Chapter Thirty-Two Production. Exchange Economies (revisited) No production, only endowments, so no...

Chapter Thirty-Two

Production

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.

Production function

Labor (hours)

Coconuts

Labor (hours)

Coconuts

Production function

Feasible productionplans

Robinson Crusoe’s Preferences

RC’s preferences: coconut is a good leisure is a good

Leisure (hours)

Coconuts

More preferred

Leisure (hours)

Coconuts

More preferred

Robinson Crusoe’s Choice

Labor (hours)

Coconuts

Production function

Labor (hours)

Coconuts

Production function

Leisure (hours)24 0

Labor (hours)

Coconuts

Production function

Leisure (hours)24 0

Labor (hours)

Coconuts

Production function

Leisure (hours)24 0

Labor (hours)

Coconuts

Production function

Leisure (hours)24 0

Labor (hours)

Coconuts

Production function

Leisure (hours)24 0

Labor (hours)

Coconuts

Production function

Leisure (hours)24 0

Labor Leisure

Labor (hours)

Coconuts

Production function

Leisure (hours)24 0

Labor Leisure

Output

Labor (hours)

Coconuts

Production function

Leisure (hours)24 0

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

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 isC wL * .

Labor (hours)

Coconuts

C wL * .Budget constraint

Labor (hours)

Coconuts

C wL * .Budget constraint; slope = w

Labor (hours)

Coconuts

More 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 = MRS quantity 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 if consumers’ preferences are convex there 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 if consumers’ preferences are convex firms’ technologies are convex there are no externalities in

consumption or production.

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.

Labor (hours)

Coconuts

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

The 2nd Theorem does require that firms’ technologies be convex.

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.

Coconuts

Production possibility frontier (ppf)

Coconuts

Production possibility frontier (ppf)

Production possibility set

Coconuts

Feasible butinefficient

Coconuts

Feasible and efficient

Coconuts

Feasible and efficient

Infeasible

Coconuts

Ppf’s slope is the marginal rateof product transformation.

Coconuts

Ppf’s slope is the marginal rateof product transformation.

Increasingly negative MRPT increasing opportunitycost to specialization.

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.

Imagine an economic system with only two goods, potatoes and meat and only two people, a potato farmer and a cattle rancher

What should each person produce?

Why should these people trade?

A PARABLE FOR THE MODERN ECONOMY

Suppose the farmer and rancher decide not to engage in trade: Each consumes only what he or she can

produce alone. The production possibilities frontier is

also the consumption possibilities frontier.

Without trade, economic gains are diminished.

Figure 1 The Production Possibilities Frontier

Potatoes (ounces)

Meat (ounces)

(a) The Farmer’ s Production Possibilities Frontier

If there is no trade, the farmer chooses this production and consumption.

Figure 1 The Production Possibilities Curve

Potatoes (ounces)

Meat (ounces)

(b) The Rancher ’s Production Possibilities Frontier

If there is no trade, the rancher chooses this production and consumption.

Production and Consumption Without

The farmer should produce potatoes.

The rancher should produce meat.

Specialization and Trade

Suppose instead the farmer and the rancher decide to specialize and trade… Both would be better off if they

specialize in producing the product they are more suited to produce, and then trade with each other.

Figure 2 How Trade Expands the Set of

Consumption Opportunities

Potatoes (ounces)

Meat (ounces)

(a) The Farmer’ s Production and Consumption

Farmer's production and consumption without trade

Farmer's consumption with trade

Farmer's production with trade

Figure 2 How Trade Expands the Set of

Consumption Opportunities

Potatoes (ounces)

Meat (ounces)

(b) The Rancher’s Production and Consumption

Rancher's consumption with trade

Rancher's production with trade

Rancher's production and consumption without trade

COMPARATIVE ADVANTAGE

Differences in the costs of production determine the following: Who should produce what? How much should be traded for each

product?

COMPARATIVE ADVANTAGE

Two ways to measure differences in costs of production: The number of hours required to

produce a unit of output (for example, one pound of potatoes).

The opportunity cost of sacrificing one good for another.

Comparative Advantage and Trade

Potato costs… The Rancher’s opportunity cost of an ounce

of potatoes is 1/2 an ounce of meat. The Farmer’s opportunity cost of an ounce

of potatoes is1/4 an ounce of meat. Meat costs…

The Rancher’s opportunity cost of a pound of meat is only 2 ounces of potatoes.

The Farmer’s opportunity cost of an ounce of meat is only 4 ounces of potatoes...

…so, the Rancher has a comparative advantage in the

production of meat but the Farmer has a comparative

advantage in the production of potatoes.

Comparative advantage and differences in opportunity costs are the basis for specialized production and trade.

Whenever potential trading parties have differences in opportunity costs, they can each benefit from trade.

Gains from Trade

Benefits of Trade

Trade can benefit everyone in a society because it allows people to specialize in activities in which they have a comparative advantage.

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.

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.

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.

Economy

Use RC to producefish before using MF.

Use MF toproducecoconuts before using RC.

Economy

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

Economy

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?

Coconuts

Output bundle is ( , ) F C

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

( , ) F C

( , ) F CRC RC

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

Coconuts

CRC CMF

MRS MRPT

Coconuts

CRC CMF

O’MFC

( , ). F CInstead produce

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.

MRS MRPT inefficient coordination of production and consumption.

Hence, MRS = MRPT 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.

& 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

& Consumptionmax . 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

constant p C p F w L w LC F RC RC MF MFwhich rearranges to

Cw L w L

FRC RC MF MF

constant p C p F w L w LC F RC RC MF MFwhich rearranges to

Cw L w L

FRC RC MF MF

intercept slope 2

& Consumption

CoconutsHigher profit

Slopes = pp

& Consumption

Coconuts

The firm’s productionpossibility set.

& Consumption

Coconuts

Slopes = pp

& Consumption

Coconuts

Profit-max. plan

Slopes = pp

& Consumption

Coconuts

Profit-max. plan

Slope = pp

& Consumption

Coconuts

Profit-max. plan

Slope = pp

CCompetitive marketsand profit-maximization

MRPTpp

& Consumption So competitive markets, profit-

maximization, and utility maximization all together cause

the condition necessary for a Pareto optimal economic state.

MRPTpp

& Consumption

Coconuts

Competitive marketsand utility-maximization

& Consumption

Coconuts

Competitive markets, utility-maximization and profit- maximization

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