Transcript Chapter Thirty

Chapter 32
Production
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.

2
Now Add Production ...

Add input markets, output markets, describe
firms’ technologies, the distributions of firms’
outputs and profits …
3
Now Add Production ...

Add input markets, output markets, describe
firms’ technologies, the distributions of firms’
outputs and profits … That’s not easy!
4
Robinson Crusoe’s 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?

5
Robinson Crusoe’s Technology

Technology: Labor produces output (coconuts)
according to a concave production function.
6
Robinson
Crusoe’s
Technology
Coconuts
Production function
Feasible production
plans
0
24
Labor (hours)
7
Robinson Crusoe’s Preferences

RC’s preferences:
 coconut
is a good
 leisure is a good
8
Robinson
Crusoe’s
Preferences
Coconuts
More preferred
0
24
Leisure (hours)
9
Robinson
Crusoe’s
Preferences
Coconuts
More preferred
24
0
Leisure (hours)
10
Robinson
Crusoe’s
Choice
Coconuts
Production function
Feasible production
plans
0
24
Labor (hours)
11
Robinson
Crusoe’s
Choice
Coconuts
Production function
Feasible production
plans
0
24
24
0
Labor (hours)
Leisure (hours)
12
Robinson
Crusoe’s
Choice
Coconuts
Production function
Feasible production
plans
0
24
24
0
Labor (hours)
Leisure (hours)
13
Robinson
Crusoe’s
Choice
Coconuts
Production function
C*
0
24
L*
24
0
Labor (hours)
Leisure (hours)
14
Robinson
Crusoe’s
Choice
Coconuts
Production function
C*
Labor
0
24
L*
24
0
Labor (hours)
Leisure (hours)
15
Robinson
Crusoe’s
Choice
Coconuts
Production function
C*
Labor
0
24
Leisure
L*
24
0
Labor (hours)
Leisure (hours)
16
Robinson
Crusoe’s
Choice
Coconuts
Production function
C*
Output
Labor
0
24
Leisure
L*
24
0
Labor (hours)
Leisure (hours)
17
Robinson
Crusoe’s
Choice
Coconuts
MRS = MPL
Production function
C*
Output
Labor
0
24
Leisure
L*
24
0
Labor (hours)
Leisure (hours)
18
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.

19
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 =  .

20
Isoprofit
Lines
Coconuts
Higher profit;  1   2
3
3
2
1
C    wL
Slopes = + w
0
24
Labor (hours)
21
Profit-Maximization
Coconuts
Production function
Feasible production
plans
0
24
Labor (hours)
22
Profit-Maximization
Coconuts
Production function
0
24
Labor (hours)
23
Profit-Maximization
Coconuts
Production function
0
24
Labor (hours)
24
Profit-Maximization
Coconuts
Production function
C*
0
L*
24
Labor (hours)
25
Profit-Maximization
Isoprofit slope = production function slope
Coconuts
i.e. w = MPL
Production function
C*
0
L*
24
Labor (hours)
26
Profit-Maximization
Isoprofit slope = production function slope
Coconuts
i.e. w = MPL = 1 MPL = MRPL.
Production function
C*
0
L*
24
Labor (hours)
27
Profit-Maximization
Isoprofit slope = production function slope
Coconuts
i.e. w = MPL = 1 MPL = MRPL.
Production function
C*
*
0
RC gets
L*
24
Labor (hours)
 *  C *  wL *
28
Profit-Maximization
Isoprofit slope = production function slope
Coconuts
i.e. w = MPL = 1 MPL = MRPL.
Production function
C*
*
Given w, RC’s firm’s quantity
demanded of labor is L*
Labor
demand
0
RC gets
L*
24
Labor (hours)
 *  C *  wL *
29
Profit-Maximization
Isoprofit slope = production function slope
Coconuts
i.e. w = MPL = 1 MPL = MRPL.
Production function
C*
*
Given w, RC’s firm’s quantity
demanded of labor is L* and
output quantity supplied is C*.
Labor Output
demand supply
0
RC gets
L*
24
Labor (hours)
 *  C *  wL *
30
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

C   *  wL.
31
Utility-Maximization
Coconuts
Budget constraint; slope = w
C   *  wL.
*
0
24
Labor (hours)
32
Utility-Maximization
Coconuts
More preferred
0
24
Labor (hours)
33
Utility-Maximization
Coconuts
Budget constraint; slope = w
C   *  wL.
*
0
24
Labor (hours)
34
Utility-Maximization
Coconuts
Budget constraint; slope = w
C   *  wL.
*
0
24
Labor (hours)
35
Utility-Maximization
Coconuts
Budget constraint; slope = w
C   *  wL.
C*
*
0
L*
24
Labor (hours)
36
Utility-Maximization
Coconuts
MRS = w
Budget constraint; slope = w
C   *  wL.
C*
*
0
L*
24
Labor (hours)
37
Utility-Maximization
Coconuts
MRS = w
Budget constraint; slope = w
C   *  wL.
C*
*
Given w, RC’s quantity
supplied of labor is L*
Labor
supply
0
L*
24
Labor (hours)
38
Utility-Maximization
Coconuts
MRS = w
Budget constraint; slope = w
C   *  wL.
C*
*
Labor Output
supply demand
0
L*
Given w, RC’s quantity
supplied of labor is L* and
output quantity demanded is C*.
24
Labor (hours)
39
Utility-Maximization & ProfitMaximization

Profit-maximization:
w
= MPL
 quantity of output supplied = C*
 quantity of labor demanded = L*
40
Utility-Maximization & ProfitMaximization

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*
41
Utility-Maximization & ProfitMaximization

Profit-maximization:
w
Coconut and labor
markets both clear.
= 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*
42
Utility-Maximization & ProfitMaximization
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*
*
0
L*
24
Labor (hours)
43
Pareto Efficiency

Must have MRS = MPL.
44
Pareto
Efficiency
Coconuts
MRS  MPL
0
24
Labor (hours)
45
Pareto
Efficiency
Coconuts
MRS  MPL
Preferred consumption
bundles.
0
24
Labor (hours)
46
Pareto
Efficiency
Coconuts
MRS = MPL
0
24
Labor (hours)
47
Pareto
Efficiency
Coconuts
MRS = MPL. The common slope  relative
wage rate w that implements
the Pareto efficient plan by
decentralized pricing.
0
24
Labor (hours)
48
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.
49
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.
50
Non-Convex Technologies

Do the Welfare Theorems hold if firms have
non-convex technologies?
51
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.

52
Non-Convex
Technologies
Coconuts
MRS = MPL The common slope  relative
wage rate w that
implements the Pareto
efficient plan by
decentralized pricing.
0
24
Labor (hours)
53
Non-Convex Technologies
Do the Welfare Theorems hold if firms have
non-convex technologies?
 The 2nd Theorem does require that firms’
technologies be convex.

54
Non-Convex
Technologies
Coconuts
MRS = MPL. The Pareto optimal allocation
cannot be implemented by
a competitive equilibrium.
0
24
Labor (hours)
55
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.

56
Production
Possibilities
Coconuts
Production possibility frontier (ppf)
Fish
57
Production
Possibilities
Coconuts
Production possibility frontier (ppf)
Production possibility set
Fish
58
Production
Possibilities
Coconuts
Feasible but
inefficient
Fish
59
Production
Possibilities
Coconuts
Feasible and efficient
Feasible but
inefficient
Fish
60
Production
Possibilities
Coconuts
Feasible and efficient
Infeasible
Feasible but
inefficient
Fish
61
Production
Possibilities
Coconuts
Ppf’s slope is the marginal rate
of product transformation.
Fish
62
Production
Possibilities
Coconuts
Ppf’s slope is the marginal rate
of transformation.
Increasingly negative MRT
 increasing opportunity
cost to specialization.
Fish
63
Production Possibilities
If there are no production externalities then a
ppf will be concave w.r.t. the origin.
 Why?

64
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.

65
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.

66
Comparative Advantage
C
RC
C
30
MF
20
50
25
F
F
67
Comparative Advantage
C
MRT = -2/3 coconuts/fish so opp. cost of one
more fish is 2/3 foregone coconuts.
20
50
RC
C
30
MF
25
F
F
68
Comparative Advantage
C
MRT = -2/3 coconuts/fish so opp. cost of one
more fish is 2/3 foregone coconuts.
20
50
RC
C
30
MF
F
MRT = -2 coconuts/fish so opp. cost of one
more fish is 2 foregone coconuts.
25
F
69
Comparative Advantage
C
MRT = -2/3 coconuts/fish so opp. cost of one
more fish is 2/3 foregone coconuts.
20
50
RC
C
30
MF
F
RC has the comparative
opp. cost advantage in
producing fish.
MRT = -2 coconuts/fish so opp. cost of one
more fish is 2 foregone coconuts.
25
F
70
Comparative Advantage
C
MRT = -2/3 coconuts/fish so opp. cost of one
more coconut is 3/2 foregone fish.
20
50
RC
C
30
MF
25
F
F
71
Comparative Advantage
C
MRT = -2/3 coconuts/fish so opp. cost of one
more coconut is 3/2 foregone fish.
20
50
RC
C
30
MF
F
MRT = -2 coconuts/fish so opp. cost of one
more coconut is 1/2 foregone fish.
25
F
72
Comparative Advantage
C
MRT = -2/3 coconuts/fish so opp. cost of one
more coconut is 3/2 foregone fish.
20
50
RC
C
30
MF
F
MRT = -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
73
Comparative Advantage
C
RC
Economy
C
20
70
50
C
30
MF
25
F
F
Use RC to produce
fish before using MF.
Use MF to
produce
coconuts before
using RC.
50
30
55
F
74
Comparative Advantage
C
RC
Economy
C
20
70
50
C
30
MF
25
F
F
Using low opp. cost
producers first results
in a ppf that is concave
w.r.t the origin.
50
30
55
F
75
Comparative Advantage
Economy
C
More producers with
different opp. costs
“smooth out” the ppf.
F
76
Coordinating Production &
Consumption
The ppf contains many technically efficient
output bundles.
 Which are Pareto efficient for consumers?

77
Coordinating Production &
Consumption
Coconuts
Output bundle is ( F  , C  )
and is the aggregate
endowment for distribution
to consumers RC and MF.
C
F
Fish
78
Coordinating Production &
Consumption
Coconuts
C
ORC
OMF
F
Output bundle is ( F  , C  )
and is the aggregate
endowment for distribution
to consumers RC and MF.
Fish
79
Coordinating Production &
Consumption
Coconuts
C
FMF

CRC

ORC
OMF
Allocate ( F  , C  ) efficiently;
say( FRC
 , CRC
 )to RC and
( FMF
 , CMF
 ) to MF.
CMF

FRC

F
Fish
80
Coordinating Production &
Consumption
Coconuts
C
FMF

CRC

ORC
OMF
CMF

FRC

F
Fish
81
Coordinating Production &
Consumption
Coconuts
C
FMF

CRC

ORC
OMF
CMF

FRC

F
Fish
82
Coordinating Production &
Consumption
Coconuts
C
FMF

CRC

ORC
OMF
MRS  MRT
CMF

FRC

F
Fish
83
Coordinating Production &
Consumption
Coconuts
C
FMF

OMF
( F  , C  ).
O’MF
C 
CRC

ORC
Instead produce
CMF

FRC

F
F 
Fish
84
Coordinating Production &
Consumption
Coconuts
C
FMF

OMF
FMF

C 
CRC

Instead produce
( F  , C  ).
Give MF same allocation
O’MF
as before.
CMF

CMF

ORC
FRC

F
F 
Fish
85
Coordinating Production &
Consumption
Coconuts
C
FMF

OMF
FMF

C 
CRC

CMF

Instead produce
( F  , C  ).
Give MF same allocation
O’MF
as before. MF’s
utility is
unchanged.
CMF

ORC
FRC

F
F 
Fish
86
Coordinating Production &
Consumption
Coconuts
OMF
C 
FMF

Instead produce
( F  , C  ).
Give MF same allocation
O’MF
as before. MF’s
utility is
unchanged
CMF

ORC
F 
Fish
87
Coordinating Production &
Consumption
Coconuts
OMF
C 
FMF

CRC

ORC
Instead produce
( F  , C  ).
Give MF same allocation
O’MF
as before. MF’s
utility is
unchanged
CMF

FRC

F 
Fish
88
Coordinating Production &
Consumption
Coconuts
OMF
C 
FMF

CRC

ORC
FRC

Instead produce
( F  , C  ).
Give MF same allocation
O’MF
as before. MF’s
utility is
unchanged, RC’s
utility is higher
CMF

F 
Fish
89
Coordinating Production &
Consumption
Coconuts
OMF
C 
FMF

CRC

ORC
FRC

Instead produce
( F  , C  ).
Give MF same allocation
O’MF
as before. MF’s
utility is
unchanged, RC’s
utility is higher;
CMF

Pareto
improvement.
F 
Fish
90
Coordinating Production &
Consumption
MRS  MRT  inefficient coordination of
production and consumption.
 Hence, MRS = MRT is necessary for a Pareto
optimal economic state.

91
Coordinating Production &
Consumption
Coconuts
C
FMF
OMF
CRC
ORC
CMF
FRC
F
Fish
92
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.

93
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
max   pC C  pF F  wRC LRC  wMF LMF .

94
Decentralized Coordination of
Production & Consumption
max   pC C  pF F  wRC LRC  wMF LMF .
Isoprofit line equation is
constant   pC C  pF F  wRC LRC  wMF LMF
95
Decentralized Coordination of
Production & Consumption
max   pC C  pF F  wRC LRC  wMF LMF .
Isoprofit line equation is
constant   pC C  pF F  wRC LRC  wMF LMF
which rearranges to
  w RC LRC  w MF LMF pF
C

F.
pC
pC
96
Decentralized Coordination of
Production & Consumption
max   pC C  pF F  wRC LRC  wMF LMF .
Isoprofit line equation is
constant   pC C  pF F  wRC LRC  wMF LMF
which rearranges to
  wRC LRC  wMF LMF pF
C
 F.
pC
pC
 
intercept
slope
97
Decentralized Coordination of
Production
&
Consumption
Coconuts
Higher profit
Slopes =
pF

pC
Fish
98
Decentralized Coordination of
Production
&
Consumption
Coconuts
The firm’s production
possibility set.
Fish
99
Decentralized Coordination of
Production
&
Consumption
Coconuts
Slopes =
pF

pC
Fish
100
Decentralized Coordination of
Production
&
Consumption
Coconuts
Profit-max. plan
Slopes =
pF

pC
Fish
101
Decentralized Coordination of
Production
&
Consumption
Coconuts
Profit-max. plan
Slope =
pF

pC
Fish
102
Decentralized Coordination of
Production
&
Consumption
Coconuts
Profit-max. plan
Competitive markets
and profit-maximization

pF
MRT  
pC
Slope =
pF

pC
.
Fish
103
Decentralized Coordination of
Production & Consumption

So competitive markets, profit-maximization,
and utility maximization all together cause
pF
MRT  
 MRS ,
pC
the condition necessary for a Pareto optimal
economic state.
104
Decentralized Coordination of
Production
&
Consumption
Coconuts
C
FMF
Competitive markets
and utility-maximization
OMF 
pF
MRS  
CRC
ORC
pC
CMF
FRC
F
Fish
105
.
Decentralized Coordination of
Production
&
Consumption
Coconuts
C
FMF
Competitive markets, utilitymaximization and profitmaximization 
OMF
CRC
ORC
pF
MRS    MRT .
pC
CMF
FRC
F
Fish
106