent 2?

What happens if Agent 1 does not know the costs of Agent 2?

What happens in the Stackelberg duopoly? Does either the leader or the follower defect?

BILATERAL AGENCY - EXPLICIT

. Explicit Bilateral AgencyStrategicPrimarily market

Imposed Explicit Agency

Example – No Fault Insurance Among Automobile Drivers

Voluntary Explicit Agency

Example – Negotiated Contract

• Explicit Bilateral Agency» Relationship is both strategic and has some

legal significance

» Imposed – A law “imposes” a relationship onto parties

» Examples: Parent – child

Car owner – accident victim

• Explicit Bilateral Agency

» Voluntary – The parties “choose” their relationship

» Examples: • Business partnerships• Landlord – Tenant leases• Buy – Sell agreements

• Restraints and incentives to the work ethic

• Effect of risk on contracts - where do agency costs originate?

. Explicit Bilateral AgencyStrategic, RelationalPrimarily Non-market

Horizontal Explicit Agency

Example – Partnership Contract

Vertical Explicit Agency

Example – Employment Contract

BILATERAL AGENCY - EXPLICIT Horizontal Contract

AGENT 2 AGENT 1

Promise of Agent 1

Promise of Agent 2

• Horizontal Contracts

» Examples:Two partners in a firm

Two joint property owners

Spouses

Explicit agencies arise when rules align the "self-interest" of the agents to the "common" objective of the agency.

The chief feature is a "rule of law" that binds the agents' self-interest to the common objective.

• Each agent exchanges the performance or execution of a promise for a payment.

• Each agent cannot observe the effort or action applied by the other party.

• This means neither agent cannot know in advance whether or not the contract will be performed. (Double Moral Hazard)

• Different “sharing rules” include:• rights to residual profits • Profit - sharing• sharing the return to an investment• performance pay• fixed wage and • piece rate.

• Agents decide to enter into a “collusive” contract with a view to:

• Overcoming the Prisoners dilemna

• Overcoming the inability to observe each others effort

• Overcoming the inability to enforce a broken contract because

»No courts or judges are available»The available courts cannot observe

the efforts and do not have evidentiary means to overcome this

»The judges accept bribes from parties before them

»The contracts are illegal

.Social Planner

AGENT 1 AGENT 2

• Agents enter into a partnership or joint venture called a “bilateral contract”:

y = F(a1,a2) = joint output of Agents 1 and 2

• As before, agents have “linear utility” in the profits they make.

• Mr. Justice Richard Posner argues on the basis that man is a rational utility maximizer in all areas of life, including legal matters (6th ed., 2004, c. 1, p. 4)

• How does Posner defend this? In terms of group behaviour – not individual aberrations. (6th ed., 2004, c. 1, p. 18)

• These agents have the following joint profit function:

(a1,a2) = py - ca1 - ca2

• For simplicity, let p = c = 1(a1,a2) = F(a1,a2) - a1 - a2

• Agents are indifferent to risk - risk neutral

• The agents agree to adopt a sharing rule, or alternatively, the social planner agrees to “impose” an optimal sharing rule on the agents.

Agent 2

PROMISEDPERFORMANCE 2

Agent 1INCENTIVE COMPATIBILITYCONSTRAINT 1

LEGAL ANALYSIS

ECONOMIC ANALYSIS

Agent 1

PROMISEDPERFORMANCE 1

Agent 2

INCENTIVE COMPATIBILITYCONSTRAINT 2

• The principle or axiom of self-interest

applies as each agent is “rational”:

d (a1,a2)/da1 = F1(a1,a2) – 1 = 0

d (a1,a2)/da2 = F2(a1,a2) – 1 = 0

Each “incentive compatibility constraint” is binding because the first order conditions hold due to the “self-interest” of each “rational” agent:

1(F1(a1,a2) – 1) > 0

2(F2(a1,a2) – 1) > 0

Each “shadow price”, 1 > 0 and 2 > 0, reflects the value to each agent of contractual performance.

On the other hand, “individual rationality constraints” are not binding. No “direct” principal makes payments to the agents.

Nor are any restrictions or constraints placed on the agents’ abilities to make transfer payments to each other.

So 1 = 0 and 2 = 0

EXPRESS BILATERAL AGENCY

Agent 2PROMISEDPERFORMANCE 2

LEGAL ANALYSIS

ECONOMIC ANALYSIS

Agent 1PROMISEDPAYMENT 1

PARTICIPATIONCONSTRAINT 1

• As before, the “social planner” acts to maximize social surplus so as to optimize the applicable legal rule:

L(a1,a2) = F(a1,a2) + F(a1,a2) - a1 - a2

+1 (F1(a1,a2) – 1) + 2 (F2(a1,a2) – 1)

where represent Agent 1’s share and represents Agent 2’s share

• The “legal problem” requires these first order conditions:

dL(a1,a2)/da1 = 0

dL(a1,a2)/da2 = 0

dL(a1,a2)/d = 0

Under the restrictive assumption of linear costs, the first order conditions are:

dL/da1 = F1 - 1 + 1F11 + 2(1-)F12 = 0dL/da2 = F2 - 1 + 1F12 + 2(1-)F22 = 0

dL/d = 1F1 - 2F2 = 0

The solution to the first order conditions generates the optimal “sharing rule”, which satisfies:

/(1- ) = (F22/F11)^1/4

Neary, Hugh and Winter, Ralph, “Output Shares in Bilateral Agency Contracts”,

(1995), 66 Journal of Economic Theory 609-614

• Exercise:

• What conclusions change, if any, when the agents are price takers, price searchers and have costs?

(a1,a2) = py - ca1 - ca2

PRINCIPAL - AGENCY

Principal

promisepayment

“SUPER”Principal Its “problem” is to maximize social

surplus

• Vertical Agency» Two parties agree on a ranking and order of conduct

Principal – first mover

Agent – second mover

» Examples: Landlord and tenant – (residential)

Employer - employee

Buyer – seller

Client - lawyer

BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency)

• “Principal Agency” Exchange

• The “principal” makes an exchange of a “payment” to an “agent” in exchange for the “agent” performing or executing a “promise” for the “principal”

• Again – note the “Stackelberg” structure of the agency

Single Moral Hazard - I

Single Moral Hazard

The principal cannot observe the effort or action applied by the agent.

This means the principal cannot know in advance whether or not the contract will be performed by the agent.

• Professor Cooter illustrates some cases of how moral hazards emerge in agency relationships:

• A used car seller knows more about the quirks of his car than the buyer

• A bank presents a “standard” deposit agreement to the customer

• (4th ed., 2004, c. 2., IX, p. 47)

• Parties enter into a “principal-agency” contract:

a1 = 0 = input of Principal

y = F(0,a2) = output of the agency

• This agency has the following profit function:

(0,a2) = py - ca2

• For simplicity, let p = c = 1(0,a2) = F(0,a2) - a2

(a2) = F(a2) - a2

F’(a2) = dF/da2 > 0 Production Concavity = Marginal Diminishing Returns

F’’(a2) = d(dF/da2)/da2 < 0

• Principal is indifferent to risk - risk neutral

• The agent is risk averse. Why?

• Most parties in the real world are risk averse. Principals are risk averse. In relative terms, agents are even more risk averse

dU(W2 - a2)/d(W2 - a2) > 0 Risk Averse Utility of Agent

d[dU(W2 - a2)/d(W2 - a2)]\d(W2 - a2) < 0

• Mr. Justice Richard Posner uses the existence of insurance markets and the higher return on stocks over bonds as empirical evidence of widespread risk aversion (6th ed., 2004, c. 1, p. 11)

F=Output

A “perfectly competitive” risk neutral Principal contracts a “complete” contract with the “risk averse” agent

Contract Equilibrium Point

The parties are paid in “output” shares

Vertical Contract – (Principal – Agency) • Professor Cooter explains that the

utility function of a “risk-averse” agent is “concave downwards” - reflecting marginal diminishing utility of income (or output shares). (4th ed., 2004, c. 2., X, p. 51)

The “participation constraint” of the Agent is binding

2 (T2 + F(a2) - a2) > 0

W2 = T2 + F(a2) “linear contract”

W2 = T2 + FT2 = “insured” payment under the contract

F = “performance” payment under the contract

BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency

• If the Agent maximizes its utility

dU(W2 - a2)/da2 = 0

dU(T2 + F(a2) - a2)/da2 = 0

(0 + F2(a2) - 1) = 0

F2(a2) – 1 = 0

BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency

• So the Agent’s “incentive compatibility constraint” is also binding

2(F2(a2) – 1) = 0

Single Moral Hazard - II

LEGAL ANALYSIS

ECONOMIC ANALYSIS

• The “social planner” acts to maximize social surplus so as to optimize the applicable legal rule:

L(a1,a2) = F(a2) - a2 +2 (F2(a2) – 1) + 2 (T2 + F(a2) – a2)

Principal

PAYMENT

PROMISED PERFORMANCE

PARTICIPATIONCONSTRAINT

INCENTIVE COMPATIBILITYCONSTRAINT

LEGAL ANALYSIS

PROMISED

ECONOMIC ANALYSIS

• The “legal problem” requires these first order conditions:

dL(a1,a2)/da2 = 0

dL(a1,a2)/d = 0

Under the restrictive assumption of linear costs, the first order condition for sharing is:

dL/d = F - 2F2 - 2F = 0

F = 2F + 2F1

1 = 2 + 2F2/F

The optimal “sharing rule”, satisfies:

1 = 2 + 2F2/F

F=Output

There is a “third” constraint” in the Principal – Agency Problem

The “Budget Constraint” of the Principal

F=Output

Short – Run Profits Of The Principal

Price CurveShort Run Average Cost CurveMarginal Cost Curve

Vertical Contract – (Principal – Agency) • If the principal is operating in a

perfectly competitive market outside of its relationship with the agent, its longrun profit function = 0

F=Output

Long Run Average Cost Curve

Long Run Price CurvePROFITS = 0

Marginal Cost Curve

Vertical Contract – (Principal – Agency)

• Long Run Profit Constraint

• F(a2) – W = 0

F(a2) – T2 – F(a2) = 0 F – T2 – F = 0 T2 = F

• The “complete” legal problem with the third constraint added is:

L(a1) = F - T2 - F

+2 (F2 – 1) + 2 (T2 + F – a2)

A Contract Equilibrium Point

Set of all feasible contracts

• As risk in output increases, either due to moral hazard or some third party cause, the risk reduces the marginal benefit of pay for performance β and thus causes the indifference curves to follow the feasible contract curve to the left.

Vertical Contract – (Principal – Agency)

• As productivity increases (technological innovation), the feasible contract curve stretches upward and the indifference curves follow the feasible contract curve to the right.

• As the Principal (firm) increases in size, either one of the two previous effects apply.

• The “Principal-Agency ” exchange is the model featured in Cooter's treatment of contract law

Double Moral Hazard

Neither agent nor principal cannot observe the effort or action applied by the other.

This means the parties cannot know in advance whether or not the contract will be performed.

In the double moral hazard version, both Principal and agent perform actions:

L = F - a1 - a2 + 1(F1 - 1) + 2((1-)F2 - 1)

+ 2(T2 + F - a2)

CompetingAgents

F=Output

A “perfectly competitive” risk neutral Principal contracts a “complete” contract with the agents

In this case two “different” agents – “two” different contracts

MICROECONOMIC ANALYSIS OF LAW September 19, 2006

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