# 1 George Mason School of Law Contracts II Modeling Bargaining Gains F.H. Buckley

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1 George Mason School of Law Contracts II Modeling Bargaining Gains F.H. Buckley fbuckley@gmu.edu

2 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*

4 Dollars in Time 1 0 Dollars in Time 2 Commodity space: Dollars consumed in two time periods More of both

5 The Budget Line: Allocating \$100 between two periods Dollars in Time 1 100 0 Dollars in Time 2 The budget line in red represents every trade-off of \$100 in two periods

6 Indifference Curves: Preferences about Consumption Dollars in Time 1 0 Dollars in T ime 2 An indifference curve represents a set of trade-offs to which the subject is indifferent

7 Indifference Curves: Preferences about Consumption Dollars in Time 1 0 Dollars in T ime 2 One is better off the further one gets from the origin

8 Dollars in Time 1 0 Dollars in Time 2 More is better: I 2 > I 1 I1I1 I2I2 More is better

9 Dollars in Time 1 0 Dollars in Time 2 Ordinal Utility: We cant say how much better I 2 is than I 1 I1I1 I2I2 I3I3

10 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 T ime 2 B C A

11 Consumption Decision: David has \$100 and is best off at A Maximization subject to the constraint of the Budget Line I3I3 Time 1 I 2 I 1 100 50 A I 2 I 1 0 100 Time 2

Ebenezer gives David another \$100: The Shift to a New Budget Line 200 I 100 A 50, 50 50 I 100 0

A new Consumption Decision B 100, 100 100 I 200 A 50, 50 50 I 100 I DR 0 50 100 Time 1 Time 2

14 What happens when the donor promises to give in the future? Uncle Ebenezer doesnt have the \$100 to give today but promises to give it to David in the next period Davids 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 I 200 A 50, 50 50 I 100 0 50 100 200 Reliance by David means spending \$100 in period 1

B 100, 100 I 100 I DR 0 50 100 A bad scenario: Detrimental Reliance: David relies and Ebenezer breaches C 100,0 D A 50, 50 50 Time 1 David spends 100 in period 1 and now has nothing left to spend in period 2

B 100, 100 I 100 I DR 0 50 100 A bad scenario: Detrimental Reliance: David relies and Ebenezer breaches C 100,0 D A 50, 50 50 Time 1 Davids reliance loss = \$CD

18 Fool me once…: Non-reliance: David assumes Ebenezer will breach Time 1 I 1 100 50 B I 1 0 100 Time 2 Now David spends only 50 in period 1

B 100, 100 100 I 200 50 E 150, 50 0 100 150 Loss of Beneficial Reliance: David doesnt rely and Ebenezer performs I no- 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

B 100, 100 100 I 200 50 E 150, 50 0 100 150 Loss of Beneficial Reliance: David doesnt rely and Ebenezer performs I no- reliance Goetz and Scott, 89 Yale L.J. 1261 (1980)

21 Enforceable Contracts provide the gains associated with beneficial reliance

Now: How parties gain from contracting 22

23 Modeling a Bargain: Mums and Roses 0 Mums Roses

24 Mums Mary Roses Two bargainers Mums Bess Roses

25 Mums Mary Roses Rotating Besss diagram I Roses Mums Bess

26 Mums Mary Roses Rotating Besss diagram II Roses Mums Bess

27 Rotating Besss diagram III Mums

28 Rotating Besss diagram IV Mums Bess Roses

29 Rotating Besss diagram V 0 0 Roses

30 Mary Edgeworth Box Function: Bargaining from endowment point A 0 Bess A 0

31 Edgeworth Box Function: Bargaining from endowment point A Mary Bess A 0 0

32 Edgeworth Box Function: Bargaining from endowment point A Mary Bess A 0 0 Roses bess Mums mary Mums bess Roses mary

33 Paretian standards Vilfredo 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

34 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

35 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)

36 Are all bargaining gains exploited at F? The bargaining lens shrinks through bargaining Mary Bess A B C D E F

37 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 F G

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