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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.

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exchange economies revisited
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
Now Add Production ...
  • Add input markets, output markets, describe firms’ technologies, the distributions of firms’ outputs and profits …
now add production1
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
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
Robinson Crusoe’s Technology
  • Technology: Labor produces output (coconuts) according to a concave production function.
robinson crusoe s technology1
Robinson Crusoe’s Technology

Coconuts

Production function

24

0

Labor (hours)

robinson crusoe s technology2
Robinson Crusoe’s Technology

Coconuts

Production function

Feasible productionplans

24

0

Labor (hours)

robinson crusoe s preferences
Robinson Crusoe’s Preferences
  • RC’s preferences:
    • coconut is a good
    • leisure is a good
robinson crusoe s preferences1
Robinson Crusoe’s Preferences

Coconuts

More preferred

24

0

Leisure (hours)

robinson crusoe s preferences2
Robinson Crusoe’s Preferences

Coconuts

More preferred

24

0

Leisure (hours)

robinson crusoe s choice
Robinson Crusoe’s Choice

Coconuts

Production function

Feasible productionplans

24

0

Labor (hours)

robinson crusoe s choice1
Robinson Crusoe’s Choice

Coconuts

Production function

Feasible productionplans

24

0

Labor (hours)

Leisure (hours)

24

0

robinson crusoe s choice2
Robinson Crusoe’s Choice

Coconuts

Production function

Feasible productionplans

24

0

Labor (hours)

Leisure (hours)

24

0

robinson crusoe s choice3
Robinson Crusoe’s Choice

Coconuts

Production function

Feasible productionplans

24

0

Labor (hours)

Leisure (hours)

24

0

robinson crusoe s choice4
Robinson Crusoe’s Choice

Coconuts

Production function

C*

L*

24

0

Labor (hours)

Leisure (hours)

24

0

robinson crusoe s choice5
Robinson Crusoe’s Choice

Coconuts

Production function

C*

Labor

L*

24

0

Labor (hours)

Leisure (hours)

24

0

robinson crusoe s choice6
Robinson Crusoe’s Choice

Coconuts

Production function

C*

Labor

Leisure

L*

24

0

Labor (hours)

Leisure (hours)

24

0

robinson crusoe s choice7
Robinson Crusoe’s Choice

Coconuts

Production function

C*

Output

Labor

Leisure

L*

24

0

Labor (hours)

Leisure (hours)

24

0

robinson crusoe s choice8
Robinson Crusoe’s Choice

Coconuts

MRS = MPL

Production function

C*

Output

Labor

Leisure

L*

24

0

Labor (hours)

Leisure (hours)

24

0

robinson crusoe as a firm
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 firm1
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
Isoprofit Lines

Coconuts

Higher profit;

Slopes = + w

24

0

Labor (hours)

profit maximization
Profit-Maximization

Coconuts

Production function

Feasible productionplans

24

0

Labor (hours)

profit maximization1
Profit-Maximization

Coconuts

Production function

24

0

Labor (hours)

profit maximization2
Profit-Maximization

Coconuts

Production function

24

0

Labor (hours)

profit maximization3
Profit-Maximization

Coconuts

Production function

C*

L*

24

0

Labor (hours)

profit maximization4
Profit-Maximization

Isoprofit slope = production function slope

Coconuts

Production function

C*

L*

24

0

Labor (hours)

profit maximization5
Profit-Maximization

Isoprofit slope = production function slope

i.e. w = MPL

Coconuts

Production function

C*

L*

24

0

Labor (hours)

profit maximization6
Profit-Maximization

Isoprofit slope = production function slope

i.e. w = MPL = 1 MPL = MRPL.

Coconuts

Production function

C*

L*

24

0

Labor (hours)

profit maximization7
Profit-Maximization

Isoprofit slope = production function slope

i.e. w = MPL = 1 MPL = MRPL.

Coconuts

Production function

C*

L*

24

0

Labor (hours)

RC gets

profit maximization8
Profit-Maximization

Isoprofit slope = production function slope

i.e. w = MPL = 1 MPL = MRPL.

Coconuts

Production function

C*

Given w, RC’s firm’s quantity

demanded of labor is L*

Labor

demand

L*

24

0

Labor (hours)

RC gets

profit maximization9
Profit-Maximization

Isoprofit slope = production function slope

i.e. w = MPL = 1 MPL = MRPL.

Coconuts

Production function

C*

Output

supply

Given w, RC’s firm’s quantity

demanded of labor is L* and

output quantity supplied is C*.

Labor

demand

L*

24

0

Labor (hours)

RC gets

utility maximization
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
utility maximization1
Utility-Maximization

Coconuts

Budget constraint

24

0

Labor (hours)

utility maximization2
Utility-Maximization

Coconuts

Budget constraint; slope = w

24

0

Labor (hours)

utility maximization3
Utility-Maximization

Coconuts

More preferred

24

0

Labor (hours)

utility maximization4
Utility-Maximization

Coconuts

Budget constraint; slope = w

24

0

Labor (hours)

utility maximization5
Utility-Maximization

Coconuts

Budget constraint; slope = w

24

0

Labor (hours)

utility maximization6
Utility-Maximization

Coconuts

Budget constraint; slope = w

C*

L*

24

0

Labor (hours)

utility maximization7
Utility-Maximization

Coconuts

MRS = w

Budget constraint; slope = w

C*

L*

24

0

Labor (hours)

utility maximization8
Utility-Maximization

Coconuts

MRS = w

Budget constraint; slope = w

C*

Given w, RC’s quantity

supplied of labor is L*

Labor

supply

L*

24

0

Labor (hours)

utility maximization9
Utility-Maximization

Coconuts

MRS = w

Budget constraint; slope = w

C*

Output

demand

Given w, RC’s quantity

supplied of labor is L* and

output quantity demanded is C*.

Labor

supply

L*

24

0

Labor (hours)

utility maximization profit maximization
Utility-Maximization & Profit-Maximization
  • Profit-maximization:
    • w = MPL
    • quantity of output supplied = C*
    • quantity of labor demanded = L*
utility maximization profit maximization1
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*
utility maximization profit maximization2
Utility-Maximization & Profit-Maximization

Coconut and labor

markets both clear.

  • 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*
utility maximization profit maximization3
Utility-Maximization & Profit-Maximization

Coconuts

MRS = w= MPL

Given w, RC’s quantity

supplied of labor = quantity

demanded of labor = L* and

output quantity demanded =

output quantity supplied = C*.

C*

L*

24

0

Labor (hours)

pareto efficiency
Pareto Efficiency
  • Must have MRS = MPL.
pareto efficiency1
Pareto Efficiency

Coconuts

MRS  MPL

24

0

Labor (hours)

pareto efficiency2
Pareto Efficiency

Coconuts

MRS  MPL

Preferred consumption

bundles.

24

0

Labor (hours)

pareto efficiency3
Pareto Efficiency

Coconuts

MRS = MPL

24

0

Labor (hours)

pareto efficiency4
Pareto Efficiency

Coconuts

MRS = MPL. The common slope  relative

wage rate w that implements the Pareto efficient plan by

decentralized pricing.

24

0

Labor (hours)

first fundamental theorem of welfare economics
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
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
Non-Convex Technologies
  • Do the Welfare Theorems hold if firms have non-convex technologies?
non convex technologies1
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.
non convex technologies2
Non-Convex Technologies

Coconuts

MRS = MPLThe common slope  relative

wage rate w that

implements the Pareto

efficient plan by

decentralized pricing.

24

0

Labor (hours)

non convex technologies3
Non-Convex Technologies
  • Do the Welfare Theorems hold if firms have non-convex technologies?
  • The 2nd Theorem does require that firms’ technologies be convex.
non convex technologies4
Non-Convex Technologies

Coconuts

MRS = MPL. The Pareto optimal allocationcannot be implemented by

a competitive equilibrium.

24

0

Labor (hours)

production possibilities
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 possibilities1
Production Possibilities

Coconuts

Production possibility frontier (ppf)

Fish

production possibilities2
Production Possibilities

Coconuts

Production possibility frontier (ppf)

Production possibility set

Fish

production possibilities3
Production Possibilities

Coconuts

Feasible but

inefficient

Fish

production possibilities4
Production Possibilities

Coconuts

Feasible and efficient

Feasible but

inefficient

Fish

production possibilities5
Production Possibilities

Coconuts

Feasible and efficient

Infeasible

Feasible but

inefficient

Fish

production possibilities6
Production Possibilities

Coconuts

Ppf’s slope is the marginal rate

of product transformation.

Fish

production possibilities7
Production Possibilities

Coconuts

Ppf’s slope is the marginal rate

of product transformation.

Increasingly negative MRPT

 increasing opportunity

cost to specialization.

Fish

production possibilities8
Production Possibilities
  • If there are no production externalities then a ppf will be concave w.r.t. the origin.
  • Why?
production possibilities9
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
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 advantage1
Comparative Advantage

C

RC

20

30

F

C

MF

50

25

F

comparative advantage2
Comparative Advantage

C

RC

MRPT = -2/3 coconuts/fish so opp. cost of one

more fish is 2/3 foregone coconuts.

20

30

F

C

MF

50

25

F

comparative advantage3
Comparative Advantage

C

RC

MRPT = -2/3 coconuts/fish so opp. cost of one

more fish is 2/3 foregone coconuts.

20

30

F

C

MF

50

MRPT = -2 coconuts/fish so opp. cost of one

more fish is 2 foregone coconuts.

25

F

comparative advantage4
Comparative Advantage

C

RC

MRPT = -2/3 coconuts/fish so opp. cost of one

more fish is 2/3 foregone coconuts.

20

RC has the comparative

opp. cost advantage in

producing fish.

30

F

C

MF

50

MRPT = -2 coconuts/fish so opp. cost of one

more fish is 2 foregone coconuts.

25

F

comparative advantage5
Comparative Advantage

C

RC

MRPT = -2/3 coconuts/fish so opp. cost of one

more coconut is 3/2 foregone fish.

20

30

F

C

MF

50

25

F

comparative advantage6
Comparative Advantage

C

RC

MRPT = -2/3 coconuts/fish so opp. cost of one

more coconut is 3/2 foregone fish.

20

30

F

C

MF

50

MRPT = -2 coconuts/fish so opp. cost of one

more coconut is 1/2 foregone fish.

25

F

comparative advantage7
Comparative Advantage

C

RC

MRPT = -2/3 coconuts/fish so opp. cost of one

more coconut is 3/2 foregone fish.

20

30

F

C

MF

50

MRPT = -2 coconuts/fish so opp. cost of one

more coconut is 1/2 foregone fish.

MF has the comparative

opp. cost advantage in

producing coconuts.

25

F

comparative advantage8
Comparative Advantage

C

RC

Economy

C

Use RC to produce

fish before using MF.

20

70

30

F

Use MF to

produce

coconuts before

using RC.

C

MF

50

50

30

55

F

25

F

comparative advantage9
Comparative Advantage

C

RC

Economy

C

Using low opp. cost

producers first results

in a ppf that is concave

w.r.t the origin.

20

70

30

F

C

MF

50

50

30

55

F

25

F

comparative advantage10
Comparative Advantage

Economy

C

More producers with

different opp. costs

“smooth out” the ppf.

F

coordinating production consumption
Coordinating Production & Consumption
  • The ppf contains many technically efficient output bundles.
  • Which are Pareto efficient for consumers?
coordinating production consumption1
Coordinating Production & Consumption

Coconuts

Output bundle is

Fish

coordinating production consumption2
Coordinating Production & Consumption

Coconuts

Output bundle is

and is the aggregate

endowment for distribution

to consumers RC and MF.

Fish

coordinating production consumption3
Coordinating Production & Consumption

Coconuts

Output bundle is

and is the aggregate

endowment for distribution

to consumers RC and MF.

OMF

ORC

Fish

coordinating production consumption4
Coordinating Production & Consumption

Coconuts

Allocate efficiently;

say to RC

OMF

ORC

Fish

coordinating production consumption5
Coordinating Production & Consumption

Coconuts

Allocate efficiently;

say to RC and

to MF.

OMF

ORC

Fish

coordinating production consumption9
Coordinating Production & Consumption

Coconuts

MRS  MRPT

OMF

ORC

Fish

coordinating production consumption10
Coordinating Production & Consumption

Coconuts

Instead produce

OMF

O’MF

ORC

Fish

coordinating production consumption11
Coordinating Production & Consumption

Coconuts

Instead produce

OMF

O’MF

ORC

Fish

coordinating production consumption12
Coordinating Production & Consumption

Coconuts

Instead produce

Give MF same allocation

as before.

OMF

O’MF

ORC

Fish

coordinating production consumption13
Coordinating Production & Consumption

Coconuts

Instead produce

Give MF same allocation

as before. MF’s

utility is

unchanged.

OMF

O’MF

ORC

Fish

coordinating production consumption14
Coordinating Production & Consumption

Coconuts

Instead produce

Give MF same allocation

as before. MF’s

utility is

unchanged

OMF

O’MF

ORC

Fish

coordinating production consumption15
Coordinating Production & Consumption

Coconuts

Instead produce

Give MF same allocation

as before. MF’s

utility is

unchanged

OMF

O’MF

ORC

Fish

coordinating production consumption16
Coordinating Production & Consumption

Coconuts

Instead produce

Give MF same allocation

as before. MF’s

utility is

unchanged, RC’s

utility is higher

OMF

O’MF

ORC

Fish

coordinating production consumption17
Coordinating Production & Consumption

Coconuts

Instead produce

Give MF same allocation

as before. MF’s

utility is

unchanged, RC’s

utility is higher;

Pareto

improvement.

OMF

O’MF

ORC

Fish

coordinating production consumption18
Coordinating Production & Consumption
  • MRS  MRPT  inefficient coordination of production and consumption.
  • Hence, MRS = MRPT is necessary for a Pareto optimal economic state.
decentralized coordination of production consumption
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 consumption1
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
decentralized coordination of production consumption3
Decentralized Coordination of Production & Consumption

Isoprofit line equation is

which rearranges to

decentralized coordination of production consumption4
Decentralized Coordination of Production & Consumption

Isoprofit line equation is

which rearranges to

decentralized coordination of production consumption6
Decentralized Coordination of Production & Consumption

Coconuts

The firm’s production

possibility set.

Fish

decentralized coordination of production consumption10

Slope =

Decentralized Coordination of Production & Consumption

Coconuts

Profit-max. plan

Competitive markets

and profit-maximization

Fish

decentralized coordination of production consumption11
Decentralized Coordination of Production & Consumption
  • So competitive markets, profit-maximization, and utility maximization all together causethe condition necessary for a Pareto optimal economic state.
decentralized coordination of production consumption12
Decentralized Coordination of Production & Consumption

Coconuts

Competitive markets

and utility-maximization

OMF

ORC

Fish

decentralized coordination of production consumption13
Decentralized Coordination of Production & Consumption

Coconuts

Competitive markets, utility-

maximization and profit-

maximization 

OMF

ORC

Fish