Production

1

Production

2

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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Labor (hours)

Coconuts

*

240

C wL * .Budget constraint;

slope = wIntercept = *

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Labor (hours)

Coconuts

More preferred

240

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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

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*.

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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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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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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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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Fish

Coconuts

Production possibility frontier (PPF)

Production possibility set

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Fish

Coconuts

Feasible butinefficient

…………………

Infeasible

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Fish

Coconuts

PPF’s slope is the ………………………………………………………

Increasingly negative MRPT increasing opportunitycost to specialization.

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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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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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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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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


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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


Contract Curve

42

Fish

Coconuts

ORC

OMFC

F

CRC CMF

FMF

FRC

However,

………………….


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


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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


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MRS MRPT inefficient coordination of production and consumption.

Hence, MRS = MRPT is necessary for a Pareto optimal economic state.


46

Fish

Coconuts

ORC

OMF

FRC

C

F

CRC

FMF

CMF


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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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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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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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Fish

Coconuts

Slopes = pp

F

C

Higher profit

The firm’s productionpossibility set.

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Fish

Coconuts

Profit-max. plan

Slope = pp

F

CCompetitive marketsand profit-maximization

MRPTpp

F

C .

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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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Fish

Coconuts

ORC

OMF

FRC

C

F

CRC

FMF

CMF

Competitive marketsand utility-maximization

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Fish

Coconuts

ORC

OMF

FRC

C

F

CRC

FMF

CMF

Competitive markets, utility-maximization and profit- maximization

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Production