1. Chapter 33
Production

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

44. Utility-Maximization & Profit-Maximization
w = MPL
quantity of output supplied = C*
quantity of labor demanded = L*

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

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

48. Pareto Efficiency
Must have MRS = MPL.

49. Pareto Efficiency
Coconuts
MRS  MPL 24
Labor (hours)

50. Pareto Efficiency Coconuts MRS  MPL Preferred consumption bundles. 2424
Labor (hours)

51. Pareto Efficiency
Coconuts
MRS = MPL 24
Labor (hours)

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

53. First Fundamental Theorem of Welfare Economics
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
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
Do the Welfare Theorems hold if firms have non-convex technologies?

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

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

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

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

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

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

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

63. Production Possibilities
Coconuts
Feasible but
inefficient
Fish

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

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

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

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

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

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

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

71. Comparative AdvantageRC 20 30 F C MF 50 25 F

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

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

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

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

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

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

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

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

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

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

82. Coordinating Production & Consumption
Coconuts
Output bundle is
Fish

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

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

85. Coordinating Production & Consumption
Coconuts
Allocate efficiently;
say to RC
OMF
ORC
Fish

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

87. Coordinating Production & Consumption
Coconuts
OMF
ORC
Fish

88. Coordinating Production & Consumption
Coconuts
OMF
ORC
Fish

89. Coordinating Production & Consumption
Coconuts
OMF
ORC
Fish

90. Coordinating Production & Consumption
Coconuts
OMF
MRS  MRPT
ORC
Fish

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

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

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

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

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

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

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

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

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

100. Coordinating Production & Consumption
Coconuts
OMF
ORC
Fish

101. Decentralized Coordination of Production & Consumption
RC and MF jointly run a firm producing coconuts and fish.
RC and MF are also consumers who can sell labor.
Price of coconut = pC.
Price of fish = pF.
RC’s wage rate = wRC.
MF’s wage rate = wMF.

102. Decentralized Coordination of Production & Consumption
LRC, LMF are amounts of labor purchased from RC and MF.
Firm’s profit-maximization problem is choose C, F, LRC and LMF 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
Coconuts
Higher profit
Slopes =
Fish

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

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

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

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

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

112. Decentralized Coordination of Production & Consumption
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
Coconuts
Competitive markets
and utility-maximization 
OMF
ORC
Fish

114. Decentralized Coordination of Production & Consumption
Coconuts
Competitive markets, utility-
maximization and profit-
maximization 
OMF
ORC
Fish