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George Mason School of Law

Contracts II

Modeling Bargaining Gains

F.H. Buckley

fbuckley@gmu.edu

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Why Enforce Contracts:Modeling Bargaining Gains

Indifference Curves The Budget Line Consumer Choice Beneficial Reliance The Edgeworth Box Function Pareto-Superiority and Pareto-

Optimality

3

0

Two dimensional Commodity Space:Every point represents a combination of the two commodities

X axis

Y axis

•A

X*

Y*

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Dollars in Time 1

0

Dollars in Time 2

Commodity space: Dollars consumed in two time periods

More of both

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The Budget Line: Allocating $100 between two periods

Dollars in Time 1

100

0

100

Dollars in Time 2

The budget line in red represents every trade-off of $100 in two periods

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Indifference Curves: Preferences about Consumption

Dollars in Time 1

0

Dollars in Time 2

An indifference curve represents a set of trade-offs to which the subject is indifferent

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Indifference Curves: Preferences about Consumption

Dollars in Time 1

0

Dollars in Time 2

One is better off the further one gets from the origin

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Dollars in Time 1

0 Dollars in Time 2

More is better:I2 > I1

I1

I2

More is better

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Dollars in Time 1

0 Dollars in Time 2

Ordinal Utility: We can’t say how much better I2 is than I1

I1

I2

I3

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A C: Subject is willing to give up $BC in Time 2 for $AB in

Time 1

Dollars in Time 1

Convexity (curve bends inward) assumes decreasing marginal utility

0

Dollars in Time 2

BC

A

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Consumption Decision:David has $100 and is best off at A

Maximization subject to the constraint of the Budget Line

I3

Time 1 I2 I1

100 50 A I2 I1

0

50

100 Time 2

Ebenezer gives David another $100: The Shift to a New Budget Line

200 I200

100 A50, 50

50

I100

0 100

A new Consumption Decision

B 100, 100

100 I200 A50, 50

50

I100

IDR

0 50 100

Time 1

Time 2

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What happens when the donor promises to give in the future?

Uncle Ebenezer doesn’t have the $100 to give today but promises to give it to David in the next period

David’s election: to rely or not to rely on the promise in the first period

The good scenario: David relies and Ebenezer performs

B 100, 100

100 I200 A50, 50

50

I100

0 50 100 200

200

Reliance by David means spending $100 in period 1

B 100, 100

I100 I DR

0 50 100

A bad scenario: Detrimental Reliance: David relies and Ebenezer breaches

C 100,0 D

A50, 50 50

Time 1David spends 100 in period 1 and now has nothing left to spend in period 2

B 100, 100

I100 I DR

0 50 100

A bad scenario: Detrimental Reliance: David relies and Ebenezer breaches

C 100,0 D

A50, 50 50

Time 1David’s reliance loss = $CD

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Fool me once…: Non-reliance: David assumes Ebenezer will breach

Time 1 I1

100 50 B I1

0 50

100 Time 2

Now David spends only 50 in period 1

B100, 100 100

I200

50

E150, 50

0 100 150

Loss of Beneficial Reliance:

David doesn’t rely and Ebenezer performs

Ino-reliance

Goetz and Scott, 89 Yale L.J. 1261 (1980)

David spends only 50 in period 1

Where David would have been had he relied

B100, 100 100

I200

50

E150, 50

0 100 150

Loss of Beneficial Reliance:

David doesn’t rely and Ebenezer performs

Ino-reliance

Goetz and Scott, 89 Yale L.J. 1261 (1980)

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Enforceable Contracts provide the gains

associated with beneficial reliance

Now: How parties gain from contracting

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Modeling a Bargain: Mums and Roses

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Mums

Roses

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Mums

Mary Roses

Two bargainers

Mums

Bess Roses

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Mums

Mary Roses

Rotating Bess’s diagram I

Roses

Mums

Bess

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Mums

Mary Roses

Rotating Bess’s diagram II

RosesMums

B

ess

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Rotating Bess’s diagram III

Mums

Mary Roses

Mums

Bess

Roses

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Rotating Bess’s diagram IV

Mums

Mary Roses

Mums

Bess

Roses

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Rotating Bess’s diagram V

0

0

Mums Roses Bess

Mums Mary

Roses

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Mary

Edgeworth Box Function: Bargaining from endowment point A

0

Bess

A

0

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Edgeworth Box Function: Bargaining from endowment point A

Mary

Bess

A

0

0

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Edgeworth Box Function: Bargaining from endowment point A

Mary

Bess

A

0

0

Rosesbess

Mumsmary Mumsbess

Rosesmary

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Paretian standardsVilfredo Pareto (1848-1923)

Pareto-superiority: A transformation from A to B is Pareto-superior if at least one person is better off and no one is worse off

Pareto-optimality: No further Pareto-superior transformations are possible

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Are these attractive moral standards?

Exclude envy: the envious person is worse off if another is better off

Exclude spite: the spiteful person is better off if another is worse off

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B and C as Pareto-superior to A D and E as Pareto-inferior

Mary

Bess

A

B

C

D

E

Coleman, 8 Hofstra L.Rev. 905 (1980)

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Are all bargaining gains exploited at F?The bargaining “lens” shrinks through bargaining

Mary

Bess

A

B

C

D

E

F

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Are all bargaining gains exploited at G?The bargaining lens disappears when the indifference

curves are tangent

Mary

Bess

A

B

C

D

E

F

G

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Mary

The Contract Curve: All possible Pareto-optimal contracts represented at the

points of tangency

Bess

A

B

C

D

E

FG