Chapter Thirty
description
Transcript of Chapter Thirty
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Chapter Thirty
Production
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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.
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Now Add Production ...
Add input markets, output markets, describe firms’ technologies, the distributions of firms’ outputs and profits …
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Now Add Production ...
Add input markets, output markets, describe firms’ technologies, the distributions of firms’ outputs and profits … That’s not easy!
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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?
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Robinson Crusoe’s Technology
Technology: Labor produces output (coconuts) according to a concave production function.
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Robinson Crusoe’s Technology
Production function
Labor (hours)
Coconuts
240
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Robinson Crusoe’s Technology
Labor (hours)
Coconuts
Production function
240
Feasible productionplans
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Robinson Crusoe’s Preferences
RC’s preferences:
– coconut is a good
– leisure is a good
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Robinson Crusoe’s Preferences
Leisure (hours)
Coconuts
More preferred
240
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Robinson Crusoe’s Preferences
Leisure (hours)
Coconuts
More preferred
24 0
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Robinson Crusoe’s Choice
Labor (hours)
Coconuts
Feasible productionplans
Production function
240
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Robinson Crusoe’s Choice
Labor (hours)
Coconuts
Feasible productionplans
Production function
240
Leisure (hours)24 0
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Robinson Crusoe’s Choice
Labor (hours)
Coconuts
Feasible productionplans
Production function
240
Leisure (hours)24 0
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Robinson Crusoe’s Choice
Labor (hours)
Coconuts
Feasible productionplans
Production function
240
Leisure (hours)24 0
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Robinson Crusoe’s Choice
Labor (hours)
Coconuts
Production function
240
Leisure (hours)24 0
C*
L*
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Robinson Crusoe’s Choice
Labor (hours)
Coconuts
Production function
240
Leisure (hours)24 0
C*
L*
Labor
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Robinson Crusoe’s Choice
Labor (hours)
Coconuts
Production function
240
Leisure (hours)24 0
C*
L*
Labor Leisure
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Robinson Crusoe’s Choice
Labor (hours)
Coconuts
Production function
240
Leisure (hours)24 0
C*
L*
Labor Leisure
Output
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Robinson Crusoe’s 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
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.
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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 = .
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Isoprofit Lines
Labor (hours)
Coconuts
24
C wL Higher profit; 1 2 3
Slopes = + w 3 21
0
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Profit-Maximization
Labor (hours)
Coconuts
Feasible productionplans
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 = 1 MPL = 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 = 1 MPL = 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 = 1 MPL = MRPL.
* * * C wL
* Given w, RC’s firm’s quantitydemanded 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 = 1 MPL = MRPL.
* Given w, RC’s firm’s quantitydemanded of labor is L* andoutput quantity supplied is C*.
Labordemand
Outputsupply
* * * C wLRC gets
0
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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 * .
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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*
MRS = wBudget constraint; slope = w
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Utility-Maximization
Labor (hours)
Coconuts
*
240
C wL * .C*
L*
Laborsupply
Budget constraint; slope = wMRS = w
Given w, RC’s quantitysupplied of labor is L*
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Utility-Maximization
Labor (hours)
Coconuts
*
240
C wL * .C*
L*
Given w, RC’s quantitysupplied of labor is L* andoutput quantity demanded is C*.
Laborsupply
Outputdemand
Budget constraint; slope = wMRS = w
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Utility-Maximization & Profit-Maximization
Profit-maximization:
– w = MPL
– quantity of output supplied = C*
– quantity of labor demanded = L*
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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*
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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 labormarkets both clear.
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Utility-Maximization & Profit-Maximization
Labor (hours)
Coconuts
24
C*
L*
*
0
MRS = w = MPL
Given w, RC’s quantitysupplied of labor = quantitydemanded of labor = L* andoutput 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 consumptionbundles.
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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 slope relative wage rate w that implements the Pareto efficient plan by decentralized pricing.
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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.
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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.
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Non-Convex Technologies
Do the Welfare Theorems hold if firms have non-convex technologies?
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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.
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Non-Convex Technologies
Labor (hours)
Coconuts
240
MRS = MPL The common slope relative wage rate w that implements the Pareto efficient plan by decentralized pricing.
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Non-Convex Technologies
Do the Welfare Theorems hold if firms have non-convex technologies?
The 2nd Theorem does require that firms’ 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 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.
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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 butinefficient
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Production Possibilities
Fish
Coconuts
Feasible butinefficient
Feasible and efficient
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Production Possibilities
Fish
Coconuts
Feasible butinefficient
Feasible and efficient
Infeasible
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Production Possibilities
Fish
Coconuts
Ppf’s slope is the marginal rateof product transformation.
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Production Possibilities
Fish
Coconuts
Ppf’s slope is the marginal rateof product transformation.
Increasingly negative MRPT increasing opportunitycost to specialization.
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Production Possibilities
If there are no production externalities then a ppf will be concave w.r.t. the origin.
Why?
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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.
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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.
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Comparative Advantage
F
C
F
C
RC
MF
20
50
30
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 fish is 2/3 foregone coconuts.
MRPT = -2 coconuts/fish so opp. cost of onemore fish is 2 foregone coconuts.
RC has the comparativeopp. cost advantage inproducing 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.
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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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Comparative Advantage
F
C
Economy
F
C
F
C
RC
MF
20
50
30
25
70
55
50
30
Using low opp. costproducers first resultsin a ppf that is concave w.r.t the origin.
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Comparative Advantage
F
C
Economy
More producers withdifferent opp. costs“smooth out” the ppf.
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Coordinating Production & Consumption
The ppf contains many technically efficient output bundles.
Which are Pareto efficient for consumers?
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Coordinating Production & Consumption
Fish
Coconuts
C
F
Output bundle is ( , ) F C
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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
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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
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Coordinating Production & Consumption
Fish
Coconuts
ORC
OMFC
F
Allocate efficiently;say to RC
( , ) F C
CRC
FRC
( , ) F CRC RC
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Coordinating Production & 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
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Coordinating Production & Consumption
Fish
Coconuts
ORC
OMFC
F
CRC CMF
FMF
FRC
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Coordinating Production & Consumption
Fish
Coconuts
ORC
OMFC
F
CRC CMF
FMF
FRC
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Coordinating Production & Consumption
Fish
Coconuts
ORC
OMFC
F
CRC CMF
FMF
FRC
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Coordinating Production & Consumption
Fish
Coconuts
ORC
OMFC
F
CRC CMF
FMF
FRC
MRS MRPT
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Coordinating Production & Consumption
Fish
Coconuts
ORC
OMFC
F
CRC CMF
FMF
FRC
O’MFC
F
( , ). F CInstead produce
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Coordinating Production & Consumption
Fish
Coconuts
ORC
OMFC
F
CRC CMF
FMF
FRC
O’MFC
F
( , ). F CInstead produce
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Coordinating Production & Consumption
Fish
Coconuts
ORC
OMFC
F
CRC CMF
FMF
FRC
C
F
( , ). F C
O’MF
CMF
Instead produceGive MF same allocation as before.FMF
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Coordinating Production & Consumption
Fish
Coconuts
ORC
OMFC
F
CRC CMF
FMF
FRC
C
F
( , ). F C
O’MF
CMF
Instead produceGive MF same allocation as before. MF’s utility is unchanged.
FMF
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Coordinating Production & Consumption
Fish
Coconuts
ORC
OMF
C
F
( , ). F C
O’MFFMF
Instead produceGive MF same allocation as before. MF’s utility is unchanged
CMF
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Coordinating Production & Consumption
Fish
Coconuts
ORC
OMF
FRC
C
F
( , ). F C
O’MF
CRC
FMF
CMF
Instead produceGive MF same allocation as before. MF’s utility is unchanged
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Coordinating Production & Consumption
Fish
Coconuts
ORC
OMF
FRC
C
F
( , ). F C
O’MF
CRC
FMF
CMF
Instead produceGive MF same allocation as before. MF’s utility is unchanged, RC’s utility is higher
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Coordinating Production & Consumption
Fish
Coconuts
ORC
OMF
FRC
C
F
( , ). F C
O’MF
CRC
FMF
CMF
Instead produceGive MF same allocation as before. MF’s utility is unchanged, RC’s utility is higher; Pareto improvement.
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Coordinating Production & Consumption
MRS MRPT inefficient coordination of production and consumption.
Hence, MRS = MRPT is necessary for a Pareto optimal economic state.
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Coordinating Production & Consumption
Fish
Coconuts
ORC
OMF
FRC
C
F
CRC
FMF
CMF
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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.
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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 . p C p F w L w LC F RC RC MF MF
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Decentralized Coordination of Production & Consumption
max . p C p F w L w LC F RC RC MF MFIsoprofit line equation is
constant p C p F w L w LC F RC RC MF MF
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Decentralized Coordination of Production & Consumption
max . p C p F w L w LC F RC RC MF MFIsoprofit line equation is
constant p C p F w L w LC F RC RC MF MFwhich rearranges to
Cw L w L
ppp
FRC RC MF MF
C
F
C
.
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Decentralized Coordination of Production & Consumption
max . p C p F w L w LC F RC RC MF MFIsoprofit line equation is
constant p C p F w L w LC F RC RC MF MFwhich rearranges to
Cw L w L
ppp
FRC RC MF MF
C
F
C
intercept slope 2
.
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Decentralized Coordination of Production & Consumption
Fish
CoconutsHigher profit
Slopes = pp
F
C
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Decentralized Coordination of Production & Consumption
Fish
Coconuts
The firm’s productionpossibility set.
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Decentralized Coordination of Production & Consumption
Fish
Coconuts
Slopes = pp
F
C
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Decentralized Coordination of Production & Consumption
Fish
Coconuts
Profit-max. plan
Slopes = pp
F
C
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Decentralized Coordination of Production & Consumption
Fish
Coconuts
Profit-max. plan
Slope = pp
F
C
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Decentralized Coordination of Production & Consumption
Fish
Coconuts
Profit-max. plan
Slope = pp
F
CCompetitive marketsand profit-maximization
MRPTpp
F
C .
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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.
MRPTpp
MRSF
C ,
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Decentralized Coordination of Production & Consumption
Fish
Coconuts
ORC
OMF
FRC
C
F
CRC
FMF
CMF
Competitive marketsand utility-maximization
MRSpp
F
C .
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Decentralized Coordination of Production & Consumption
Fish
Coconuts
ORC
OMF
FRC
C
F
CRC
FMF
CMF
Competitive markets, utility-maximization and profit- maximization
MRSpp
MRPTF
C .