16.4 Competitive Market Efficiency

1. 16.4 Competitive Market Efficiency • Pareto Efficient • No alternate allocation of inputs and goods makes one consumer better off without hurting another consumer • If another allocation improves AT LEAST ONE CONSUMER (without making anyone else worse off), the first allocation was Pareto Inefficient.

2. 16.4 Competitive Market Efficiency • Pareto Efficiency has three requirements: • Exchange Efficiency • Goods cannot be traded to make a consumer better off • 2) Input Efficiency • Inputs cannot be rearranged to produce more goods

3. 16.4 Competitive Market Efficiency • 3) Substitution Efficiency • Substituting one good for another will not make one consumer better off without harming another consumer

4. 1) Exchange Efficiency Model Assumptions • Assumptions: • 2 people • 2 goods, each of fixed quantity • This allows us to construct an EDGEWORTH BOX – a graph showing all the possible allocations of goods in a two-good economy, given the total available supply of each good

5. 1) Edgeworth Box Example • Two people: Maka and Susan • Two goods: Food (f) & Video Games (V) • We put Maka on the origin, with the y-axis representing food and the x axis representing video games • If we connect a “flipped” graph of Susan’s goods, we get an EDGEWORTH BOX, where y is all the food available and x is all the video games:

6. 1) Maka’s Goods Graph Ou is Maka’s food, and Ox is Maka’s Video Games u Food O x Video Games Maka

7. 1) Edgeworth Box Susan y O’ O’w is Susan’s food, and O’y is Susan’s Video Games r Total food in the market is Or(=O’s) and total Video Games is Os (=O’r) u Food w Each point in the Edgeworth Box represents one possible good allocation O s x Video Games Maka

8. 1) Edgeworth and utility • We can then add INDIFFERENCE curves to Maka’s graph (each curve indicating all combinations of goods with the same utility) • Curves farther from O have a greater utility • We can then superimpose Susan’s utility curves • Curves farther from O’ have a greater utility Remember that:

9. 1) Maka’s Utility Curves Maka’s utility is greatest at M3 Food M3 M2 M1 O Video Games Maka

10. 1) Edgeworth Box and Utility Susan O’ Susan has the highest utility at S3 r S1 A S2 At point A, Maka has utility of M3 and Susan has Utility of S2 S3 Food M3 M2 M1 O s Video Games Maka

11. 1) Edgeworth Box and Utility Susan O’ If consumption is at A, Maka has utility M1 while Susan has utility S3 r A B S3 By moving to point B and then point C, Maka’s utility increases while Susan’s remains constant C Food M3 M2 M1 O s Video Games Maka

12. 1) Exchange Efficiency Susan O’ Point C, where the indifference curves barely touch is EXCHANGE EFFICIENT, as one person can’t be made better off without harming the other. r S3 C Food M3 M2 M1 O s Video Games Maka

13. 1) Pareto Improvement • When an allocation is NOT exchange efficient, it is wasteful (at least one person could be made better off)… • A PARETO IMPROVEMENT makes one person better off without making anyone else worth off (like the move from A to C)… • However, there may be more than one pareto improvement:

14. 1) Pareto Improvements Susan O’ If we start at point A: -C is a pareto improvement that makes Maka better off -D is a pareto improvement that makes Susan better off -E is a pareto improvement that makes both better off r A S3 C S4 Food S5 E M3 M2 D M1 O s Video Games Maka

15. 1) The Contract Curve • Assuming all possible starting points, we can find all possible exchange efficient points and join them to create a CONTRACT CURVE • All along the contract curve, opposing indifferent curves are TANGENT to each other • Since each individual maximizes where his indifference curve is tangent to his budget line:

16. 1) The Contract Curve Susan O’ r Food O s Video Games Maka

17. 1) Example: House and Chase Assume that House and Chase have the following utilities for books and coffee: • The Exchange Efficiency Condition therefore becomes:

18. 1) MATH – House and Chase If there are 10 books, and 4 cups of coffee, then the contract curve is expressed as: • If House has 6 books, an exchange efficient allocation would be:

19. 1) MATH – House and Chase Therefore, House would have 6 books and 2.4 cups of coffee, and Chase would have 4 (10-6) books and 1.6 (4-2.4) cups of coffee, for utilities of:

20. 2) Input EfficiencyModel Assumptions • Assumptions: • 2 producers/firms • 2 inputs (Labor and Capital), each of fixed quantity • This lead to a EDGEWORTH BOX FOR INPUTS– a graph showing all the possible allocations of fixed quantities of labor and capital between two producers

21. 2) Edgeworth Box For Inputs Example • Two firms: Apple and Google • Two inputs: Labor (L) and capital (K) • We put Apple the origin, with the y-axis representing capital and the x axis representing labor • If we connect a “flipped” graph of Google’s inputs, we get an EDGEWORTH BOX FOR INPUTS, where y is all the capital available and x is all the labor:

22. 2) Apple’s Input Graph Ou is Apple’s capital, and Ox is Apple’s labor. u Capital O x Labor Apple

23. 2) Edgeworth Box For Inputs Google y O’ O’w is Google’s capital, and O’y is Google’s labor r Total capital in the market is Or(=O’s) and total labor is Os (=O’r) u Capital w Each point in the Edgeworth Box represents one possible input allocation O s x Labor Apple

24. 2) Edgeworth and Production • We can then add ISOQUANT curves to APPLE’s graph (each curve indicating all combinations of inputs producing the same output) • Curves farther from O produce more • We can then superimpose Google’s Isoquants • Curves farther from O’ produce more Remember that the slope of the Isoquant is MRTS and:

25. 2) Apple’s Isoquants Apple produces the mostat A3 Capital A3 A2 A1 O Labor Apple

26. 2) Edgeworth Box for Inputs Google O’ Google produces the most at G3 r G1 A G2 At point A, Apple makes A3 Google produces G2 G3 Capital A3 A2 A1 O s Labor Apple

27. 2) Edgeworth Box and Utility Google O’ If production is at A, Apple produces A1 while Google produces G3 r A B G3 By moving to point B and then point C, Apple produces more while Google’s production remains constant C Capital A3 A2 A1 O s Labor Apple

28. 2) Input Efficiency Google O’ Point C, where the isoquant curves barely touch is INPUT EFFICIENT, as one firm can’t produce more without the other firm producing less. r G3 C Capital A3 A2 A1 O s Labor Apple

29. 2) Pareto Improvement • When an input allocation is NOT input efficient, it is wasteful (at least one firm COULD produce more)… • A PARETO IMPROVEMENT allows one firm to produce more without reducing the output of the other firm(like the move from A to C) • However, there may be more than one pareto improvement:

30. 2) Pareto Improvements Google O’ If we start at point A: -C is a pareto improvement where Apple produces more -D is a pareto improvement where Google produces more -E is a pareto improvement where both firms produce more r A G3 C G4 Capital G5 E A3 A2 D A1 O s Labor Apple

31. 2) Input Contract Curve • Similar to the goods market, a contract curve can be derived in the input market: • All along the contract curve, opposing isoquant curves are TANGENT to each other • Since each firm maximizes where their isoquant curve is tangent to their isocost line:

32. 2) Input Contract Curve Google O’ r Capital O s Labor Apple

33. 2) Example: Apple and Google Assume that Apple and Google have the following production functions: • The Exchange Efficiency Condition therefore becomes:

34. The isoquant slope for Apple is:

35. The isoquant slope for Google is:

36. 2) MATH – Apple and Google If there are 1000 workers, and 125 capital in Silicon valley, then the contract curve is expressed as:

37. 2) MATH – Apple and Google Is the market input efficient if Apple has 200 workers and 50 capital? • No – Apple needs fewer capital (Google needs more capital) AND/OR • Google needs fewer workers (Apple needs more workers)

38. 3) Substitution Efficiency • Substitution Efficiency can be analyzed using the PRODUCTION POSSIBILITIES CURVE/FRONTIER • The PPC shows all combinations of 2 goods that can be produced using available inputs • The slope of the PPC shows how much of one good must be SUBSTITUTED to produce more of the other good, or MARGINAL RATE OF TRANSFORMATION (x for y) (MRTxy)

39. Production Possibilities Curve Here the MRTSpr is equal to (7-5)/(2-1)=-2, or two robots must be given up for an extra pizza. 10 9 8 The marginal cost of the 3rd pizza, or MCp=2 robots 7 6 The marginal cost of the 6th and 7th robots, or MCr=1 pizza Robots 5 4 Therefore, MRTxy=MCx/MCy 3 2 Therefore, MRTpr=2/1=2 1 1 2 3 4 5 6 7 8 Pizzas

40. 3) Substitution Efficiency and Production • If production is possible in an economy, the Pareto efficiency condition becomes: • Assume MRTpr=3 and MRSpr=2. • -Therefore Maka could get 3 more robots by transforming 1 pizza • -BUT Maka would exchange 2 robots for 1 pizzas to maintain utility • -Therefore 1 pizza is sacrificed for 3 robots, increasing Maka’s utility through the 3rd robot • -The Market isn’t Pareto Efficient

41. The First Fundamental Theorem Of Welfare Economics IF • All consumers and producers act as perfect competitors (no one has market power) and 2) A market exists for each and every commodity Then Resource allocation is Pareto Efficient

42. First Fundamental Theorem of Welfare Economics Proof: • From microeconomic consumer theory, we know that: • Since prices are the same for all people: • Therefore perfect competition leads to exchange efficiency

43. First Fundamental Theorem of Welfare Economics Proof: • From microeconomic theory of the firm, we know that: • Since each firm in an industry faces the same wages and rents: • Perfect competition leads to input efficiency

44. First Fundamental Theorem of Welfare Economics Origins • From the PPF, we know that • Therefore a perfectly competitive market is Pareto Efficient:

45. Efficiency≠Fairness • If Pareto Efficiency was the only concern, competitive markets automatically achieve it and there would be very little need for government: • Government would exist to protect property rights • Laws, Courts, and National Defense • But Pareto Efficiency doesn’t consider distribution. One person could get all society’s resources while everyone else starves. This isn’t typically socially optimal.

46. Fairness Susan O’ r Points A and B are Pareto efficient, but either Susan or Maka get almost all society’s resources B C Food A Many would argue C is better for society, even though it is not Pareto efficient O s Video Games Maka

47. Fairness • For each utility level of one person, there is a maximum utility of the other • Graphing each utility against the other gives us the UTILITY POSSIBILITIES CURVE:

48. Utility Possibilities Curve All points on the curve are Pareto efficient, while all points below the curve are not. Any point above the curve is unobtainable B Maka’s Utility C A O Susan’s Utility Maka

49. Fairness • Typical utility is a function of goods consumed: U=f(x,y) • Societal utility can be seen as a function of individual utilities: W=f(U1,U2) • This is the SOCIAL WELFARE FUNCTION, and can produce SOCIAL INDIFFERENCE CURVES:

50. Typical Social Indifference Curves An indifference curve farther from the origin represents a higher level of social welfare. Maka’s Utility O Susan’s Utility Maka