1. MICROECONOMIC ANALYSIS OF LAW September 19, 2006

2. MICROECONOMIC ANALYSIS OF LAW September 19, 2006 CLEA Conference Friday, September 29 to Saturday, September 30

3. MICROECONOMIC ANALYSIS OF LAW September 19, 2006 Posted at: http://www.canlecon.org/

4. MICROECONOMIC ANALYSIS OF LAW September 19, 2006 http://www.cooter-ulen.com Answers to End of Chapter - Problems

5. Lecture II Bilateral Agency

6. BILATERAL AGENCY Bilateral Agency Bilateral Contracts Principal Agency Principal Agency Contracts Double Moral Hazard Adverse Selection

7. 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.

8. BILATERAL AGENCY. Bilateral Agency Implicit Bilateral Agency Strategic Primarily market Example – Cournot Duopoly Explicit Bilateral Agency Strategic, relational Primarily non-market Example – Joint Venture

9. BILATERAL AGENCY - IMPLICIT Implicit Bilateral Agency »Relationship is strategic in nature Examples: Duopoly – substitutes Duopoly – complements

10. BILATERAL AGENCY - IMPLICIT In many economic contexts implied agencies arise. These agencies involve non-legally binding strategic interaction between two or more agents.

11. BILATERAL AGENCY - IMPLICIT COURNOT DUOPOLY The most well known is the Cournot duopoly, but there many other cases.

12. BILATERAL AGENCY - IMPLICIT COURNOT DUOPOLY Agents operate economically similar firms – sole proprietorships: a 1 = input of Agent 1 a 2 = input of Agent 2 y 1 = F(a 1 ) = output of Agent 1 y 2 = F(a 2 ) = output of Agent 2

13. BILATERAL AGENCY - IMPLICIT COURNOT DUOPOLY Agents have “linear utility” in the profits they make. What does this mean? U(  1 ) =  1 = utility of Agent 1 U(  2 ) =  2 = utility of Agent 2 Agents are indifferent to risk - risk neutral

14. BILATERAL AGENCY - IMPLICIT COURNOT DUOPOLY These agents have the following profit functions  1 (a 1,a 2 ) = (p-c)y 1 = (1-y 1 -y 2 -c)y 1 = y 1 -y 1 y 1 -y 1 y 2 -cy 1  2 (a 1,a 2 ) = (p-c)y 2 = (1-y 1 -y 2 -c)y 2 = y 2 -y 2 y 1 -y 2 y 2 -cy 2

15. BILATERAL AGENCY - IMPLICIT COURNOT DUOPOLY These agents act in their own self - interest (reaction curves) d  1 (a 1,a 2 )/da 1 = 0 d  2 (a 1,a 2 )/da 2 = 0 F 1 (a 1 ) – 2F(a 1 )F 1 (a 1 ) - F 1 (a 1 )y 2 -cF 1 (a 1 ) = 0 F 2 (a 2 ) – 2F(a 2 )F 2 (a 1 ) - F 2 (a 2 )y 2 -cF 2 (a 2 ) = 0

16. BILATERAL AGENCY - IMPLICIT COURNOT DUOPOLY Set of Cost Minimizers Set of Profit Maximizers

17. BILATERAL AGENCY - IMPLICIT COURNOT DUOPOLY – NASH EQUILIBRIUM The principle or axiom of self-interest is (reflected in reaction curves) F(a 1 ) = (1/2)(1 - F(a 2 ) - c) F(a 2 ) = (1/2)(1 - F(a 1 ) - c)

18. BILATERAL AGENCY - IMPLICIT COURNOT DUOPOLY – NASH EQUILIBRIUM Equilibrium occurs where these “self- interested” actions intersect – Nash Equilibrium a* 1 = a* 2 = F -1 [(1/3)(1–c)] John Forbes Nash, 1928 -

19. BILATERAL AGENCY - IMPLICIT COURNOT DUOPOLY – NASH EQUILIBRIUM a2a2 a1a1 AGENT 1 producing a 1 a 1 = ½(1- a 2 -c) AGENT 2 producing a 2 a 2 = ½(1- a 2 – c) E[(1/3)(1-c), (1/3)(1-c)]

20. BILATERAL AGENCY - IMPLICIT COURNOT DUOPOLY – NASH EQUILIBRIUM 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)

21. BILATERAL AGENCY - IMPLICIT COURNOT DUOPOLY – NASH EQUILIBRIUM If F (a) = a, the agents have the following iso-profit functions :  * 1 = a 1 -a 1 a 1 -a 1 a 2 -ca 1 a 2 = - a 1 -  /a 1 + (1-c) - Agent 1  * 2 = a 2 -a 2 a 2 -a 2 a 1 -ca 2 a 1 = - a 2 -  /a 2 + (1-c) – Agent 2

22. BILATERAL AGENCY - IMPLICIT COURNOT DUOPOLY – NASH EQUILIBRIUM Axes a2a2 a1a1 E[1/3(1-c), 1/3(1-c)] Iso-Profit Curve For Agent 1 Iso-Profit Curve For Agent 2

23. BILATERAL AGENCY - IMPLICIT COURNOT DUOPOLY – NASH EQUILIBRIUM Professor Cooter both defines Nash equilibrium and distinguishes it from Pareto efficiency – (4th ed., 2004, c. 2., VII, p. 41)

24. BILATERAL AGENCY - IMPLICIT Economic Measures

25. BILATERAL AGENCY - IMPLICIT Market Efficiency Efficiency An allocation of resources is efficient when no further increases to production can be made.

26. BILATERAL AGENCY - IMPLICIT Market Efficiency Perfect CompetitionDuopoly [0,1] Consumer Demand [(1-c), c] Producer Supply [1,0] [(2/3)(1-c), (1/3)(1+2c)] P = 1-x [0,1] Consumer Demand DECREASE in EFFICIENCY

27. BILATERAL AGENCY - IMPLICIT Market Competitiveness Competitiveness An allocation of resources is competitive when no further decreases to price can be made.

28. BILATERAL AGENCY - IMPLICIT Market Competitiveness Perfect CompetitionDuopoly [0,1] Consumer Demand [(1-c), c] Producer Supply [1,0] [(2/3)(1-c), (1/3)(1+2c)] P = 1-x [0,1] Consumer Demand DECREASE in Competitiveness

29. BILATERAL AGENCY - IMPLICIT Market 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”

30. BILATERAL AGENCY - IMPLICIT 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.

31. BILATERAL AGENCY - IMPLICIT Market Optimality 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)

32. BILATERAL AGENCY - IMPLICIT Market Optimality Perfect CompetitionDuopoly [0,1] Consumer Surplus [(1-c), c] Producer Surplus [1,0] Duopolists’ Surplus P = 1-x [0,1] Consumer Surplus DECREASE in Social Surplus

33. BILATERAL AGENCY - IMPLICIT Market Optimality 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.

34. BILATERAL AGENCY - IMPLICIT Market Optimality 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)

35. BILATERAL AGENCY - IMPLICIT Market Optimality. Kaldor-Hicks Criterion Pareto Criterion

36. BILATERAL AGENCY - IMPLICIT Market Optimality 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

37. BILATERAL AGENCY - IMPLICIT Market Optimality 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.

38. BILATERAL AGENCY - IMPLICIT. Implicit Bilateral AgencyStrategicPrimarily marketExample – CournotDuopoly Horizontal Implicit Agency Example – Cournot Duopoly Vertical Implicit Agency Example – Stackelberg Duopoly

39. Cournot DuopolyStackelberg Duopoly BILATERAL AGENCY - IMPLICIT AGENT 1 AGENT 2 PRINCIPAL AGENT

40. 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.

41. BILATERAL AGENCY - IMPLICIT STACKELBERG DUOPOLY The Stackelberg game lies behind many of the vertical relationships to be examined. Heinrich von Stackelberg, 1905- 1946

42. BILATERAL AGENCY - IMPLICIT STACKELBERG DUOPOLY Recall that the principle or axiom of self-interest for the Cournot duopoly was F(a 1 ) = (1/2)(1 - F(a 2 ) - c) F(a 2 ) = (1/2)(1 - F(a 1 ) - c) reflecting a “game” of simultaneous moves

43. BILATERAL AGENCY - IMPLICIT STACKELBERG DUOPOLY The principle or axiom of self-interest for the Stackelberg duopoly is F(a 1 ) = (1/2)(1 – [(1/2)(1 - F(a 1 ) - 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.

44. BILATERAL AGENCY - IMPLICIT STACKELBERG DUOPOLY DuopolyStackelberg 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

45. BILATERAL AGENCY - IMPLICIT STACKELBERG DUOPOLY 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)]

46. BILATERAL AGENCY - IMPLICIT Cournot DuopolyStackelberg Duopoly [(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- a 1 - a 2

47. BILATERAL AGENCY - IMPLICIT STACKELBERG DUOPOLY Nash Equilibrium Simultaneous Solution a 1 = a 2 = (1/3)(1-c) Nash Equilibrium Sequential Solution a 1 = (1/2)(1-c) a 2 = (1/4)(1-c)

48. BILATERAL AGENCY - IMPLICIT Cournot DuopolyStackelberg Duopoly [0,1] [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] [0,(1/4)(1+ 3c)] P = 1- a 1 - a 2

49. BILATERAL AGENCY - IMPLICIT COURNOT DUOPOLY 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)

50. BILATERAL AGENCY - IMPLICIT Cournot Benchmarks Efficiency a 1 + a 2 = (2/3)(1-c) Competitiveness p = (1/3)(1 + 2c) Producers Surplus PS = (2/9)(1-c)(1-c) Social Surplus SS = (4/9)(1-c)(1-c) Stackelberg Benchmarks Efficiency a 1 + a 2 = (3/4)(1-c) Competitiveness p = (1/4)(1 + 3c) Producers Surplus PS = (3/16)(1-c)(1-c) Social Surplus SS = (15/32)(1-c)(1-c)

51. BILATERAL AGENCY - IMPLICIT Collusive Duopoly

52. With no property rules - can contracts still exist? BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY

53. Axes a2a2 a1a1 New Nash Equilibrium New Iso-Profit Curve For Firm X New Iso-Profit Curve For Firm Y

54. 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 BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY

55. Perfect CompetitionCollusive Duopoly [0,1] Consumer Demand [(1-c), c] Producer Supply [1,0] [(1/2)(1-c), (1/2)(1+c)] P = 1-x [0,1] Consumer Demand BIGGER DECREASE in EFFICIENCY

56. BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY Perfect CompetitionCollusive Duopoly [0,1] Consumer Demand [(1-c), c] Producer Supply [1,0] [(1/2)(1-c), (1/2)(1+c)]] P = 1-x [0,1] Consumer Demand BIGGER DECREASE in Competitiveness

57. BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY Perfect CompetitionCollusive Duopoly [0,1] Consumer Surplus [(1-c), c] Producer Surplus [1,0] Duopolists’ Surplus P = 1-x [0,1] Consumer Surplus BIGGER DECREASE in Social Surplus

58. BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY OPTIMAL LAW

59. BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY 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?

60. BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY 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!

61. BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY 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)

62. BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY. Social Planner AGENT 1 AGENT 2

63. BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY Note the “Stackelberg” nature of the “legal problem”? Coincidence or are there any worthwhile analogies?

64. BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY Maximize SS Subject to F 1 (a 1 ) – 2F(a 1 )F 1 (a 1 ) - F 1 (a 1 )y 2 -cF 1 (a 1 ) = 0 Subject to F 2 (a 2 ) – 2F(a 2 )F 2 (a 1 ) - F 2 (a 2 )y 2 -cF 2 (a 2 ) = 0 Simple case F(a) = a: Maximize SS Subject to 1 – 2F(a 1 ) - F(a 2 ) – c = 0 Subject to 1 – 2F(a 2 ) - F(a 1 ) – c = 0

65. BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY L = SS(a 1,a 2 ) + 1 (1 – 2F(a 1 ) - F(a 2 ) – c) + 2 (1 – 2F(a 2 ) - F(a 1 ) – c) The “legal problem” adds these first order conditions to the “duopoly problem”: dL(a 1,a 2 )/da 1 = 0 dL(a 1,a 2 )/da 2 = 0

66. BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY Note the “self-interest” of each duopolistic agent still “applies” or is “binding”: d  1 (a 1,a 2 )/da 1 = 0 d  2 (a 1,a 2 )/da 2 = 0 So this means: 1 ≠ 0 2 ≠ 0

67. BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY Outcome 2: A law or a rule here that would “ignore” collusive contracts, but choose not to enforce them should they be breached! Best satisfies the “legal problem” This closely approximates the common law as it existed in Canada until 1889

68. BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY What happened? In 1889 after complaints about a Toronto coal cartel, fire insurance cartel, etc, the government “criminalized” collusive agreements – 1889 to 1990

69. BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY 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

70. BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY After 1990 – collusive agreements were decriminalized and are now subject to an elaborate administrative process supervised by the Competition Bureau

71. BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY 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?

72. BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY 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”

73. BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY Return to this specific issue under “Firms” This issue and related “antitrust” issues are studied in ECO310Y5 Industrial Organization and Public Policy

74. BILATERAL AGENCY - IMPLICIT DEFECTION

75. BILATERAL AGENCY - IMPLICIT PRISONERS DILEMNA Cooter explains the Prisoner's dilemna – (4th ed., 2004, c. 2., VII, p. 39)

76. BILATERAL AGENCY - IMPLICIT PRISONERS DILEMNA Outcome 2: A law or a rule here that would “ignore” collusive contracts, but choose not to enforce them should they be breached! 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

77. BILATERAL AGENCY - IMPLICIT PRISONERS DILEMNA 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)

78. BILATERAL AGENCY - IMPLICIT PRISONERS DILEMNA Axes a2a2 a1a1 Collusive New Iso-Profit Curve For Firm X Collusive Iso-Profit Curve For Firm Y

79. BILATERAL AGENCY - IMPLICIT PRISONERS DILEMNA 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)

80. BILATERAL AGENCY - IMPLICIT PRISONERS DILEMNA 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)

81. BILATERAL AGENCY - IMPLICIT PRISONERS DILEMNA 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)

82. BILATERAL AGENCY - IMPLICIT PRISONERS DILEMNA Axes a2a2 a1a1 E[1/3(1-c), 1/3(1-c)] Iso-Profit Curve For Agent 1 Iso-Profit Curve For Agent 2

83. Is there a way to make the collusive contract more stable? BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY

84. What happens if Agent 1 cannot observe the effort of Agent 2? BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY

85. What happens if Agent 1 does not know the costs of Agent 2? BILATERAL AGENCY - IMPLICIT COLLUSIVE DUOPOLY

86. What happens in the Stackelberg duopoly? Does either the leader or the follower defect? BILATERAL AGENCY - IMPLICIT STACKELBERG DUOPOLY

88. BILATERAL AGENCY - EXPLICIT. Explicit Bilateral AgencyStrategicPrimarily market Imposed Explicit Agency Example – No Fault Insurance Among Automobile Drivers Voluntary Explicit Agency Example – Negotiated Contract

89. BILATERAL AGENCY - EXPLICIT 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

90. BILATERAL AGENCY - EXPLICIT Explicit Bilateral Agency » Voluntary – The parties “choose” their relationship » Examples: Business partnerships Landlord – Tenant leases Buy – Sell agreements

91. BILATERAL AGENCY - EXPLICIT Restraints and incentives to the work ethic Effect of risk on contracts - where do agency costs originate?

92. BILATERAL AGENCY - EXPLICIT. Explicit Bilateral AgencyStrategic, RelationalPrimarily Non-market Horizontal Explicit Agency Example – Partnership Contract Vertical Explicit Agency Example – Employment Contract

93. BILATERAL AGENCY - EXPLICIT Horizontal Contract AGENT 2 AGENT 1 Promise of Agent 1 Promise of Agent 2

94. BILATERAL AGENCY - EXPLICIT Horizontal Contracts » Examples:Two partners in a firm Two joint property owners Spouses

95. BILATERAL AGENCY - EXPLICIT Horizontal Contract 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.

96. BILATERAL AGENCY - EXPLICIT Horizontal Contract 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)

97. BILATERAL AGENCY - EXPLICIT Horizontal Contract Different “sharing rules” include: rights to residual profits Profit - sharing sharing the return to an investment performance pay fixed wage and piece rate.

98. BILATERAL AGENCY - EXPLICIT Horizontal Contract Agents decide to enter into a “collusive” contract with a view to: Overcoming the Prisoners dilemna Overcoming the inability to observe each others effort

99. BILATERAL AGENCY - EXPLICIT Horizontal Contract 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

100. BILATERAL AGENCY - EXPLICIT Horizontal Contract. SocialPlanner AGENT 1 AGENT 2

101. BILATERAL AGENCY - EXPLICIT Horizontal Contract Agents enter into a partnership or joint venture called a “bilateral contract”: a 1 = input of Agent 1 a 2 = input of Agent 2 y = F(a 1,a 2 ) = joint output of Agents 1 and 2

102. BILATERAL AGENCY - EXPLICIT Horizontal Contract As before, agents have “linear utility” in the profits they make. U(  1 ) =  1 = utility of Agent 1 U(  2 ) =  2 = utility of Agent 2

103. BILATERAL AGENCY - EXPLICIT Horizontal Contract 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)

104. BILATERAL AGENCY - EXPLICIT Horizontal Contract These agents have the following joint profit function:  (a 1,a 2 ) = py - ca 1 - ca 2 For simplicity, let p = c = 1  (a 1,a 2 ) = F(a 1,a 2 ) - a 1 - a 2

105. BILATERAL AGENCY - EXPLICIT Horizontal Contract 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.

106. BILATERAL AGENCY - EXPLICIT Horizontal Contract Agent 2 PROMISED PERFORMANCE 2 Agent 1 INCENTIVE COMPATIBILITY CONSTRAINT 1 LEGAL ANALYSIS ECONOMIC ANALYSIS Agent 1 PROMISED PERFORMANCE 1 Agent 2 INCENTIVE COMPATIBILITY CONSTRAINT 2

107. BILATERAL AGENCY - EXPLICIT Horizontal Contract The principle or axiom of self-interest applies as each agent is “rational”: d  (a 1,a 2 )/da 1 =  F 1 (a 1,a 2 ) – 1 = 0 d  (a 1,a 2 )/da 2 =  F 2 (a 1,a 2 ) – 1 = 0

108. BILATERAL AGENCY - EXPLICIT Horizontal Contract Each “incentive compatibility constraint” is binding because the first order conditions hold due to the “self-interest” of each “rational” agent: 1 (  F 1 (a 1,a 2 ) – 1) > 0 2 (  F 2 (a 1,a 2 ) – 1) > 0

109. BILATERAL AGENCY - EXPLICIT Horizontal Contract Each “shadow price”, 1 > 0 and 2 > 0, reflects the value to each agent of contractual performance.

110. BILATERAL AGENCY - EXPLICIT Horizontal Contract 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

111. EXPRESS BILATERAL AGENCY Agent 2 PROMISED PERFORMANCE 2 INCENTIVE COMPATIBILITY CONSTRAINT 1 LEGAL ANALYSIS ECONOMIC ANALYSIS Agent 1 PROMISED PERFORMANCE 1 INCENTIVE COMPATIBILITY CONSTRAINT 2 Agent 1 PROMISED PAYMENT 1 Agent 2 PROMISED PAYMENT 2 PARTICIPATION CONSTRAINT 1 PARTICIPATION CONSTRAINT 2

112. BILATERAL AGENCY - EXPLICIT Horizontal Contract As before, the “social planner” acts to maximize social surplus so as to optimize the applicable legal rule: L(a 1,a 2 ) =  F(a 1,a 2 ) +  F(a 1,a 2 ) - a 1 - a 2 +  1 (  F 1 (a 1,a 2 ) – 1) + 2 (  F 2 (a 1,a 2 ) – 1) where  represent Agent 1’s share and  represents Agent 2’s share

113. BILATERAL AGENCY - EXPLICIT Horizontal Contract The “legal problem” requires these first order conditions: dL(a 1,a 2 )/da 1 = 0 dL(a 1,a 2 )/da 2 = 0 dL(a 1,a 2 )/d  = 0

114. BILATERAL AGENCY - EXPLICIT Horizontal Contract Under the restrictive assumption of linear costs, the first order conditions are: dL/d a 1 = F 1 - 1 + 1  F 11 + 2 (1-  )F 12 = 0 dL/d a 2 = F 2 - 1 + 1  F 12 + 2 (1-  )F 22 = 0 dL/d  = 1 F 1 - 2 F 2 = 0

115. BILATERAL AGENCY - EXPLICIT Horizontal Contract The solution to the first order conditions generates the optimal “sharing rule”, which satisfies:  /(1-  ) = (F 22 /F 11 )^ 1/4 Neary, Hugh and Winter, Ralph, “Output Shares in Bilateral Agency Contracts”, (1995), 66 Journal of Economic Theory 609-614

116. BILATERAL AGENCY - EXPLICIT Horizontal Contract Exercise: What conclusions change, if any, when the agents are price takers, price searchers and have costs?  (a 1,a 2 ) = py - ca 1 - ca 2

117. PRINCIPAL - AGENCY Principal AGENT promise payment “SUPER” PrincipalIts “problem” is to maximize social surplus

118. BILATERAL AGENCY - EXPLICIT 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

119. 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

120. BILATERAL AGENCY - EXPLICIT Single Moral Hazard - I

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

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

123. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) Parties enter into a “principal-agency” contract: a 1 = 0 = input of Principal a 2 = input of Agent 2 y = F(0,a 2 ) = output of the agency

124. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) This agency has the following profit function:  (0,a 2 ) = p  y - ca 2 For simplicity, let p = c = 1  (0,a 2 ) =  F(0,a 2 ) - a 2  (a 2 ) =  F(a 2 ) - a 2

125. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency)  (a 2 ) =  F(a 2 ) - a 2  F’(a 2 ) = dF/da 2 > 0 Production Concavity = Marginal Diminishing Returns  F’’(a 2 ) = d(dF/da 2 )/da 2 < 0

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

127. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency)  dU(W 2 - a 2 )/d(W 2 - a 2 ) > 0 Risk Averse Utility of Agent  d[dU(W 2 - a 2 )/d(W 2 - a 2 )]\d(W 2 - a 2 ) < 0

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

129. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) U(F) F=Output E 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

130. BILATERAL AGENCY - EXPLICIT 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)

131. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) The “participation constraint” of the Agent is binding  2 (T 2 +  F(a 2 ) - a 2 ) > 0

132. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) W 2 = T 2 +  F(a 2 ) “linear contract” W 2 = T 2 +  F T 2 = “insured” payment under the contract  F = “performance” payment under the contract

133. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency If the Agent maximizes its utility dU(W 2 - a 2 )/da 2 = 0 dU(T 2 +  F(a 2 ) - a 2 )/da 2 = 0 (0 +  F 2 (a 2 ) - 1) = 0  F 2 (a 2 ) – 1 = 0

134. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency So the Agent’s “incentive compatibility constraint” is also binding 2 (  F 2 (a 2 ) – 1) = 0 2 > 0  2 > 0

135. BILATERAL AGENCY - EXPLICIT Single Moral Hazard - II

136. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) Agent 2 PROMISED PERFORMANCE 2 INCENTIVE COMPATIBILITY CONSTRAINT 1 LEGAL ANALYSIS ECONOMIC ANALYSIS Agent 1 PROMISED PERFORMANCE 1 INCENTIVE COMPATIBILITY CONSTRAINT 2 Agent 1 PROMISED PAYMENT 1 Agent 2 PROMISED PAYMENT 2 PARTICIPATION CONSTRAINT 1 PARTICIPATION CONSTRAINT 2

137. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) The “social planner” acts to maximize social surplus so as to optimize the applicable legal rule: L(a 1,a 2 ) =  F(a 2 ) - a 2 +  2 (  F 2 (a 2 ) – 1) +  2 (T 2 +  F(a 2 ) – a 2 )

138. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) Principal PAYMENT Agent PROMISED PERFORMANCE Agent PARTICIPATION CONSTRAINT INCENTIVE COMPATIBILITY CONSTRAINT LEGAL ANALYSIS PROMISED ECONOMIC ANALYSIS

139. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) The “legal problem” requires these first order conditions: dL(a 1,a 2 )/da 2 = 0 dL(a 1,a 2 )/d  = 0

140. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) Under the restrictive assumption of linear costs, the first order condition for sharing is: dL/d  = F - 2 F 2 -  2 F = 0 F =  2 F + 2 F 1 1 =  2 + 2 F 2 /F

141. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) The optimal “sharing rule”, satisfies: 1 =  2 + 2 F 2 /F

142. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) U(F) F=Output E There is a “third” constraint” in the Principal – Agency Problem The “Budget Constraint” of the Principal

143. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) $ F=Output Short – Run Profits Of The Principal Price Curve Short Run Average Cost Curve Marginal Cost Curve

144. BILATERAL AGENCY - EXPLICIT 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

145. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) $ F=Output Long Run Average Cost Curve Long Run Price Curve PROFITS = 0 Marginal Cost Curve

146. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) Long Run Profit Constraint F(a 2 ) – W = 0 F(a 2 ) – T 2 –  F(a 2 ) = 0  F – T 2 –  F = 0  T 2 =  F

147. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) The “complete” legal problem with the third constraint added is: L(a 1 ) = F - T 2 -  F +  2 (  F 2 – 1) +  2 (T 2 +  F – a 2 )

148. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) T 2  A Contract Equilibrium Point Set of all feasible contracts

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

150. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) T 2  A Contract Equilibrium Point Set of all feasible contracts

151. BILATERAL AGENCY - EXPLICIT 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.

152. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) T 2  A Contract Equilibrium Point Set of all feasible contracts

153. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) As the Principal (firm) increases in size, either one of the two previous effects apply.

154. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) The “Principal-Agency ” exchange is the model featured in Cooter's treatment of contract law

155. BILATERAL AGENCY - EXPLICIT Double Moral Hazard

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

157. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) In the double moral hazard version, both Principal and agent perform actions: L =  F - a 1 - a 2 + 1 (  F 1 - 1) + 2 ((1-  )F 2 - 1) +  2 (T 2 +  F - a 2 )

158. BILATERAL AGENCY - EXPLICIT Competing Agents

159. BILATERAL AGENCY - EXPLICIT Vertical Contract – (Principal – Agency) U(F) F=Output E H E L A “perfectly competitive” risk neutral Principal contracts a “complete” contract with the agents In this case two “different” agents – “two” different contracts