Chapter 32 Production. Exchange Economies (revisited) No production, only endowments, so no...
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Transcript of Chapter 32 Production. Exchange Economies (revisited) No production, only endowments, so no...
![Page 1: Chapter 32 Production. Exchange Economies (revisited) No production, only endowments, so no description of how resources are converted to consumables.](https://reader035.fdocuments.us/reader035/viewer/2022062401/5a4d1b507f8b9ab0599a76b2/html5/thumbnails/1.jpg)
Chapter 32Production
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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
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)
CoconutsMore 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
240Leisure (hours)24 0
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Robinson Crusoe’s Choice
Labor (hours)
Coconuts
Feasible productionplans
Production function
240Leisure (hours)24 0
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Robinson Crusoe’s Choice
Labor (hours)
Coconuts
Production function
240Leisure (hours)24 0
C*
L*
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Robinson Crusoe’s Choice
Labor (hours)
Coconuts
Production function
240Leisure (hours)24 0
C*
L*Labor
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Robinson Crusoe’s Choice
Labor (hours)
Coconuts
Production function
240Leisure (hours)24 0
C*
L*Labor Leisure
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Robinson Crusoe’s Choice
Labor (hours)
Coconuts
Production function
240Leisure (hours)24 0
C*
L*Labor Leisure
Output
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Robinson Crusoe’s Choice
Labor (hours)
Coconuts
Production function
240Leisure (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
24
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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 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; slope = w
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Utility-Maximization
Labor (hours)
CoconutsMore 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 = MRSquantity 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 = MRSquantity 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 ifconsumers’ preferences are convexthere 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 ifconsumers’ preferences are convexfirms’ technologies are convexthere 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
CoconutsProduction possibility frontier (ppf)
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Production Possibilities
Fish
CoconutsProduction 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
CoconutsPpf’s slope is the marginal rateof product transformation.
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Production Possibilities
Fish
CoconutsPpf’s slope is the marginal rateof transformation.
Increasingly negative MRT 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
5030
25 67
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Comparative Advantage
F
C
F
C
RC
MF
20
5030
25
MRT = -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
5030
25
MRT = -2/3 coconuts/fish so opp. cost of onemore fish is 2/3 foregone coconuts.
MRT = -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
5030
25
MRT = -2/3 coconuts/fish so opp. cost of onemore fish is 2/3 foregone coconuts.
MRT = -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
5030
25
MRT = -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
5030
25
MRT = -2/3 coconuts/fish so opp. cost of onemore coconut is 3/2 foregone fish.
MRT = -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
5030
25
MRT = -2/3 coconuts/fish so opp. cost of onemore coconut is 3/2 foregone fish.
MRT = -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
CEconomy
F
C
F
C
RC
MF
20
5030
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
CEconomy
F
C
F
C
RC
MF
20
5030
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
CEconomy
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 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 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
MRS MRT
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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 MRT inefficient coordination
of production and consumption. Hence, MRS = MRT 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 tomax . p C p F w L w LC F RC RC MF MF
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Decentralized Coordination of Production & Consumptionmax . p C p F w L w LC F RC RC MF MF
Isoprofit line equation isconstant p C p F w L w LC F RC RC MF MF
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Decentralized Coordination of Production & Consumptionmax . p C p F w L w LC F RC RC MF MF
Isoprofit line equation isconstant p C p F w L w LC F RC RC MF MF
which rearranges to
C w L w Lp
pp
FRC RC MF MFC
FC
.
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Decentralized Coordination of Production & Consumptionmax . p C p F w L w LC F RC RC MF MF
Isoprofit line equation isconstant p C p F w L w LC F RC RC MF MF
which rearranges to
.
slopeintercept
Fpp
pLwLwC
C
F
C
MFMFRCRC
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Decentralized Coordination of Production & Consumption
Fish
Coconuts Higher profit
Slopes = pp
FC
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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
FC
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Decentralized Coordination of Production & Consumption
Fish
Coconuts
Profit-max. plan
Slopes = pp
FC
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Decentralized Coordination of Production & Consumption
Fish
Coconuts
Profit-max. plan
Slope = pp
FC
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Decentralized Coordination of Production & Consumption
Fish
Coconuts
Profit-max. plan
Slope = pp
FC
Competitive marketsand profit-maximization
.C
F
ppMRT
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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.
,MRSppMRTC
F
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Decentralized Coordination of Production & Consumption
Fish
Coconuts
ORC
OMF
FRC
C
F
CRC
FMF
CMF
Competitive marketsand utility-maximization
MRS pp
FC
.
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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
.MRTppMRSC
F
106