Chapter Thirty-Two

1
Chapter Thirty-Two

• 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 Thats not easy!

5
Robinson Crusoes Economy

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

6
Robinson Crusoes Technology

• Technology Labor produces output (coconuts)
  according to a concave production function.

7
Robinson Crusoes Technology
Coconuts
Production function
24
0
Labor (hours)
8
Robinson Crusoes Technology
Coconuts
Production function
Feasible productionplans
24
0
Labor (hours)
9
Robinson Crusoes Preferences

• RCs preferences
• coconut is a good
• leisure is a good

10
Robinson Crusoes Preferences
Coconuts
More preferred
24
0
Leisure (hours)
11
Robinson Crusoes Preferences
Coconuts
More preferred
Leisure (hours)
24
0
12
Robinson Crusoes Choice
Coconuts
Production function
Feasible productionplans
24
0
Labor (hours)
13
Robinson Crusoes Choice
Coconuts
Production function
Feasible productionplans
24
0
Labor (hours)
Leisure (hours)
24
0
14
Robinson Crusoes Choice
Coconuts
Production function
Feasible productionplans
24
0
Labor (hours)
Leisure (hours)
24
0
15
Robinson Crusoes Choice
Coconuts
Production function
Feasible productionplans
24
0
Labor (hours)
Leisure (hours)
24
0
16
Robinson Crusoes Choice
Coconuts
Production function
C
24
L
0
Labor (hours)
Leisure (hours)
24
0
17
Robinson Crusoes Choice
Coconuts
Production function
C
Labor
24
L
0
Labor (hours)
Leisure (hours)
24
0
18
Robinson Crusoes Choice
Coconuts
Production function
C
Labor
Leisure
24
L
0
Labor (hours)
Leisure (hours)
24
0
19
Robinson Crusoes Choice
Coconuts
Production function
C
Output
Labor
Leisure
24
L
0
Labor (hours)
Leisure (hours)
24
0
20
Robinson Crusoes Choice
Coconuts
MRS MPL
Production function
C
Output
Labor
Leisure
24
L
0
Labor (hours)
Leisure (hours)
24
0
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.
• RCs wage rate is w.
• Coconut output level is C.

22
Robinson Crusoe as a Firm

• RCs firms 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
0
Labor (hours)
24
Profit-Maximization
Coconuts
Production function
Feasible productionplans
24
0
Labor (hours)
25
Profit-Maximization
Coconuts
Production function
24
0
Labor (hours)
26
Profit-Maximization
Coconuts
Production function
24
0
Labor (hours)
27
Profit-Maximization
Coconuts
Production function
C
24
L
0
Labor (hours)
28
Profit-Maximization
Isoprofit slope production function slope
Coconuts
Production function
C
24
L
0
Labor (hours)
29
Profit-Maximization
Isoprofit slope production function slope
i.e. w MPL
Coconuts
Production function
C
24
L
0
Labor (hours)
30
Profit-Maximization
Isoprofit slope production function slope
i.e. w MPL 1? MPL MRPL.
Coconuts
Production function
C
24
L
0
Labor (hours)
31
Profit-Maximization
Isoprofit slope production function slope
i.e. w MPL 1? MPL MRPL.
Coconuts
Production function
C
24
L
0
Labor (hours)
RC gets
32
Profit-Maximization
Isoprofit slope production function slope
i.e. w MPL 1? MPL MRPL.
Coconuts
Production function
C
Given w, RCs firms quantity demanded of labor
is L
Labor demand
24
L
0
Labor (hours)
RC gets
33
Profit-Maximization
Isoprofit slope production function slope
i.e. w MPL 1? MPL MRPL.
Coconuts
Production function
C
Output supply
Given w, RCs firms quantity demanded of labor
is L and output quantity supplied is C.
Labor demand
24
L
0
Labor (hours)
RC gets
34
Utility-Maximization

• Now consider RC as a consumer endowed with ?
  who can work for w per hour.
• What is RCs most preferred consumption bundle?
• Budget constraint is

35
Utility-Maximization
Coconuts
Budget constraint
24
0
Labor (hours)
36
Utility-Maximization
Coconuts
Budget constraint slope w
24
0
Labor (hours)
37
Utility-Maximization
Coconuts
More preferred
24
0
Labor (hours)
38
Utility-Maximization
Coconuts
Budget constraint slope w
24
0
Labor (hours)
39
Utility-Maximization
Coconuts
Budget constraint slope w
24
0
Labor (hours)
40
Utility-Maximization
Coconuts
Budget constraint slope w
C
24
L
0
Labor (hours)
41
Utility-Maximization
Coconuts
MRS w
Budget constraint slope w
C
24
L
0
Labor (hours)
42
Utility-Maximization
Coconuts
MRS w
Budget constraint slope w
C
Given w, RCs quantity supplied of labor is L
Labor supply
24
L
0
Labor (hours)
43
Utility-Maximization
Coconuts
MRS w
Budget constraint slope w
C
Output demand
Given w, RCs quantity supplied of labor is L
and output quantity demanded is C.
Labor supply
24
L
0
Labor (hours)
44
Utility-Maximization Profit-Maximization

• Profit-maximization
• w MPL
• quantity of output supplied C
• quantity of labor demanded L

45
Utility-Maximization Profit-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

• 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, RCs quantity supplied of labor
quantity demanded of labor L and output
quantity demanded output quantity supplied C.
C
24
L
0
Labor (hours)
48
Pareto Efficiency

• Must have MRS MPL.

49
Pareto Efficiency
Coconuts
MRS ? MPL
24
0
Labor (hours)
50
Pareto Efficiency
Coconuts
MRS ? MPL
Preferred consumption bundles.
24
0
Labor (hours)
51
Pareto Efficiency
Coconuts
MRS MPL
24
0
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
0
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
0
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
0
Labor (hours)
60
Production Possibilities

• Resource and technological limitations restrict
  what an economy can produce.
• The set of all feasible output bundles is the
  economys production possibility set.
• The sets 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
Ppfs slope is the marginal rate of product
transformation.
Fish
67
Production Possibilities
Coconuts
Ppfs 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 Advantage
C
RC
20
30
F
C
MF
50
25
F
72
Comparative Advantage
C
RC
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 Advantage
C
RC
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 Advantage
C
RC
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 Advantage
C
RC
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 Advantage
C
RC
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 Advantage
C
RC
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 Advantage
C
RC
Economy
C
Use RC to produce fish before using MF.
20
70
30
F
Use MF to produce coconuts before using RC.
C
MF
50
50
55
30
F
25
F
79
Comparative Advantage
C
RC
Economy
C
Using low opp. cost producers first results in a
ppf that is concave w.r.t the origin.
20
70
30
F
C
MF
50
50
55
30
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
MRS ? MRPT
OMF
ORC
Fish
91
Coordinating Production Consumption
Coconuts
Instead produce
OMF
OMF
ORC
Fish
92
Coordinating Production Consumption
Coconuts
Instead produce
OMF
OMF
ORC
Fish
93
Coordinating Production Consumption
Coconuts
Instead produce Give MF same allocation
as before.
OMF
OMF
ORC
Fish
94
Coordinating Production Consumption
Coconuts
Instead produce Give MF same allocation
as before. MFs utility
is unchanged.
OMF
OMF
ORC
Fish
95
Coordinating Production Consumption
Coconuts
Instead produce Give MF same allocation
as before. MFs utility
is unchanged
OMF
OMF
ORC
Fish
96
Coordinating Production Consumption
Coconuts
Instead produce Give MF same allocation
as before. MFs utility
is unchanged
OMF
OMF
ORC
Fish
97
Coordinating Production Consumption
Coconuts
Instead produce Give MF same allocation
as before. MFs utility
is unchanged, RCs
utility is higher
OMF
OMF
ORC
Fish
98
Coordinating Production Consumption
Coconuts
Instead produce Give MF same allocation
as before. MFs utility
is unchanged, RCs
utility is higher
Pareto improvement.
OMF
OMF
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.
• RCs wage rate wRC.
• MFs wage rate wMF.

102
Decentralized Coordination of Production
Consumption

• LRC, LMF are amounts of labor purchased from RC
  and MF.
• Firms 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
Fish
107
Decentralized Coordination of Production
Consumption
Coconuts
The firms production possibility set.
Fish
108
Decentralized Coordination of Production
Consumption
Coconuts
Fish
109
Decentralized Coordination of Production
Consumption
Coconuts
Profit-max. plan
Fish
110
Decentralized Coordination of Production
Consumption
Coconuts
Profit-max. plan
Fish
111
Decentralized Coordination of Production
Consumption
Coconuts
Profit-max. plan
Competitive markets and profit-maximization ?
Fish
112
Decentralized Coordination of Production
Consumption

• So competitive markets, profit-maximization, and
  utility maximization all together causethe
  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