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Production. Exchange Economies (revisited). No production, only endowments, so no description of how resources are converted to consumables. General equilibrium: all markets clear simultaneously. Now Add Production.

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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.
now add production
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, 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?
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

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 choice
Robinson Crusoe’s Choice

Coconuts

More preferred

Production function

Feasible productionplans

24

0

Labor (hours)

Leisure (hours)

24

0

robinson crusoe s choice1

=

Output

Labor

Leisure

Robinson Crusoe’s Choice

Coconuts

Production function

C*

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  …………………..…, the equation of an isoprofit line.
  • Slope = + w .
  • Intercept = .
isoprofit lines
Isoprofit Lines

Coconuts

Higher profit; ………………

Slopes = + w

24

0

Labor (hours)

profit maximization

Isoprofit slope = production function slope

i.e. w = ………………………………….

Output

supply

Given w, RC’s firm’s quantity

demanded of labor is L* and

output quantity supplied is C*.

Labor

demand

RC as a firm gets

Profit-Maximization

Coconuts

Production function

C*

L*

24

0

Labor (hours)

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;

slope = w

Intercept =

24

0

Labor (hours)

utility maximization2
Utility-Maximization

Coconuts

More preferred

24

0

Labor (hours)

utility maximization3

MRS = w

Output

demand

Given w, RC’s quantity

supplied of labor is L* and

output quantity demanded is C*.

Labor

supply

Utility-Maximization

Coconuts

Budget constraint; slope = w

C*

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:
    • w = MRS
    • quantity of output demanded = C*
    • quantity of labor supplied = L*

Coconut and labor

markets both clear.

slide20

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

Coconuts

……………

……………………

24

0

Labor (hours)

  • MRS  MPL, not Pareto efficient
pareto efficiency1
Pareto Efficiency
  • To achieve Pareto Efficiency

must have MRS = MPL.

pareto efficiency2
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)

  • MRS = MPL, ………………………..
first fundamental theorem of welfare economics
First Fundamental Theorem of Welfare Economics
  • A competitive market equilibrium is Pareto efficient if
    • consumers’ preferences are ………..
    • there are …………………….…. 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 ……………….
    • firms’ technologies are ……………….
    • there are ………………………. in consumption or production.
non convex technologies
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 technologies1
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 technologies2
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 technologies3
Non-Convex Technologies

Coconuts

MRS = MPL. The Pareto optimal allocation……… 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 ……………………...
  • The set’s outer boundary is the …………… ………...
production possibilities1
Production Possibilities

Coconuts

Production possibility frontier (PPF)

Production possibility set

Fish

production possibilities2
Production Possibilities

Coconuts

…………………

Infeasible

Feasible but

inefficient

Fish

production possibilities3
Production Possibilities

Coconuts

PPF’s slope is the ………………

………………………………………

Increasingly negative MRPT

 increasing opportunity

cost to specialization.

Fish

production possibilities4
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

C

RC

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

more fish is …… 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 …… foregone coconuts.

25

F

comparative advantage1
Comparative Advantage

C

RC

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

more coconut is …… foregone fish.

20

30

F

C

MF

50

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

more coconut is …… foregone fish.

MF has the comparative

opp. cost advantage in

producing coconuts.

25

F

comparative advantage2
Comparative Advantage

C

RC

Economy

C

20

Use ….. to produce

fish before using ……

70

30

F

C

MF

50

Use ….. to

produce

coconuts before

using …..

50

30

55

F

25

F

comparative advantage3
Comparative Advantage

Economy

C

Using low opp. cost

producers first results

in a ppf that is concave

w.r.t the origin.

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?
slide40

Coordinating Production & Consumption

Coconuts

Output bundle is

and is the aggregate

endowment for distribution

to consumers RC and MF.

Fish

slide41

Allocate efficiently;

say to RC and

to MF.

Coordinating Production & Consumption

Coconuts

OMF

Contract Curve

ORC

Fish

slide42

Coordinating Production & Consumption

Coconuts

However,

………………….

OMF

RC’s indifferent curve

MF’s indifferent curve

ORC

Fish

slide43

O'MF

Coordinating Production & Consumption

Coconuts

If instead produce

and give MF same allocation as before. → MF’s utility is ………………..

OMF

ORC

Fish

slide44

Coordinating Production & Consumption

Coconuts

MF’s utility is unchanged,

But RC’s utility is ……..…. ;

Pareto improvement

OMF

O’MF

ORC

Fish

slide45

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
  • 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
decentralized coordination of production consumption1
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 consumption2
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

Equation for Isoprofit line is

which rearranges to

decentralized coordination of production consumption4

Slopes =

Decentralized Coordination of Production & Consumption

Coconuts

Higher profit

The firm’s production

possibility set.

Fish

decentralized coordination of production consumption5

Slope =

Decentralized Coordination of Production & Consumption

Coconuts

Profit-max. plan

Competitive markets

and profit-maximization

Fish

decentralized coordination of production consumption6
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 consumption7
Decentralized Coordination of Production & Consumption

Coconuts

Competitive markets

and utility-maximization

OMF

ORC

Fish

decentralized coordination of production consumption8
Decentralized Coordination of Production & Consumption

Coconuts

Competitive markets, utility-

maximization and profit-

maximization 

OMF

ORC

Fish