Production
description
Transcript of Production
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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.
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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, Robinson Crusoe (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 Choice
Labor (hours)
Coconuts
Feasible productionplans
Production function
240
Leisure (hours)24 0
More preferred
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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 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 …………………..…, the equation of
an isoprofit line. Slope = + w . Intercept = .
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Isoprofit Lines
Labor (hours)
Coconuts
24
C wL Higher profit; ………………
Slopes = + w 3 21
0
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Profit-Maximization
Labor (hours)
Coconuts
Production function
24
C*
L*
Isoprofit slope = production function slope i.e. w = ………………………………….
*
* * * C wLRC as a firm gets
0
Given w, RC’s firm’s quantitydemanded of labor is L* andoutput quantity supplied is C*.Labor
demand
Outputsupply
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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 = wIntercept = *
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Utility-Maximization
Labor (hours)
Coconuts
More preferred
240
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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*.Labor
supply
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*
Utility-maximization: w = MRSquantity of output demanded = C*quantity of labor supplied = L*
Coconut and labormarkets both clear.
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Labor (hours)
Coconuts
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C*
L*
*
0
MRS = w = MPL
Given w, RC’s quantitysupplied of labor = quantitydemanded of labor = L* andoutput quantity demanded =output quantity supplied = C*.
Utility-Maximization & Profit-Maximization
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Pareto Efficiency
Labor (hours)
Coconuts
240
……………
……………………
MRS MPL, not Pareto efficient
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Pareto Efficiency
To achieve Pareto Efficiency
must have 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.
MRS = MPL, ………………………..
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First Fundamental Theorem of Welfare Economics
A competitive market equilibrium is Pareto efficient ifconsumers’ preferences are ………..
there are …………………….…. 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 ……………….
firms’ technologies are ……………….
there are ………………………. in consumption or production.
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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 ……… 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 ……………………...
The set’s outer boundary is the …………… ………...
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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
…………………
Infeasible
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Production Possibilities
Fish
Coconuts
PPF’s slope is the ………………………………………………………
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? Because efficient production requires
exploitation of comparative advantages.
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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 …… foregone coconuts.
MRPT = -2 coconuts/fish so opp. cost of onemore fish is …… 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 …… foregone fish.
MRPT = -2 coconuts/fish so opp. cost of onemore coconut is …… 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 ….. to producefish before using ……
Use ….. toproducecoconuts before using …..
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Comparative Advantage
F
C
Economy
More producers withdifferent opp. costs“smooth out” the ppf.
Using low opp. costproducers first resultsin a ppf that is concave w.r.t the origin.
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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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Fish
Coconuts
C
F
Output bundle is and is the aggregateendowment for distribution to consumers RC and MF.
( , ) F C
Coordinating Production & Consumption
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Fish
Coconuts
ORC
OMFC
F
CRC CMF
FMF
FRC
Allocate efficiently;say to RC and to MF.
( , ) F C( , ) F CRC RC
( , ) F CMF MF
Coordinating Production & Consumption
Contract Curve
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Fish
Coconuts
ORC
OMFC
F
CRC CMF
FMF
FRC
However,
………………….
Coordinating Production & Consumption
RC’s indifferent curve
MF’s indifferent curve
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Fish
Coconuts
ORC
OMFC
F
CRC CMF
FMF
FRC
C
F
( , ). F C
O'MF
If instead produce and give MF same
allocation as before. → MF’s utility is ………………..
CMF
FMF
Coordinating Production & Consumption
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Fish
Coconuts
ORC
OMF
FRC
C
F
O’MF
CRC
FMF
CMF
MF’s utility is unchanged, But RC’s utility is ……..…. ; Pareto improvement
Coordinating Production & Consumption
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MRS MRPT inefficient coordination of production and consumption.
Hence, MRS = MRPT is necessary for a Pareto optimal economic state.
Coordinating Production & Consumption
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Fish
Coconuts
ORC
OMF
FRC
C
F
CRC
FMF
CMF
Coordinating Production & Consumption
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Decentralized Coordination of Production & Consumption The above Pareto optimal production and
consumption can be achieved by decentralized behaviours of firms and consumers
Competitive markets, profit-maximization, and utility maximization all together can result in a Pareto optimal economic state
MRPTpp
MRSF
C ,
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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
Equation for Isoprofit line is
constant p C p F w L w LC F RC RC MF MF
which rearranges to
Cw L w L
ppp
FRC RC MF MF
C
F
C
.
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Decentralized Coordination of Production & Consumption
Fish
Coconuts
Slopes = pp
F
C
Higher profit
The firm’s productionpossibility set.
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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
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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