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MICROECONOMIC ANALYSIS OF LAW September 19, 2006 PowerPoint Presentation
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MICROECONOMIC ANALYSIS OF LAW September 19, 2006

MICROECONOMIC ANALYSIS OF LAW September 19, 2006

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MICROECONOMIC ANALYSIS OF LAW September 19, 2006

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  1. MICROECONOMIC ANALYSIS OF LAW September 19, 2006

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

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

  4. MICROECONOMIC ANALYSIS OF LAWSeptember 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 Moral Hazard Adverse Selection Double Moral Hazard

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

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

  12. BILATERAL AGENCY - IMPLICITCOURNOT DUOPOLY • Agents operate economically similar firms – sole proprietorships: a1 = input of Agent 1 a2 = input of Agent 2 y1 = F(a1) = output of Agent 1 y2 = F(a2) = output of Agent 2

  13. BILATERAL AGENCY - IMPLICITCOURNOT DUOPOLY • Agents have “linear utility” in the profits they make. What does this mean? U(p1) = p1 = utility of Agent 1 U(p2) = p2 = utility of Agent 2 • Agents are indifferent to risk - risk neutral

  14. BILATERAL AGENCY - IMPLICITCOURNOT DUOPOLY • These agents have the following profit functions p1(a1,a2) = (p-c)y1 = (1-y1-y2-c)y1 = y1-y1y1-y1y2-cy1 p2(a1,a2) = (p-c)y2 = (1-y1-y2-c)y2 = y2-y2y1-y2y2-cy2

  15. BILATERAL AGENCY - IMPLICITCOURNOT DUOPOLY • These agents act in their own self - interest (reaction curves) dp1(a1,a2)/da1 = 0 dp2(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

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

  17. BILATERAL AGENCY - IMPLICITCOURNOT 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)

  18. BILATERAL AGENCY - IMPLICITCOURNOT 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 - IMPLICITCOURNOT DUOPOLY – NASH EQUILIBRIUM a2 AGENT 1 producing a1 a1 = ½(1- a2-c) E[(1/3)(1-c),(1/3)(1-c)] AGENT 2 producing a2 a2 = ½(1- a2– c) a1

  20. BILATERAL AGENCY - IMPLICITCOURNOT DUOPOLY – NASH EQUILIBRIUM • If F (a) = a, the agents have the following Nash equilibrium: a*1 = a*2 = (1/3)(1 – c) p*1 = p*2 = (1/9)(1 – c)(1 – c) p* = 1 - (2/3)(1 – c) = (1/3)(1 + 2c)

  21. BILATERAL AGENCY - IMPLICITCOURNOT DUOPOLY – NASH EQUILIBRIUM • If F (a) = a, the agents have the following iso-profit functions : p*1 = a1-a1a1-a1a2-ca1 a2 = - a1 - p/a1 + (1-c) - Agent 1 p*2 = a2-a2a2-a2a1-ca2 a1 = - a2 - p/a2 + (1-c) – Agent 2

  22. BILATERAL AGENCY - IMPLICITCOURNOT DUOPOLY – NASH EQUILIBRIUM a2 Axes Iso-Profit Curve For Agent 2 E[1/3(1-c), 1/3(1-c)] Iso-Profit Curve For Agent 1 a1

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

  24. Economic Measures BILATERAL AGENCY - IMPLICIT

  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 Competition • Duopoly [0,1] Consumer Demand [0,1] Consumer Demand P = 1-x P = 1-x [(2/3)(1-c), (1/3)(1+2c)] [(1-c), c] Producer Supply [1,0] [1,0] 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 Competition • Duopoly [0,1] Consumer Demand [0,1] Consumer Demand P = 1-x P = 1-x [(2/3)(1-c), (1/3)(1+2c)] [(1-c), c] Producer Supply [1,0] [1,0] DECREASE in Competitiveness

  29. 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”

  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 - IMPLICITMarket 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 Competition • Duopoly [0,1] Consumer Surplus [0,1] Consumer Surplus P = 1-x P = 1-x [(1-c), c] Producer Surplus [1,0] [1,0] Duopolists’ Surplus DECREASE in Social Surplus

  33. BILATERAL AGENCY - IMPLICITMarket 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 - IMPLICITMarket 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 - IMPLICITMarket Optimality • . Kaldor-Hicks Criterion Pareto Criterion

  36. BILATERAL AGENCY - IMPLICITMarket 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 - IMPLICITMarket 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 Agency Strategic Primarily market Example – Cournot Duopoly . Vertical Implicit Agency Example – Stackelberg Duopoly Horizontal Implicit Agency Example – Cournot Duopoly

  39. BILATERAL AGENCY - IMPLICIT • Cournot Duopoly • Stackelberg Duopoly AGENT 2 PRINCIPAL AGENT 1 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(a1) = (1/2)(1 - F(a2) - c) F(a2) = (1/2)(1 - F(a1) - 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(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.

  44. BILATERAL AGENCY - IMPLICIT STACKELBERG DUOPOLY • Duopoly • Stackelberg Duopoly Isoprofit Curve of Firm II Agent I [0,(1-c)] Agent I Isoprofit Curve of Firm I [0,(1/2)(1-c)] [0,(1/2)(1-c)] [(1/2)(1-c), (1/4)(1-c)] [(1/3)(1-c), (1/3)(1-c)] Agent II Agent II [(1/2)(1-c), 0] [(1/2)(1-c), 0] [(1-c), 0]

  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 Duopoly • Stackelberg Duopoly P = 1- a1- a2 P = 1- a1 - a2 [(1/3)(1-c), 0] [(2/3)(1-c), 0][1,0] [(1-c)/2,0] [(3/4)(1-c), 0] [1,0]

  47. BILATERAL AGENCY - IMPLICIT STACKELBERG DUOPOLY • Nash Equilibrium • Simultaneous Solution a1 = a2 = (1/3)(1-c) • Nash Equilibrium • Sequential Solution a1 = (1/2)(1-c) a2 = (1/4)(1-c)

  48. BILATERAL AGENCY - IMPLICIT • Cournot Duopoly • Stackelberg Duopoly [0,1] [0,(1/4)(1+ 3c)] [0,1] [0,(1/3)(1+2c)] P = 1- a1- a2 P = 1- a1- a2 [(1/3)(1-c), 0] [(2/3)(1-c), 0][1,0] [(1-c)/2,0] [(3/4)(1-c), 0] [1,0]

  49. BILATERAL AGENCY - IMPLICITCOURNOT DUOPOLY • If F (a) = a, the agents have the following Nash equilibrium: a*1 = (1/2)(1 – c) a*2 = (1/4)(1 – c) p*1 = (1/8)(1 – c)(1 – c) p*2 = (1/16)(1 – c)(1 – c) p* = 1 - (3/4)(1 – c) = (1/4)(1 + 3c)

  50. BILATERAL AGENCY - IMPLICIT • Cournot Benchmarks • Efficiency a1 + a2 = (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 a1 + a2= (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)