ch30 production
TRANSCRIPT
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Chapter Thirty
Production
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Now Add Production ...
Add input markets, output markets,describe firms technologies, the
distributions of firms outputs andprofits
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Now Add Production ...
Add input markets, output markets,describe firms technologies, the
distributions of firms outputs andprofits Thats not easy!
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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?
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Robinson Crusoes Technology
Technology: Labor produces output(coconuts) according to a concaveproduction function.
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Robinson Crusoes Technology
Production function
Labor (hours)
Coconuts
240
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Robinson Crusoes Preferences
RCs preferences:
coconut is a good
leisure is a good
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Robinson Crusoes Choice
Labor (hours)
Coconuts
Feasible production
plans
Production function
240
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Robinson Crusoes Choice
Labor (hours)
Coconuts
Feasible production
plans
Production function
240
Leisure (hours)24 0
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Robinson Crusoes Choice
Labor (hours)
Coconuts
Feasible production
plans
Production function
240
Leisure (hours)24 0
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Robinson Crusoes Choice
Labor (hours)
Coconuts
Production function
240
Leisure (hours)24 0
C*
L*
Labor
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Robinson Crusoes Choice
Labor (hours)
Coconuts
Production function
240
Leisure (hours)24 0
C*
L*
Labor Leisure
MRS = MPL
Output
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Robinson Crusoe as a Firm
RCs firms profit is = C -wL .
= C -wL C = +wL , the
equation of an isoprofit line.Slope = + w .
Intercept = .
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Isoprofit Lines
Labor (hours)
Coconuts
24
C wL Higher profit; 1 2 3
Slopes = + w32
1
0
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Profit-Maximization
Labor (hours)
Coconuts
Feasible production
plans
Production function
240
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Profit-Maximization
Labor (hours)
Coconuts
Production function
240
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Profit-Maximization
Labor (hours)
Coconuts
Production function
240
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Profit-Maximization
Labor (hours)
Coconuts
Production function
24
C*
L*0
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Profit-Maximization
Labor (hours)
Coconuts
Production function
24
C*
L*
Isoprofit slope = production function slope
0
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Profit-Maximization
Labor (hours)
Coconuts
Production function
24
C*
L*
Isoprofit slope = production function slope
i.e. w= MPL
0
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Profit-Maximization
Labor (hours)
Coconuts
Production function
24
C*
L*
Isoprofit slope = production function slope
i.e. w= MPL= 1MPL=MRPL.
0
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Profit-Maximization
Labor (hours)
Coconuts
Production function
24
C*
L*
Isoprofit slope = production function slope
i.e. w= MPL= 1MPL=MRPL.
*
* * * C wLRC gets
0
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Profit-Maximization
Labor (hours)
Coconuts
Production function
24
C*
L*
Isoprofit slope = production function slope
i.e. w= MPL= 1MPL=MRPL.
* * * C wL
* Given w, RCsfirms quantity
demanded of labor is L*Labor
demand
RC gets
0
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Profit-Maximization
Labor (hours)
Coconuts
Production function
24
C*
L*
Isoprofit slope = production function slope
i.e. w= MPL= 1MPL=MRPL.
* Given w, RCsfirms quantity
demanded of labor is L*and
output quantity supplied is C*.Labor
demand
Output
supply
* * * C wLRC gets
0
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Utility-Maximization
Now consider RC as a consumerendowed with $*who can work for$wper hour.
What is RCs most preferred
consumption bundle?
Budget constraint is C wL * .
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Utility-Maximization
Labor (hours)
Coconuts
*
240
C wL * .
Budget constraint
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Utility-Maximization
Labor (hours)
Coconuts
*
240
C wL * .
Budget constraint; slope = w
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Utility-Maximization
Labor (hours)
Coconuts
More preferred
240
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Utility-Maximization
Labor (hours)
Coconuts
*
240
C wL * .
Budget constraint; slope = w
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Utility-Maximization
Labor (hours)
Coconuts
*
Budget constraint; slope = w
240
C wL * .
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Utility-Maximization
Labor (hours)
Coconuts
*
240
C wL * .C*
L*
Budget constraint; slope = w
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Utility-Maximization
Labor (hours)
Coconuts
*
240
C wL * .C*
L*
Labor
supply
Budget constraint; slope = w
MRS = w
Given w, RCsquantity
supplied of labor is L*
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Utility-Maximization
Labor (hours)
Coconuts
*
240
C wL * .C*
L*
Given w, RCsquantity
supplied of labor is L*and
output quantity demanded is C*.Labor
supply
Output
demand
Budget constraint; slope = w
MRS = w
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Utilit M i i ti & P fit
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Utility-Maximization & Profit-
Maximization
Labor (hours)
Coconuts
24
C*
L*
*
0
MRS = w= MPL
Given w, RCsquantity
supplied of labor = quantity
demanded of labor = L*and
output quantity demanded =
output quantity supplied = C*.
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Pareto Efficiency
Must have MRS = MPL.
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Pareto Efficiency
Labor (hours)
Coconuts
240
MRS MPL
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Pareto Efficiency
Labor (hours)
Coconuts
240
MRS MPL
Preferred consumption
bundles.
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Pareto Efficiency
Labor (hours)
Coconuts
240
MRS = MPL
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Pareto Efficiency
Labor (hours)
Coconuts
240
MRS = MPL. The common sloperelativewage rate wthat implements
the Pareto efficient plan by
decentralized pricing.
Fi t F d t l Th f
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First Fundamental Theorem of
Welfare Economics
A competitive market equilibrium isPareto efficient if
consumers preferences are convex there are no externalities in
consumption or production.
S d F d t l Th f
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Second Fundamental Theorem of
Welfare Economics
Any Pareto efficient economic statecan be achieved as a competitivemarket equilibrium if
consumers preferences are convex
firms technologies are convex
there are no externalities inconsumption or production.
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Non-Convex Technologies
Do the Welfare Theorems hold iffirms have non-convextechnologies?
The 1st Theorem does not rely uponfirms technologies being convex.
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Non-Convex Technologies
Labor (hours)
Coconuts
240
MRS = MPL The common sloperelativewage rate wthat
implements the Pareto
efficient plan by
decentralized pricing.
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Non-Convex Technologies
Do the Welfare Theorems hold iffirms have non-convextechnologies?
The 2nd Theorem does require thatfirms technologies be convex.
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Non-Convex Technologies
Labor (hours)
Coconuts
240
MRS = MPL. The Pareto optimal allocation
cannot be implemented by
a competitive equilibrium.
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Production Possibilities
Resource and technologicallimitations restrict what an economycan produce.
The set of all feasible output bundlesis the economys productionpossibility set.
The sets outer boundary is the
production possibility frontier.
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Production Possibilities
Fish
Coconuts
Production possibility frontier (ppf)
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Production Possibilities
Fish
Coconuts
Production possibility frontier (ppf)
Production possibility set
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Production Possibilities
Fish
Coconuts
Feasible but
inefficient
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Production Possibilities
Fish
Coconuts
Feasible but
inefficient
Feasible and efficient
Infeasible
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Production Possibilities
Fish
Coconuts
Ppfs slope is the marginal rateof product transformation.
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Production Possibilities
Fish
Coconuts
Ppfs slope is the marginal rateof product transformation.
Increasingly negative MRPT
increasing opportunitycost to specialization.
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Production Possibilities
If there are no productionexternalities then a ppf will beconcave w.r.t. the origin.
Why?
Because efficient productionrequires exploitation of comparativeadvantages.
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Comparative Advantage
F
C
F
C
RC
MF
20
5030
25
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Comparative Advantage
F
C
F
C
RC
MF
20
50
30
25
MRPT = -2/3 coconuts/fish so opp. cost of onemore fish is 2/3 foregone coconuts.
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Comparative Advantage
F
C
F
C
RC
MF
20
50
30
25
MRPT = -2/3 coconuts/fish so opp. cost of onemore fish is 2/3 foregone coconuts.
MRPT = -2 coconuts/fish so opp. cost of onemore fish is 2 foregone coconuts.
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Comparative Advantage
F
C
F
C
RC
MF
20
50
30
25
MRPT = -2/3 coconuts/fish so opp. cost of onemore coconut is 3/2 foregone fish.
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Comparative Advantage
F
C
F
C
RC
MF
20
50
30
25
MRPT = -2/3 coconuts/fish so opp. cost of onemore coconut is 3/2 foregone fish.
MRPT = -2 coconuts/fish so opp. cost of onemore coconut is 1/2 foregone fish.
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Comparative Advantage
F
C
F
C
RC
MF
20
50
30
25
MRPT = -2/3 coconuts/fish so opp. cost of onemore coconut is 3/2 foregone fish.
MRPT = -2 coconuts/fish so opp. cost of onemore coconut is 1/2 foregone fish.
MF has the comparativeopp. cost advantage inproducing coconuts.
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Comparative Advantage
F
C
Economy
F
C
F
C
RC
MF
20
50
30
25
70
55
50
30
Use RC to producefish before using MF.
Use MF toproducecoconuts before
using RC.
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C i Ad
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Comparative Advantage
F
C
Economy
More producers withdifferent opp. costssmooth out the ppf.
Coordinating Production &
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Coordinating Production &
Consumption
The ppf contains many technicallyefficient output bundles.
Which are Pareto efficient forconsumers?
Coordinating Production &
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Coordinating Production &
Consumption
Fish
Coconuts
C
F
Output bundle is ( , )F C
Coordinating Production &
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Coordinating Production &
Consumption
Fish
Coconuts
C
F
Output bundle isand is the aggregateendowment for distribution
to consumers RC and MF.
( , )F C
Coordinating Production &
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Coordinating Production &
Consumption
Fish
Coconuts
ORC
OMFC
F
Output bundle isand is the aggregateendowment for distribution
to consumers RC and MF.
( , )F C
Coordinating Production &
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Coo d a g oduc o &
Consumption
Fish
Coconuts
ORC
OMFC
F
Allocate efficiently;say to RC
( , )F C
CRC
FRC
( , )F CRC RC
Coordinating Production &
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g
Consumption
Fish
Coconuts
ORC
OMFC
F
Allocate efficiently;say to RC and
to MF.
( , )F C
CRC CMF
FMF
FRC
( , )F CRC RC( , )F CMF MF
Coordinating Production &
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g
Consumption
Fish
Coconuts
ORC
OMFC
F
CRC CMF
FMF
FRC
Coordinating Production &
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g
Consumption
Fish
Coconuts
ORC
OMFC
F
CRC CMF
FMF
FRC
Coordinating Production &
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g
Consumption
Fish
Coconuts
ORC
OMFC
F
CRC CMF
FMF
FRC
Coordinating Production &
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g
Consumption
Fish
Coconuts
ORC
OMFC
F
CRC CMF
FMF
FRC
MRS MRPT
Coordinating Production &
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g
Consumption
Fish
Coconuts
ORC
OMFC
F
CRC CMF
FMF
FRC
OMFC
F
( , ). F CInstead produce
Coordinating Production &
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g
Consumption
Fish
Coconuts
ORC
OMFC
F
CRC CMF
FMF
FRC
OMFC
F
( , ). F CInstead produce
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Coordinating Production &
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g
Consumption
Fish
Coconuts
ORC
OMFC
F
CRC CMF
FMF
FRC
C
F
( , ). F COMF
CMF
Instead produceGive MF same allocation
as before. MFsutility is
unchanged.
FMF
Coordinating Production &
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g
Consumption
Fish
Coconuts
ORC
OMF
C
F
( , ). F COMFFMF
Instead produceGive MF same allocation
as before. MFsutility is
unchanged
CMF
Coordinating Production &
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g
Consumption
Fish
Coconuts
ORC
OMF
FRC
C
F
( , ). F COMF
CRC
FMF
CMF
Instead produceGive MF same allocation
as before. MFsutility is
unchanged
Coordinating Production &
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g
Consumption
Fish
Coconuts
ORC
OMF
FRC
C
F
( , ). F COMF
CRC
FMF
CMF
Instead produceGive MF same allocation
as before. MFsutility is
unchanged, RCsutility is higher
Coordinating Production &
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g
Consumption
Fish
Coconuts
ORC
OMF
FRC
C
F
( , ). F COMF
CRC
FMF
CMF
Instead produceGive MF same allocation
as before. MFsutility is
unchanged, RCsutility is higher;
Paretoimprovement.
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Coordinating Production &
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Consumption
Fish
Coconuts
ORC
OMF
FRC
C
F
CRC
FMF
CMF
Decentralized Coordination of
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Production & Consumption
RC and MF jointly run a firmproducing 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.
Decentralized Coordination of
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Production & Consumption
LRC, LMFare amounts of laborpurchased from RC and MF.
Firms profit-maximization problem ischoose C, F, LRCand LMFto
max . p C p F w L w LC F RC RC MF MF
Decentralized Coordination of
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Production & Consumption
max . p C p F w L w LC F RC RC MF MF Isoprofit line equation is
constant p C p F w L w LC F RC RC MF MF
Decentralized Coordination of
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Production & Consumption
max . p C p F w L w LC F RC RC MF MF Isoprofit line equation is
constant p C p F w L w LC F RC RC MF MF which rearranges to
C w L w L
p
p
p
FRC RC MF MF
C
F
C
.
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Decentralized Coordination of
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Production & Consumption
Fish
Coconuts
Slopes = pp
F
C
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Decentralized Coordination of
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Production & Consumption
Fish
Coconuts
Profit-max. plan
Slope = pp
F
C
Decentralized Coordination of
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Production & Consumption
Fish
Coconuts
Profit-max. plan
Slope = pp
F
CCompetitive marketsand profit-maximization
MRPT
p
p
F
C
.
Decentralized Coordination of
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Production & Consumption
So competitive markets, profit-maximization, and utilitymaximization all together cause
the condition necessary for a Paretooptimal economic state.
MRPT p
pMRSF
C
,
Decentralized Coordination of
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Production & Consumption
Fish
Coconuts
ORC
OMF
FRC
C
F
CRC
FMF
CMF
Competitive marketsand utility-maximization
MRS
p
p
F
C
.
Decentralized Coordination of
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Production & ConsumptionCoconuts
O
OMFC
CRC
FMF
CMF
Competitive markets, utility-maximization and profit-
maximization
MRS
p
p MRPTF
C
.