1. Chapter Thirty Production

2. Exchange Economies (revisited) u No production, only endowments, so no description of how resources are converted to consumables. u General equilibrium: all markets clear simultaneously. u 1st and 2nd Fundamental Theorems of Welfare Economics.

3. Now Add Production... u Add input markets, output markets, describe firms’ technologies, the distributions of firms’ outputs and profits …

4. Now Add Production... u Add input markets, output markets, describe firms’ technologies, the distributions of firms’ outputs and profits … That’s not easy!

5. Robinson Crusoe’s Economy u One agent, RC. u Endowed with a fixed quantity of one resource -- 24 hours. u Use time for labor (production) or leisure (consumption). u Labor time = L. Leisure time = 24 - L. u What will RC choose?

6. Robinson Crusoe’s Technology u Technology: Labor produces output (coconuts) according to a concave production function.

7. Robinson Crusoe’s Technology Production function Labor (hours) Coconuts 24 0

8. Robinson Crusoe’s Technology Labor (hours) Coconuts Production function 24 0 Feasible production plans

9. Robinson Crusoe’s Preferences u RC’s preferences: –coconut is a good –leisure is a good

10. Robinson Crusoe’s Preferences Leisure (hours) Coconuts More preferred 24 0

11. Robinson Crusoe’s Preferences Leisure (hours) Coconuts More preferred 240

12. Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 24 0

13. Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 24 0 Leisure (hours) 240

14. Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 24 0 Leisure (hours) 240

15. Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 24 0 Leisure (hours) 240

16. Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L*

17. Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L* Labor

18. Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L* LaborLeisure

19. Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L* LaborLeisure Output

20. Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L* LaborLeisure MRS = MP L Output

21. Robinson Crusoe as a Firm u Now suppose RC is both a utility- maximizing consumer and a profit- maximizing firm. u Use coconuts as the numeraire good; i.e. price of a coconut = $1. u RC’s wage rate is w. u Coconut output level is C.

22. Robinson Crusoe as a Firm u RC’s firm’s profit is  = C - wL. u  = C - wL  C =  + wL, the equation of an isoprofit line. u Slope = + w. u Intercept = .

23. Isoprofit Lines Labor (hours) Coconuts 24 Higher profit; Slopes = + w 0

24. Profit-Maximization Labor (hours) Coconuts Feasible production plans Production function 24 0

25. Profit-Maximization Labor (hours) Coconuts Production function 24 0

26. Profit-Maximization Labor (hours) Coconuts Production function 24 0

27. Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* 0

28. Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope 0

29. Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MP L 0

30. Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MP L = 1  MP L = MRP L. 0

31. Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MP L = 1  MP L = MRP L. RC gets 0

32. Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MP L = 1  MP L = MRP L. Given w, RC’s firm’s quantity demanded of labor is L* Labor demand RC gets 0

33. Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MP L = 1  MP L = MRP L. Given w, RC’s firm’s quantity demanded of labor is L* and output quantity supplied is C*. Labor demand Output supply RC gets 0

34. Utility-Maximization u Now consider RC as a consumer endowed with $  * who can work for $w per hour. u What is RC’s most preferred consumption bundle? u Budget constraint is

35. Utility-Maximization Labor (hours) Coconuts 24 0 Budget constraint

36. Utility-Maximization Labor (hours) Coconuts 24 0 Budget constraint; slope = w

37. Utility-Maximization Labor (hours) Coconuts More preferred 24 0

38. Utility-Maximization Labor (hours) Coconuts 24 0 Budget constraint; slope = w

39. Utility-Maximization Labor (hours) Coconuts Budget constraint; slope = w 24 0

40. Utility-Maximization Labor (hours) Coconuts 24 0 C* L* Budget constraint; slope = w

41. Utility-Maximization Labor (hours) Coconuts 24 0 C* L* MRS = w Budget constraint; slope = w

42. Utility-Maximization Labor (hours) Coconuts 24 0 C* L* Labor supply Budget constraint; slope = w MRS = w Given w, RC’s quantity supplied of labor is L*

43. Utility-Maximization Labor (hours) Coconuts 24 0 C* L* Given w, RC’s quantity supplied of labor is L* and output quantity demanded is C*. Labor supply Output demand Budget constraint; slope = w MRS = w

44. Utility-Maximization & Profit- Maximization u Profit-maximization: –w = MP L –quantity of output supplied = C* –quantity of labor demanded = L*

45. Utility-Maximization & Profit- Maximization u Profit-maximization: –w = MP L –quantity of output supplied = C* –quantity of labor demanded = L* u Utility-maximization: –w = MRS –quantity of output demanded = C* –quantity of labor supplied = L*

46. Utility-Maximization & Profit- Maximization u Profit-maximization: –w = MP L –quantity of output supplied = C* –quantity of labor demanded = L* u Utility-maximization: –w = MRS –quantity of output demanded = C* –quantity of labor supplied = L* Coconut and labor markets both clear.

47. Utility-Maximization & Profit- Maximization Labor (hours) Coconuts 24 C* L* 0 MRS = w = MP L Given w, RC’s quantity supplied of labor = quantity demanded of labor = L* and output quantity demanded = output quantity supplied = C*.

48. Pareto Efficiency u Must have MRS = MP L.

49. Pareto Efficiency Labor (hours) Coconuts 24 0 MRS  MP L

50. Pareto Efficiency Labor (hours) Coconuts 24 0 MRS  MP L Preferred consumption bundles.

51. Pareto Efficiency Labor (hours) Coconuts 24 0 MRS = MP L

52. Pareto Efficiency Labor (hours) Coconuts 24 0 MRS = MP L. The common slope  relative wage rate w that implements the Pareto efficient plan by decentralized pricing.

53. First Fundamental Theorem of Welfare Economics u A competitive market equilibrium is Pareto efficient if –consumers’ preferences are convex –there are no externalities in consumption or production.

54. Second Fundamental Theorem of Welfare Economics u Any Pareto efficient economic state can be achieved as a competitive market equilibrium if –consumers’ preferences are convex –firms’ technologies are convex –there are no externalities in consumption or production.

55. Non-Convex Technologies u Do the Welfare Theorems hold if firms have non-convex technologies?

56. Non-Convex Technologies u Do the Welfare Theorems hold if firms have non-convex technologies? u The 1st Theorem does not rely upon firms’ technologies being convex.

57. Non-Convex Technologies Labor (hours) Coconuts 24 0 MRS = MP L The common slope  relative wage rate w that implements the Pareto efficient plan by decentralized pricing.

58. Non-Convex Technologies u Do the Welfare Theorems hold if firms have non-convex technologies? u The 2nd Theorem does require that firms’ technologies be convex.

59. Non-Convex Technologies Labor (hours) Coconuts 24 0 MRS = MP L. The Pareto optimal allocation cannot be implemented by a competitive equilibrium.

60. Production Possibilities u Resource and technological limitations restrict what an economy can produce. u The set of all feasible output bundles is the economy’s production possibility set. u The set’s outer boundary is the production possibility frontier.

61. Production Possibilities Fish Coconuts Production possibility frontier (ppf)

62. Production Possibilities Fish Coconuts Production possibility frontier (ppf) Production possibility set

63. Production Possibilities Fish Coconuts Feasible but inefficient

64. Production Possibilities Fish Coconuts Feasible but inefficient Feasible and efficient

65. Production Possibilities Fish Coconuts Feasible but inefficient Feasible and efficient Infeasible

66. Production Possibilities Fish Coconuts Ppf’s slope is the marginal rate of product transformation.

67. Production Possibilities Fish Coconuts Ppf’s slope is the marginal rate of product transformation. Increasingly negative MRPT  increasing opportunity cost to specialization.

68. Production Possibilities u If there are no production externalities then a ppf will be concave w.r.t. the origin. u Why?

69. Production Possibilities u If there are no production externalities then a ppf will be concave w.r.t. the origin. u Why? u Because efficient production requires exploitation of comparative advantages.

70. Comparative Advantage u Two agents, RC and Man Friday (MF). u RC can produce at most 20 coconuts or 30 fish. u MF can produce at most 50 coconuts or 25 fish.

71. Comparative Advantage F C F C RC MF 20 50 30 25

72. Comparative Advantage F C F C RC MF 20 50 30 25 MRPT = -2/3 coconuts/fish so opp. cost of one more fish is 2/3 foregone coconuts.

73. Comparative Advantage F C F C RC MF 20 50 30 25 MRPT = -2/3 coconuts/fish so opp. cost of one more fish is 2/3 foregone coconuts. MRPT = -2 coconuts/fish so opp. cost of one more fish is 2 foregone coconuts.

74. Comparative Advantage F C F C RC MF 20 50 30 25 MRPT = -2/3 coconuts/fish so opp. cost of one more fish is 2/3 foregone coconuts. MRPT = -2 coconuts/fish so opp. cost of one more fish is 2 foregone coconuts. RC has the comparative opp. cost advantage in producing fish.

75. Comparative Advantage F C F C RC MF 20 50 30 25 MRPT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish.

76. Comparative Advantage F C F C RC MF 20 50 30 25 MRPT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish. MRPT = -2 coconuts/fish so opp. cost of one more coconut is 1/2 foregone fish.

77. Comparative Advantage F C F C RC MF 20 50 30 25 MRPT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish. MRPT = -2 coconuts/fish so opp. cost of one more coconut is 1/2 foregone fish. MF has the comparative opp. cost advantage in producing coconuts.

78. Comparative Advantage F C Economy F C F C RC MF 20 50 30 25 70 55 50 30 Use RC to produce fish before using MF. Use MF to produce coconuts before using RC.

79. Comparative Advantage F C Economy F C F C RC MF 20 50 30 25 70 55 50 30 Using low opp. cost producers first results in a ppf that is concave w.r.t the origin.

80. Comparative Advantage F C Economy More producers with different opp. costs “smooth out” the ppf.

81. Coordinating Production & Consumption u The ppf contains many technically efficient output bundles. u Which are Pareto efficient for consumers?

82. Coordinating Production & Consumption Fish Coconuts Output bundle is

83. Coordinating Production & Consumption Fish Coconuts Output bundle is and is the aggregate endowment for distribution to consumers RC and MF.

84. Coordinating Production & Consumption Fish Coconuts O RC O MF Output bundle is and is the aggregate endowment for distribution to consumers RC and MF.

85. Coordinating Production & Consumption Fish Coconuts O RC O MF Allocate efficiently; say to RC

86. Coordinating Production & Consumption Fish Coconuts O RC O MF Allocate efficiently; say to RC and to MF.

87. Coordinating Production & Consumption Fish Coconuts O RC O MF

88. Coordinating Production & Consumption Fish Coconuts O RC O MF

89. Coordinating Production & Consumption Fish Coconuts O RC O MF

90. Coordinating Production & Consumption Fish Coconuts O RC O MF MRS  MRPT

91. Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce

92. Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce

93. Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before.

94. Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. MF’s utility is unchanged.

95. Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. MF’s utility is unchanged

96. Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. MF’s utility is unchanged

97. Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. MF’s utility is unchanged, RC’s utility is higher

98. Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. MF’s utility is unchanged, RC’s utility is higher; Pareto improvement.

99. Coordinating Production & Consumption u MRS  MRPT  inefficient coordination of production and consumption. u Hence, MRS = MRPT is necessary for a Pareto optimal economic state.

100. Coordinating Production & Consumption Fish Coconuts O RC O MF

101. Decentralized Coordination of Production & Consumption u RC and MF jointly run a firm producing coconuts and fish. u RC and MF are also consumers who can sell labor. u Price of coconut = p C. u Price of fish = p F. u RC’s wage rate = w RC. u MF’s wage rate = w MF.

102. Decentralized Coordination of Production & Consumption u L RC, L MF are amounts of labor purchased from RC and MF. u Firm’s profit-maximization problem is choose C, F, L RC and L MF to

103. Decentralized Coordination of Production & Consumption Isoprofit line equation is

104. Decentralized Coordination of Production & Consumption Isoprofit line equation is which rearranges to

105. Decentralized Coordination of Production & Consumption Isoprofit line equation is which rearranges to

106. Decentralized Coordination of Production & Consumption Fish Coconuts Higher profit Slopes =

107. Decentralized Coordination of Production & Consumption Fish Coconuts The firm’s production possibility set.

108. Decentralized Coordination of Production & Consumption Fish Coconuts Slopes =

109. Decentralized Coordination of Production & Consumption Fish Coconuts Profit-max. plan Slopes =

110. Decentralized Coordination of Production & Consumption Fish Coconuts Profit-max. plan Slope =

111. Decentralized Coordination of Production & Consumption Fish Coconuts Profit-max. plan Slope = Competitive markets and profit-maximization 

112. Decentralized Coordination of Production & Consumption u So competitive markets, profit- maximization, and utility maximization all together cause the condition necessary for a Pareto optimal economic state.

113. Decentralized Coordination of Production & Consumption Fish Coconuts O RC O MF Competitive markets and utility-maximization 

114. Decentralized Coordination of Production & Consumption Fish Coconuts O RC O MF Competitive markets, utility- maximization and profit- maximization 