Classical Vs Keynenesian System

8/7/2019 Classical Vs Keynenesian System

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TheClassicalModel

Chapter7

Lecturenotespostedonline

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TheClassicalModel

Modelofoutputdeterminationandeconomy

wideequilibrium

Canbeusedtostudyeconomicgrowthand

businesscycles

Consideredamorecompletedescriptionofthe

longrunthantheshortrun

3

KeyBuildingBlocks

Closedeconomy(noexportsandimports)

Populatedbytwotypesofagents

Households

Firms

(Laterwillalsoaddgovernment)

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KeyBuildingBlocks

Agentsinteractinthree markets

GoodsMarket(GM)

LoanableFundsMarket(LFM)

LaborMarket(LM)

Marketsarecompetitive

LikeinEcon101,demandandsupply

determinetheequilibriumoutcome

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Labor Market

Goods market

Loanable Funds

MarketHouseholds Firms

AgentsandMarketsinClassicalModel

laborlabor

goods

funds for

investmentsavings

goods

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Markets

Goodsmarket iswherefirmsselltheiroutputto

households(consumptiongoods)andotherfirms

(investmentgoods)

Loanablefundsmarket iswherehouseholdsavefundsforinterest,andfirmsseekfundstofinance

investmentprojects

Labormarket iswherehouseholdsofferlabor,

andfirmshirethemtoproducegoods


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Households

Recipientsofallfactorpaymentsbyfirms=

income

Maketwo importantdecisions:

Givenincome,decidehowmuchtosaveSand

consumeC

Giventimeendowment,decidehowmuch

labortosupplytothemarket,andhowmuch

leisuretoconsume

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Firms

Produceoutputusingcapital(machines)and

labor(people)

Maketwoimportantdecisions:

Howmuchlabortoemploy

Howmuchtoinvestinnewmachines,thatwill

resultinmorecapitalinthefuture

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Savings/ConsumptionDecisionofHH

Willassumehouseholdsdecidetosavea

constantfractionoftheirincome: S=sY

Impliesconsumptionisalsoaconstantfraction

ofincome:C=YS=(1s)Y

Example:s=1/3,ifincomeis150,S=50,

consumptionisC=YS=(11/3)150=100

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ImpliedSupplyofSavings

Supplyofsavingsbyhouseholdsasfunctionof

interestrate(returnonsavings)

Interest

rate

Savings

sY

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Labor/LeisureChoiceofHH

Assumehouseholdssupply1unitoflaboreach,

andsosupplyoflaborsimplyequalspopulation

size=L

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SupplyofLabor

Supplyoflaborbyhouseholdsasafunctionof

realwage(realcompensationoflabor)

Real

wage

Labor

L


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ProductioninFirms

Produceoutputusingcapital(machines)Kandlabor(people)L

Productionsummarizedisbyaproductionfunction

Example:

Assumedpropertiesoftheproductionfunction:

Outputincreasinginlaborandcapital

Diminishingreturnsfromlaborandcapital

Returnstoscaleareconstant

Y = KL

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PropertiesofProductionFunction

Increasinginlaborandcapital

Addlabororcapital outputwillincrease

Diminishingreturnsfromlaborandcapital

Addlaborwhilekeepingcapitalfixed outputincreases,butincrementssmallerandsmallerasyoukeepaddingmoreandmorelabor

Returnstoscaleareconstant productionprocessisreplicable doublelaborandcapital,andoutputwillexactlydouble

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DiminishingReturnsFromLabor

Fix capital: K=10 (for example)

Labor L

Output

Same change

in labor

Big

Tiny

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DiminishingReturnsFromCapital

Fix labor: L=10 (for example)

Capital K

Output

Same change

in capital

Big

Tiny

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DemandforLabor

Diminishingreturnsfromlabor demandfor

labordecreasingfunctionofrealwage

GivenafixedlevelofcapitalK,each

incrementalworker

adds

less

and

less to

production

Costofhiringaworkerincreases firmsare

willingtohirefewerworkers

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DemandforLabor

Demandforlabor(forafixedlevelofcapitalK)

Real wage

(W/P)

Labor

(people)

Labor

demand


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DemandforLabor

IncreaseincapitalKshiftslabordemand

Real wage

(W/P)

Labor

(people)

Labor

demand

More

capital

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DemandforInvestment(Funds)

Diminishingreturnsfromcapital demandfor

investmentdecreasingfunctionofinterestrate

GivenafixedleveloflaborL,eachincremental

unitofcapitaladdslessandlesstoproduction

Costoffundsincreases firmswantto

investless

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Demandforfunds(forafixedleveloflabor)

Interest Rate

Number of

Machines

Demand for

more

machines

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Increaseinlaborforce(here=population)shifts

demandforinvestment

Interest Rate

Number of

machines

Demand for

more

machines

Population

growth

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Recap

Sofar,determineddemandandsupplyin

Labormarket

Loanablefundsmarket

Now,needtoanswerwhatwillbetheoutcomeintheentireeconomy

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WhatisGoingtoHappen?

Equilibriumofasystemisastateofthesystemin

whichtherearenointernalforcesinthesystem

toproduceachange

This is notan equil ibrium This is an equil ibrium


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WhatisGoingtoHappen?

Equilibriuminthismodeliswhenallmarkets

clear

Demandforlabor=supplyoflabor

Demandforinvestment=supplyoffunds

Alloutputgetssold,i.e.plannedconsumption

andplannedinvestmentequalsoutput(C+I=Y)

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EquilibriumEmploymentL

LabormarketequilibriumdeterminesL

Real wage

(W/P)

Labor

(people)

Labor supply = L

Labor demand

L

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EquilibriumOutputY

YdeterminedbyL(capitalKpredetermined)

Output

Labor

(people)

Labor supply = L

Labor demand

Production function (at fixed level of K)

Real wage

(W/P)

Labor

(people)

Y

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Equilibrium(Planned)InvestmentI

LoanablefundsmarketdeterminesinvestmentI

Interest Rate

Investment

sY

Demand for

investment I

I=sY

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SaysLaw:SpendingPurchasesOutput

Intheclassicalmodel,alloutputgetssold

automatically,andsoC+I=Y

Wedonotneedtoworryaboutthegoods

market Followsfromasimpleaccountingidentity

impliedbythecircularflows

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CircularFlowsintheClassicalModel

Labor Market

Households Firms

Consumption+Investment

Expenditures

Goods market

GoodsCo

nsump

tionEx

penditu

res

Goods

Loanable Funds

Market

Savings SSupply

of Funds

Investment I

Investment

Projects

Demand

for Funds

Incom

elabo

rIncome

labor


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SaysLaw:Outflows=Inflows

Labor Market

Households Firms

Consumption+Investment

Expenditures

Goods market

GoodsCo

nsump

tionExpen

ditures

Good

s

Loanable Funds

Market

Savings SSupply

of Funds

Investment I

Investment

Projects

Demand

for Funds

Incom

elabo

rIncome

labor YY=C+S

S

CC+I=C+S=Y

I=S

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SaysLaw:Outflows=Inflows

Yflowsfromfirmstohouseholds(bydefinition

Y=C+S)

Ontheexpenditureside

Sflowsout

Iflowsin

Sinceinequilibriumintheloanablefunds

marketS=I,outflows=inflows,andsoC+I=Y

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TodaysKpredetermined,butfutureKevolves

withinvestment

Capitaltomorrow=capitaltoday

depreciationofcapital+investment

Where isdepreciationrateofcapital(fraction

ofcapitalwornoutinproduction)

WhatHappenstoCapitalK?

(1 )tomorrow today

K K I= +

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WhatHappenstoCapitalK?

Ourequilibriumisastaticequilibrium

Givencapital,wepindowninvestment,

employmentandoutput

Itraisesquestionswheretheeconomyisheading

inthefuture

Willmakecapitalpartofouranalysissoon

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AddingGovernmenttotheModel

Keyassumptions:

GovernmenttakesawaynettaxesTfrom

householdsfactorincomeYandspendsG in

thegoods

market

on

goods

and

services

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AddingGovernmenttotheModel

Households Firms

DisposableIncome

=Y-T

Gover

nmen

t

Expen

dituresG

Consu

mption

Expen

ditures

C

Facto

rpaym

ents=

Y

Totalexpenditures

C+I+G

InvestmentI

NetTaxesT

Government

Savings


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KeyModifications

GovernmentsavingsTG(ordeficitifnegative)

affectstheloanablefundsmarket

WhenTG>0,governmentssavesandsupplies

fundstotheLFmarket

WhenTG0

Governmentborrows intheloanablefunds

market

Budgetsurplus isasituationwhengovernment

nettaxreceiptsexceedsspendingTG>0

Governmentsaves intheloanablefunds

market

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ModifiedLoanableFundsMarket

1.75 Trillions of Dollars

Interest Rate

E

S+T-G(private savings+ government

savings)

Total Demandfor Funds(planned

investment byprivate sector)

S+T-G=I

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SaysLawHoldswithGovernment

Again,thinkintermsofinflowsandoutflows

Yflowsfromfirmstohouseholds

SandTflowsout

IandGflowsin

S+TG=Iinequilibriuminloanablefundsmarket

So,again,whatflowsoutS+T,flowsinasI+G,and

soC+I+G=Y

Algebraically, C+I+G=C+S+TG+G=C+S+T=Y

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SaysLawHolds:Red =Green

Households Firms

DisposableIncome

=Y-T

Gover

nmen

t

Expen

dituresG

Consu

mption

Expen

ditures

C

Facto

rpaym

ents=

Y

Totalexpenditures

C+I+G

InvestmentI

NetTaxesT

Savings

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NumericalExample

Suppose,G=0,T=0,s=.2,L=10,K=10,and

Y=K1/2L1/2,calculateoutputandinvestmentinthe

equilibriumoftheclassicalmodel

Assumedepreciation

rate

of

capital

=10%

(10%

ofcapitalstockwearsouteachperioddueto

aging).Whatwillbethelevelofcapitalnext

period?

Isitmoreorlessthantoday?


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Solution

Y=K1/2L1/2=10

S=s(YT)=.2x10=2

Inequilibrium,I=S+TG,andsoI=2

Ktomorrow=.9Ktoday+2=.9x10+2=11

11>10,Kisgrowing

Ktoday=10

Ktomorrow=11

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Dynamic(Longrun)Equilibrium

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DynamicEquilibrium

Sofar,silentaboutK

GivenpredeterminedcapitalK,determined:

output,investmentandemployment

Inotherwords,determinedstaticequilibrium

(withinaperiod)butnotdynamic(across

periods)

Ourgoal:Findoutwheretheeconomyisheading

inthefuture?

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BasicIdea

Futureoutput,investmentandemployment

dependsontodaysinvestment

Evolutionofcapitalfromoneperiodtothenext

criticaltodeterminewheretheeconomyis

heading

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EvolutionofCapital

Recallourassumption:

IMPLIES:FuturecapitaldependshowinvestmentI comparestodepreciationK

(1 )tomorrow today K K I= +

(1 ) ,

ands o,

tomorrow today today today

tomorrow today today

K K I K K I

K K I K

=

= + = +

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EvolutionofCapital

Theaboveequationimplies:

I> Ktoday capitalKgrows

I


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FindingOutWhereEconomyIsHeading

Capital K

Output (determined

by productionfunction and

capital K)

L fixed = population size (always true in static equilibrium)

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Capital K

Output Y

Investment = sY

Constant fraction of

output

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Capital K

Output Y

Investment = sY

Constant fraction of

output

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Capital K

Output Y

Investment sY

Capital Depreciation K

A straight line

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Capital K

Output Y

Investment sY

Investment>Depreciation InvestmentDepreciation Investment


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Capital K

Output Y

Investment sY

Dynamic

equilibrium

Investment>Depreciation Investment

Classical Vs Keynenesian System

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