chapter 32 production. exchange economies (revisited) no production, only endowments, so no...

Chapter 32Production

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.

Now Add Production ... Add input markets, output markets,

describe firms’ technologies, the distributions of firms’ outputs and profits …

Now Add Production ... Add input markets, output markets,

describe firms’ technologies, the distributions of firms’ outputs and profits … That’s not easy!

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?

Robinson Crusoe’s Technology Technology: Labor produces output

(coconuts) according to a concave production function.

Robinson Crusoe’s Technology

Labor (hours)

Coconuts

Production function

Feasible productionplans

Robinson Crusoe’s Preferences RC’s preferences:

coconut is a good leisure is a good

Robinson Crusoe’s Preferences

Leisure (hours)

Coconuts

More preferred

Robinson Crusoe’s Preferences

Leisure (hours)

CoconutsMore preferred

Robinson Crusoe’s Choice

Labor (hours)

Coconuts

Production function

Labor (hours)

Coconuts

Production function

240Leisure (hours)24 0

Labor (hours)

Coconuts

Production function

Labor (hours)

Coconuts

Production function

Labor (hours)

Coconuts

Production function

L*Labor

Labor (hours)

Coconuts

Production function

L*Labor Leisure

Labor (hours)

Coconuts

Production function

L*Labor Leisure

Output

Labor (hours)

Coconuts

Production function

L*Labor Leisure

MRS = MPL

Output

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.

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 = .

Isoprofit Lines

Labor (hours)

Coconuts

C wL Higher profit; 1 2 3

Slopes = + w 3 21

Profit-Maximization

Labor (hours)

Coconuts

Production function

Profit-Maximization

Labor (hours)

Coconuts

Production function

Profit-Maximization

Labor (hours)

Coconuts

Production function

Profit-Maximization

Labor (hours)

Coconuts

Production function

Profit-Maximization

Labor (hours)

Coconuts

Production function

Isoprofit slope = production function slope i.e. w = MPL

Profit-Maximization

Labor (hours)

Coconuts

Production function

Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL.

Profit-Maximization

Labor (hours)

Coconuts

Production function

* * * C wLRC gets

Profit-Maximization

Labor (hours)

Coconuts

Production function

* * * C wL

* Given w, RC’s firm’s quantitydemanded of labor is L*Labor

demand

RC gets

Profit-Maximization

Labor (hours)

Coconuts

Production function

* Given w, RC’s firm’s quantitydemanded of labor is L* andoutput quantity supplied is C*.

Labordemand

Outputsupply

* * * C wLRC gets

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 * .

Utility-Maximization

Labor (hours)

Coconuts

C wL * .Budget constraint; slope = w

Labor (hours)

CoconutsMore preferred

Labor (hours)

Coconuts

C wL * .Budget constraint; slope = w

Labor (hours)

Coconuts

Budget constraint; slope = w

C wL * .

Labor (hours)

Coconuts

C wL * .C*

Budget constraint; slope = w

Labor (hours)

Coconuts

C wL * .C*

MRS = wBudget constraint; slope = w

Labor (hours)

Coconuts

C wL * .C*

Laborsupply

Budget constraint; slope = wMRS = w

Given w, RC’s quantitysupplied of labor is L*

Labor (hours)

Coconuts

C wL * .C*

Given w, RC’s quantitysupplied of labor is L* andoutput quantity demanded is C*.

Laborsupply

Outputdemand

Budget constraint; slope = wMRS = w

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.

Labor (hours)

Coconuts

MRS = w = MPL

Given w, RC’s quantitysupplied of labor = quantitydemanded of labor = L* andoutput quantity demanded =output quantity supplied = C*.

Pareto Efficiency Must have MRS = MPL.

Pareto Efficiency

Labor (hours)

Coconuts

MRS MPL

Pareto Efficiency

Labor (hours)

Coconuts

MRS MPL

Preferred consumptionbundles.

Pareto Efficiency

Labor (hours)

Coconuts

MRS = MPL

Pareto Efficiency

Labor (hours)

Coconuts

MRS = MPL. The common slope relative wage rate w that implements the Pareto efficient plan by decentralized pricing.

First Fundamental Theorem of Welfare Economics

A competitive market equilibrium is Pareto efficient ifconsumers’ preferences are convexthere are no externalities in

consumption or production.

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.

Non-Convex Technologies Do the Welfare Theorems hold if

firms have non-convex technologies?

firms have non-convex technologies? The 1st Theorem does not rely upon

firms’ technologies being convex.

Non-Convex Technologies

Labor (hours)

Coconuts

MRS = MPL The common slope relative wage rate w that implements the Pareto efficient plan by decentralized pricing.

firms have non-convex technologies? The 2nd Theorem does require that

firms’ technologies be convex.

Non-Convex Technologies

Labor (hours)

Coconuts

MRS = MPL. The Pareto optimal allocation cannot be implemented by a competitive equilibrium.

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.

Production Possibilities

CoconutsProduction possibility frontier (ppf)

Production possibility set

Coconuts

Feasible butinefficient

Coconuts

Feasible and efficient

Coconuts

Feasible and efficient

Infeasible

CoconutsPpf’s slope is the marginal rateof product transformation.

CoconutsPpf’s slope is the marginal rateof transformation.

Increasingly negative MRT increasing opportunitycost to specialization.

Production Possibilities If there are no production

externalities then a ppf will be concave w.r.t. the origin.

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.

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.

Comparative Advantage

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.

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.

CEconomy

Use RC to producefish before using MF.

Use MF toproducecoconuts before using RC.

CEconomy

Using low opp. costproducers first resultsin a ppf that is concave w.r.t the origin.

CEconomy

More producers withdifferent opp. costs“smooth out” the ppf.

Coordinating Production & Consumption The ppf contains many technically

efficient output bundles. Which are Pareto efficient for

consumers?

Coordinating Production & Consumption

Coconuts

Output bundle isand is the aggregateendowment for distribution to consumers RC and MF.

( , ) F C

Coconuts

Output bundle isand is the aggregateendowment for distribution to consumers RC and MF.

( , ) F C

Coconuts

Allocate efficiently;say to RC and to MF.

( , ) F C

CRC CMF

( , ) F CRC RC( , ) F CMF MF

Coconuts

CRC CMF

Coconuts

CRC CMF

Coconuts

CRC CMF

MRS MRT

Coconuts

CRC CMF

O’MFC

( , ). F CInstead produce

Coconuts

CRC CMF

( , ). F C

O’MF

Instead produceGive MF same allocation as before.FMF

Coconuts

CRC CMF

( , ). F C

O’MF

Instead produceGive MF same allocation as before. MF’s utility is unchanged.

Coconuts

( , ). F C

O’MFFMF

Instead produceGive MF same allocation as before. MF’s utility is unchanged

Coconuts

( , ). F C

O’MF

Instead produceGive MF same allocation as before. MF’s utility is unchanged

Coconuts

( , ). F C

O’MF

Instead produceGive MF same allocation as before. MF’s utility is unchanged, RC’s utility is higher

Coconuts

( , ). F C

O’MF

Instead produceGive MF same allocation as before. MF’s utility is unchanged, RC’s utility is higher; Pareto improvement.

Coordinating Production & Consumption MRS MRT inefficient coordination

of production and consumption. Hence, MRS = MRT is necessary for a

Pareto optimal economic state.

Coconuts

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.

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

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

FRC RC MF MFC

which rearranges to

slopeintercept

pLwLwC

MFMFRCRC

Decentralized Coordination of Production & Consumption

Coconuts Higher profit

Slopes = pp

Coconuts

The firm’s productionpossibility set.

Coconuts

Slopes = pp

Coconuts

Profit-max. plan

Slopes = pp

Coconuts

Profit-max. plan

Slope = pp

Coconuts

Profit-max. plan

Slope = pp

Competitive marketsand profit-maximization

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

Coconuts

Competitive marketsand utility-maximization

MRS pp

Coconuts

Competitive markets, utility-maximization and profit- maximization

.MRTppMRSC

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