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George Mason School of Law
Contracts II
Modeling Bargaining Gains
F.H. Buckley
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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
0
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
38
Mary
The Contract Curve: All possible Pareto-optimal contracts represented at the
points of tangency
Bess
A
B
C
D
E
FG