Ch30 Production

8/13/2019 Ch30 Production

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Chapter Thirty

Production


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Now Add Production ...

Add input markets, output markets,describe firms technologies, the

distributions of firms outputs andprofits


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Now Add Production ...

Add input markets, output markets,describe firms technologies, the

distributions of firms outputs andprofits Thats not easy!


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Robinson Crusoes 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?


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Robinson Crusoes Technology

Technology: Labor produces output(coconuts) according to a concaveproduction function.


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Robinson Crusoes Technology

Production function

Labor (hours)

Coconuts

240


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Robinson Crusoes Preferences

RCs preferences:

coconut is a good

leisure is a good


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Robinson Crusoes Choice

Labor (hours)

Coconuts

Feasible production

plans

Production function

240


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Labor (hours)

Coconuts

Feasible production

plans

Production function

240

Leisure (hours)24 0


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Labor (hours)

Coconuts

Feasible production

plans

Production function

240

Leisure (hours)24 0


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Labor (hours)

Coconuts

Production function

240

Leisure (hours)24 0

C*

L*

Labor


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Labor (hours)

Coconuts

Production function

240

Leisure (hours)24 0

C*

L*

Labor Leisure

MRS = MPL

Output


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Robinson Crusoe as a Firm

RCs firms profit is = C -wL .

= 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; 1 2 3

Slopes = + w32

1

0


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Profit-Maximization

Labor (hours)

Coconuts

Feasible production

plans

Production function

240


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Profit-Maximization

Labor (hours)

Coconuts

Production function

240


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Profit-Maximization

Labor (hours)

Coconuts

Production function

240


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Profit-Maximization

Labor (hours)

Coconuts

Production function

24

C*

L*0


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Profit-Maximization

Labor (hours)

Coconuts

Production function

24

C*

L*

Isoprofit slope = production function slope

0


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Profit-Maximization

Labor (hours)

Coconuts

Production function

24

C*

L*


i.e. w= MPL

0


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Profit-Maximization

Labor (hours)

Coconuts

Production function

24

C*

L*


i.e. w= MPL= 1MPL=MRPL.

0


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Profit-Maximization

Labor (hours)

Coconuts

Production function

24

C*

L*



*

* * * C wLRC gets

0


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Profit-Maximization

Labor (hours)

Coconuts

Production function

24

C*

L*



* * * C wL

* Given w, RCsfirms quantity

demanded of labor is L*Labor

demand

RC gets

0


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Profit-Maximization

Labor (hours)

Coconuts

Production function

24

C*

L*



* Given w, RCsfirms quantity

demanded of labor is L*and

output quantity supplied is C*.Labor

demand

Output

supply

* * * C wLRC gets

0


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Utility-Maximization

Now consider RC as a consumerendowed with $*who can work for$wper hour.

What is RCs most preferred

consumption bundle?

Budget constraint is C wL * .


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Labor (hours)

Coconuts

*

240

C wL * .

Budget constraint


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Labor (hours)

Coconuts

*

240

C wL * .

Budget constraint; slope = w


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Labor (hours)

Coconuts

More preferred

240


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Labor (hours)

Coconuts

*

240

C wL * .



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Labor (hours)

Coconuts

*


240

C wL * .


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Labor (hours)

Coconuts

*

240

C wL * .C*

L*



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Labor (hours)

Coconuts

*

240

C wL * .C*

L*

Labor

supply


MRS = w

Given w, RCsquantity

supplied of labor is L*


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Labor (hours)

Coconuts

*

240

C wL * .C*

L*


supplied of labor is L*and

output quantity demanded is C*.Labor

supply

Output

demand


MRS = w


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Utilit M i i ti & P fit


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Utility-Maximization & Profit-

Maximization

Labor (hours)

Coconuts

24

C*

L*

*

0

MRS = w= MPL


supplied of labor = quantity

demanded of labor = L*and

output quantity demanded =

output quantity supplied = C*.


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Pareto Efficiency

Must have MRS = MPL.


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Pareto Efficiency

Labor (hours)

Coconuts

240

MRS MPL


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Pareto Efficiency

Labor (hours)

Coconuts

240

MRS MPL

Preferred consumption

bundles.


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Pareto Efficiency

Labor (hours)

Coconuts

240

MRS = MPL


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Pareto Efficiency

Labor (hours)

Coconuts

240

MRS = MPL. The common sloperelativewage rate wthat implements

the Pareto efficient plan by

decentralized pricing.

Fi t F d t l Th f


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First Fundamental Theorem of

Welfare Economics

A competitive market equilibrium isPareto efficient if

consumers preferences are convex there are no externalities in

consumption or production.

S d F d t l Th f


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Second Fundamental Theorem of

Welfare Economics

Any Pareto efficient economic statecan be achieved as a competitivemarket equilibrium if

consumers preferences are convex

firms technologies are convex

there are no externalities inconsumption or production.


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Non-Convex Technologies

Do the Welfare Theorems hold iffirms have non-convextechnologies?

The 1st Theorem does not rely uponfirms technologies being convex.


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Labor (hours)

Coconuts

240

MRS = MPL The common sloperelativewage rate wthat

implements the Pareto

efficient plan by

decentralized pricing.


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Do the Welfare Theorems hold iffirms have non-convextechnologies?

The 2nd Theorem does require thatfirms technologies be convex.


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Labor (hours)

Coconuts

240

MRS = MPL. The Pareto optimal allocation

cannot be implemented by

a competitive equilibrium.


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Production Possibilities

Resource and technologicallimitations restrict what an economycan produce.

The set of all feasible output bundlesis the economys productionpossibility set.

The sets outer boundary is the

production possibility frontier.


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Fish

Coconuts

Production possibility frontier (ppf)


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Fish

Coconuts

Production possibility frontier (ppf)

Production possibility set


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Fish

Coconuts

Feasible but

inefficient


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Fish

Coconuts

Feasible but

inefficient

Feasible and efficient

Infeasible


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Fish

Coconuts

Ppfs slope is the marginal rateof product transformation.


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Fish

Coconuts

Ppfs slope is the marginal rateof product transformation.

Increasingly negative MRPT

increasing opportunitycost to specialization.


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If there are no productionexternalities then a ppf will beconcave w.r.t. the origin.

Why?

Because efficient productionrequires exploitation of comparativeadvantages.


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Comparative Advantage

F

C

F

C

RC

MF

20

5030

25


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F

C

F

C

RC

MF

20

50

30

25

MRPT = -2/3 coconuts/fish so opp. cost of onemore fish is 2/3 foregone coconuts.


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F

C

F

C

RC

MF

20

50

30

25

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.


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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 3/2 foregone fish.


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F

C

F

C

RC

MF

20

50

30

25


MRPT = -2 coconuts/fish so opp. cost of onemore coconut is 1/2 foregone fish.


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F

C

F

C

RC

MF

20

50

30

25


MRPT = -2 coconuts/fish so opp. cost of onemore coconut is 1/2 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 RC to producefish before using MF.

Use MF toproducecoconuts before

using RC.


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C i Ad


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F

C

Economy

More producers withdifferent opp. costssmooth out the ppf.

Coordinating Production &


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Consumption

The ppf contains many technicallyefficient output bundles.

Which are Pareto efficient forconsumers?



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Consumption

Fish

Coconuts

C

F

Output bundle is ( , )F C



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Consumption

Fish

Coconuts

C

F

Output bundle isand is the aggregateendowment for distribution

to consumers RC and MF.

( , )F C



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Consumption

Fish

Coconuts

ORC

OMFC

F

Output bundle isand is the aggregateendowment for distribution

to consumers RC and MF.

( , )F C



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Coo d a g oduc o &

Consumption

Fish

Coconuts

ORC

OMFC

F

Allocate efficiently;say to RC

( , )F C

CRC

FRC

( , )F CRC RC



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g

Consumption

Fish

Coconuts

ORC

OMFC

F

Allocate efficiently;say to RC and

to MF.

( , )F C

CRC CMF

FMF

FRC

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



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g

Consumption

Fish

Coconuts

ORC

OMFC

F

CRC CMF

FMF

FRC



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g

Consumption

Fish

Coconuts

ORC

OMFC

F

CRC CMF

FMF

FRC



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g

Consumption

Fish

Coconuts

ORC

OMFC

F

CRC CMF

FMF

FRC



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g

Consumption

Fish

Coconuts

ORC

OMFC

F

CRC CMF

FMF

FRC

MRS MRPT



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g

Consumption

Fish

Coconuts

ORC

OMFC

F

CRC CMF

FMF

FRC

OMFC

F

( , ). F CInstead produce



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g

Consumption

Fish

Coconuts

ORC

OMFC

F

CRC CMF

FMF

FRC

OMFC

F

( , ). F CInstead produce


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g

Consumption

Fish

Coconuts

ORC

OMFC

F

CRC CMF

FMF

FRC

C

F

( , ). F COMF

CMF

Instead produceGive MF same allocation

as before. MFsutility is

unchanged.

FMF



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g

Consumption

Fish

Coconuts

ORC

OMF

C

F

( , ). F COMFFMF



unchanged

CMF



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g

Consumption

Fish

Coconuts

ORC

OMF

FRC

C

F

( , ). F COMF

CRC

FMF

CMF



unchanged



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g

Consumption

Fish

Coconuts

ORC

OMF

FRC

C

F

( , ). F COMF

CRC

FMF

CMF



unchanged, RCsutility is higher



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g

Consumption

Fish

Coconuts

ORC

OMF

FRC

C

F

( , ). F COMF

CRC

FMF

CMF



unchanged, RCsutility is higher;

Paretoimprovement.


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Consumption

Fish

Coconuts

ORC

OMF

FRC

C

F

CRC

FMF

CMF

Decentralized Coordination of


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Production & Consumption

RC and MF jointly run a firmproducing coconuts and fish.

RC and MF are also consumers who

can sell labor.Price of coconut = pC.

Price of fish = pF.

RCs wage rate = wRC.

MFs wage rate = wMF.



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LRC, LMFare amounts of laborpurchased from RC and MF.

Firms profit-maximization problem ischoose C, F, LRCand LMFto

max . p C p F w L w LC F RC RC MF MF



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max . p C p F w L w LC F RC RC MF MF Isoprofit line equation is

constant p C p F w L w LC F RC RC MF MF



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max . p C p F w L w LC F RC RC MF MF Isoprofit line equation is

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

C w L w L

p

p

p

FRC RC MF MF

C

F

C

.


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Fish

Coconuts

Slopes = pp

F

C


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Fish

Coconuts

Profit-max. plan

Slope = pp

F

C



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Fish

Coconuts

Profit-max. plan

Slope = pp

F

CCompetitive marketsand profit-maximization

MRPT

p

p

F

C

.



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So competitive markets, profit-maximization, and utilitymaximization all together cause

the condition necessary for a Paretooptimal economic state.

MRPT p

pMRSF

C

,



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Fish

Coconuts

ORC

OMF

FRC

C

F

CRC

FMF

CMF

Competitive marketsand utility-maximization

MRS

p

p

F

C

.



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Production & ConsumptionCoconuts

O

OMFC

CRC

FMF

CMF

Competitive markets, utility-maximization and profit-

maximization

MRS

p

p MRPTF

C

.

Documents

Ch30 Production