8_long run economic growth (1)

8/13/2019 8_Long Run Economic Growth (1)

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Fundamental of Economic Growth

LongRun

Why Output Grow in Log run????

DoYouHelptheEconomyMoreifYouSpendorifYouSave?

Economics in Your Life


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TheFactsofGrowth

TheWorldEconomy

TotalGDP(2012):$83T

Population(2012):7B

GDPperCapita(2012):$12,500

PopulationGrowth(2012):1.1%

GDPGrowth(2012):3.3%

GDPpercapitaisprobablythebestmeasureofacountrysoverallwellbeing


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Region GDP % of

World

GDP

GDP Per

Capita

Real GDP

Growth

United States $15T 18% $48,000 1.3%

European Union $16T 19% $33,000 1.0%

Japan $4.3T 6% $34,200 -0.4%

China $7.8T 11% $6,000 9.8%

India $3.2T 5% $2,800 5.6%

Ethiopia $66.3B .09% $800 8.5%

Note.However,thatgrowthratesvarysignificantlyacrosscountries/regions. Doyouseeapatternhere?

Source:CIAWorldFactbook

TheWorldEconomy201213

Atthecurrenttrends,thestandardoflivinginChinawillsurpassthatoftheUSin25years!Or,willthey?

PerCapitaIncome

Thatis,canChinamaintainitscurrentgrowthrate?

TheWorldEconomy


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Income GDP/Capita GDP Growth

Low $510 6.3%

Middle $2,190 7.0%

High $32,040 3.2%

Asageneralrule,lowincome(developing)countriestendtohavehigheraverageratesofgrowththandohighincomecountries

Theimplicationhereisthateventually,poorercountriesshouldeventuallycatch

up

towealthiercountriesintermsofpercapitaincome aconcept

knownasconvergence

TheWorldEconomy

Somecountries,however,dontfitthenormalpatternofdevelopment

Sudan

GDP:$80B(#80)

GDPPerCapita:$2,400(#184)

GDPGrowth:11.2%(#219)

Qatar

GDP:$150B(#59)

GDPPerCapita:$179,000(#1)

GDPGrowth:

16.3%

(#1)

So,whatisSudandoingwrong?(Or,whatisQatardoingright?)

Atcurrenttrends,PercapitaincomeinQatarwillquadrupleto$716,000overthenextdecade.Overthesametimeperiod,percapitaGDPinSudanwilldropbyroughly40%to$670!!!

TheWorldEconomy


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Growth and Happiness

Happiness and Income per Person across Countries

Developed Country

Lessdeveloped Country

Economists takefor granted thathigher outputper capitameans higherutility andincreasedhappiness.

The evidenceon directmeasures of

happiness,however, pointsto a morecomplex picture.

RealGDPLevelVsGrowthRatei.e.GDPatFC(constantprice)baseyear(19992000)

0

500000

1000000

1500000

2000000

2500000

3000000

3500000

4000000

1951-52

1954-55

1957-58

1960-61

1963-64

1966-67

1969-70

1972-73

1975-76

1978-79

1981-82

1984-85

1987-88

1990-91

1993-94

1996-97

1999-00

2002-03

2005-06

2008-09

GDPFC at Constant Price (Real GDP)

-6.00

-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

10.00

12.00

1951-52

1954-55

1957-58

1960-61

1963-64

1966-67

1969-70

1972-73

1975-76

1978-79

1981-82

1984-85

1987-88

1990-91

1993-94

1996-97

1999-00

2002-03

2005-06

2008-09

Trend Line Or Potential Growth

Indias Economic Growth


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Factors Affecting Indias Economic Growth

1. Interest Rates

2. Inflation

3. Currency Strength

4. Tax Levels

5. Govt. Intervention in Industries

6. Environmental Impact

7. Overall Economic Health

8. Natural Calamities

9. Monsoon

10. Business Cycles

11. Other Factors:

Population Growth (N), Human Capital, Natural Resources, FDI, Infrastructure,

Political structure, legal determinants, and Geoography in economic growth

3 sector

1. Agriculture : major source of livelihood and Employment generation2. Industry : Mixed system

3. Service Sector : Recently growing


Nehru- Mahalanobis Model of Growth

Mahalanobis model is a model of economic development, created byIndian statistician Prasanta Chandra Mahalanobis in 1953.

It is essentially a developmental planning model and not an economicgrowth model of the Harrod-Domar or Solow model variety

Largely follow Soviet Union growth strategy.

Centrally plan structure of growth. Adopted different 5 yr plan forgrowth.

The issue of allocation of capital was to be solved in a manner thateconomic growth rate could be enhanced.

Agricultural growth was given importance in 1st 5 yr Plan.

Higher investment in heavy industries could boost the economic growth( 2nd 5 yr plan).

Allocating a larger share of Govt. investment in the capital goods sectorand a lower share of investment to the consumption goods sector.


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GDP Growth

Long Run Economic Growth

What determines growth in Log run?


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1.4 Economic Growth: A Primer

Questions:

What determines growth?

What is the role of capital accumulation?

What is the role of technological progress?

What is the role of Population Growth

To analyze this, we use the framework of analysis

developed by Robert Solow, from MIT, in the late 1950s.

1. PF in aggregate terms: Y = F (K,N)

2. PF assume constant returns to scale:

xY = F (xK,xN ) for anyx > 0

3. Per Worker Production Function

Define: y = Y/N= output per worker

k= K/N= capital per worker

Letx = 1/N. Then Y/N = F (K/N, N/N)

=> y = F (k, 1) or y = f(k)

wheref(k) = F(k, 1)


The Production Function

.(1)

.(2)

.(3)


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4: The Production Function F(K,L) satisfies the Inada Conditions

0),(limand),(lim 0 LKFLKF KKKK

0),(limand),(lim 0 LKFLKF LLLL

Note: Asf (k)=FK have that

0)('limand)('lim 0 kfkf kk

Production Functions satisfying 1,2, 3 and 4 often calledNeo-Classical

Production Functions



Inada conditions (named afterKen-Ichi Inada) are assumptions about the shape of a production function

that guarantee the stability of an economic growth path in a neo classical growth model.

..(4)

Y

K

),,( NKAF

As the capital stock

increases (given a fixed

level of employment), the

productivity of capital

declines!!

K

YMP K

Change in Capital Stock

Change in Production

An economy cant grow through capital accumulation alone forever!

AKNY

K

Y

K

Y




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Per worker Production Function :(Output per worker and Capital per worker)

Increases in capital

per worker lead to

smaller and smaller

increases in output

per worker.


Y

NF

K

N

N

NF

K

N

, ,1

With Constant returns to scale:

The per worker and per capita PF will bexY F xK xN ( , )

=> y = f(k) .(3)

The Sources of Growth

1. Savings and Capital Accumulation: (K)

Increases in output per worker (Y/N) can come from

increases in capital per worker (K/N). Higher capital leads to

higher output.

2. Technological Progress (A):

Improvements in the state of technology, shift the

production function, F, and lead to more output per

worker given capital per worker.

3. Population Growth (N):4. Other Factors:

Human Capital, Natural Resources, FDI, Infrastructure,

Political structure, legal determinants, and geography in

economic growth



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A. Savings, Capital Accumulation

and Output Growth

The effects of the saving rate - the ratio of saving to GDP

on capital and output per capita.

4.1.InteractionsbetweenOutput(Y)andCapital(K)

TheRelation ofCapital,Output,Savings andCapitalAccumulation


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Under CRS, the relation between Y and K per worker is as follows:

Two Assumption we make

The size of the population, the participation rate, and the

unemployment rate are all constant.

There is no technological progress

Under this assumption,

(i) First Relationship is bt Yt and Kt is

, 1Y K

FN N

a. The Effects of Capital (Kt) on Output(Yt)

4.1. Interactions between Output (Y) and Capital(K)

Y

Nf

K

N

t t

Or yt = f(kt)

from eq (3)

.(5)

.(6)

Three assumptions to derive the relation between output and investment:

(a) the economy is closed. Y=C+I+G =>

(b) public saving and T G, is equal to zero, means G=0,T=0 and NX=0

( c) private saving is proportional to income,

since

Combining these two relations gives:

where, i=I/N, i.e. investment per worker

I S T G ( )

I sYt t

S sYI S

(i)OutputandInvestment

4.1.InteractionsbetweenOutput(Y)andCapital(K)

b.TheEffectsofOutput(Yt)onCapitalAccumulation(Kt+1)

i.Therelationbetweenoutputandinvestment.IiTherelationbetweeninvestment andcapitalaccumulation

(ii)TheSecondRelationshipis btYtandKt+1is

Or it=syt=sf(kt)

(7)

.(8)

(9)


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Depreciation

Depreciation per

worker, k

Capital per

worker, k

k

= the rate of depreciation= the rate of depreciation

1

4.1. Interactions between Output (Y) and Capital(K)

Assume rate of depreciation () is constant

Our two main relations are (Summary):

Combining the two relations, we can study the behavior of output and capital

over time.

Y

Nf

K

N

t t

K

N

K

Ns

Y

N

K

N

t t t t

1

4-2 Savings, Capital Accumulation and Growth:

The Implications of Alternative Saving Rates

1. First relation Capital determines Output (eqn 5):

2.Second relation Output determines Capital accumulation (eqn 12):


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Dynamics of Capital Accumulation and Output

Substituting first relation into second, (eqn 5 into eqn 12)we get

N

K

N

Ksf

N

K

N

K tttt

1

Inferences

If it>kt , then kt>0

If it0 If it


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Dynamics of Capital Accumulation and Output

At K*/N, output per worker and capital per worker remain constant at their long-run

equilibrium levels.

s f(kt) = kt



When capital and outputare low, investment

exceeds depreciation,

and capital increases.

When capital and outputare high, investment is

less than depreciation,

and capital decreases.

Steady-State Capital and Output

kt= sf(kt) kt



Steady State means a Variables of interest grow at

constantrate (balanced growth path or BGP)

If investment is just enough to cover depreciation i.e. sf(kt) =

kt,then capital per worker will remain constant: kt = 0. This occurs

at one value of k, denoted k*, called the steady state capital stock.


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Investment

and

depreciation

Capital per

worker, k

sf(kt)

kt

k*

Steady-State Capital and Output

k t= sf(kt) kt



k*, iscalledthesteadystatecapitalstock.

A Numerical Example

Production function (aggregate): Cobb-Douglas Type of PF

1 / 2 1 / 2( , )Y F K L K L K L

1 / 21 / 2 1 / 2Y K L K

L L L

1 / 2( )y f k k

To derive the per-worker production function, divide through byL:

Then substitutey = Y/L and k=K/L to get

Let Assume: s = 0.3; = 0.1 and initial value of k= 4.0


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Exercise: Solve for the steady state

Continue to assume: s = 0.3, = 0.1, and y = k

Use the equation of motion: k= s f(k) kto solve for the steady-state values of k,y, and c.

def. of steady statek 0

a n d y k * * 3

eq'n of mo tion withs f k k k ( *) * 0

using assumed valuesk k0.3 * 0.1 *

Finally, c s y * (1 ) * 0.7 3 2.1

=>

=>

=>

So solve to get :

With

=>

So, with s=0.3, k*=9, y*=3 and c*=2.1

Approaching the steady state:

A numerical example

Year k y c i k k

1 4.000 2.000 1.400 0.600 0.400 0.200

2 4.200 2.049 1.435 0.615 0.420 0.195

3 4.395 2.096 1.467 0.629 0.440 0.189

Assumptions: ; 0.3; 0.1; initial 4.0y k s k

4 4.584 2.141 1.499 0.642 0.458 0.184

10 5.602 2.367 1.657 0.710 0.560 0.150

25 7.351 2.706 1.894 0.812 0.732 0.080

100 8.962 2.994 2.096 0.898 0.896 0.002

9.000 3.000 2.100 0.900 0.900 0.000


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Application:CapitalAccumulationandGrowthin

France intheAftermathofWorldWarII

Table 1 Proportion of the French Capital Stock Destroyed by the End of

World War II

Railways Tracks 6% Rivers Waterways 86%

Stations 38% Canal Locks 11%

Engines 21% Barges 80%

Hardware 60% Buildings (numbers)

Roads Cars 31% Dwellings 1,229,000

Trucks 40% Industrial 246,000

WhenWWIIendedin1945,FrancehadsufferedsomeoftheheaviestlossesofallEuropeancountries. AvividpictureofthedestructionofcapitalisprovidedbythenumbersinTable1.

Policies to Promote Growth

1. Are we saving enough? Too much or too little?

2. What policies may change the savings rate?

3. How should we allocate savings between physical

and human capital?

4. What policies could generate faster technological

progress?


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Question.

Does savings rate affect the growth rate of output per worker?

Three Possible observations are:

1. The saving rate has no effect on the long run growth rate of output per

worker, which is equal to zero.

2. Nonetheless,the saving rate determines the level of output per worker in

the long run. Other things equal, countries with a higher saving rate will

achieve higher output per worker in the long run.

3. An increase in the saving rate will lead to higher growth of output per

worker for some time, but not forever.

4-3 Different Saving Rates and Growth

The Saving Rate and Output

Solow model predicts

that a country with a

higher saving rate

achieves a higher

steady- state level ofoutput per worker in

the long run.

The Effects of Different

Saving Rates

An increase in the saving rate raises investment causing kto grow toward a

new steady state.




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An increase in the

saving rate leads

to a period of

higher growth

until outputreaches its new,

higher steady-state

level.

The Effects of an

Increase in the Saving

Rate on Output per

Worker



An increase in the

saving rate leads to

a period of higher

growth until output

reaches a new,

higher path.

The Effects of an Increase in

the Saving Rate on Output per

Worker in an Economy with

Technological Progress




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SocialSecurity,Saving,andCapitalAccumulationin

theUnitedStates

Onewaytorunasocialsecuritysystemisthefullyfundedsystem,whereworkersaretaxed,theircontributionsinvested

infinancialassets,andwhenworkersretire,theyreceivetheprincipalplustheinterestpaymentsontheirinvestments.

Anotherwaytorunasocialsecuritysystemisthepayasyougosystem,wherethetaxesthatworkerspayarethebenefitsthatcurrentretireesreceive.

Inanticipationofdemographicchanges,theSocialSecuritytaxratehasseenincreases,andcontributionsarenowlargerthanbenefits,leadingtotheaccumulationofaSocialSecuritytrustfund.

4-4.4.The Golden Rule: Savings and Growth

Different values of s lead to different steady states.

How do we know which is the best steady state?

Definition: Golden Rule,, it is the saving rate that maximises

consumption in the steady-state.

Max. c* = (1s) f(k*).

An increase in s

leads to higher k*andy*, which raises c*

reduces consumptions share of income (1s), which lowers c*.

So, how do we find the s and k*that maximize c*?


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The Golden Rule capital stock

the Golden Rule level of capital,

the steady state value of k

that maximizes consumption.

*

goldk

To find it, first express c* in terms of k*:

c* = y* i*= f (k*) i*

= f (k*) k*

In the steady state:

i* = k*becausek= 0.

4-4.4.The Golden Rule: Savings and Growth

As C=Y-S

Or C=Y-I

.(16)

Then, graph

f(k *) and k*,

look for the

point where

the gap between

them is biggest.

Then, graph

f(k *) and k*,

look for the

point where

the gap between

them is biggest.

steady stateoutput and

depreciation

steady-statecapital perworker, k*

f(k*)

k*

*

goldk

*

goldc

* *

gold gold i k* *( )gold gold y f k


4.4.TheGoldenRule:SavingsandGrowth


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c* = f(k *) k*

is biggest where

the slope of the

production

function equals

the slope of the

depreciation line:

c* = f(k *) k*

is biggest where

the slope of the

production

function equals

the slope of the

depreciation line:

steady-statecapital perworker, k*

f(k*)

k*

*

goldk

*

goldc

MPK =



AchievingtheGoldenRulerequiresthatpolicymakersadjusts.

Table The Saving Rate and the Steady-state Levels of

Capital, Output, and Consumption per Worker

Saving Rate, sCapital per

Worker, (K/N)Output per

Worker, (Y/N)Consumption per

Worker, (C/N)

0.0 0.0 0.0 0.0

0.1 1.0 1.0 0.9

0.2 4.0 2.0 1.6

0.3 9.0 3.0 2.1

0.4 16.0 4.0 2.4

0.5 25.0 5.0 2.5

0.6 36.0 6.0 2.4

1.0 100.0 10.0 0.0

The U.S. Saving Rate and the Golden Rule



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The set of skills of the workers in the economy is called

human capital.

An economy with many highly skilled workers is likely to be

much more productive than an economy in which most

workers cannot read or write.

The conclusions drawn about physical capital accumulation

remain valid after the introduction of human capital in the

analysis.

4.5 Physical versus Human Capital

ExtendingtheProductionFunction

Whenthelevelofoutputperworkersdependsonboththelevelofphysicalcapitalperworker,K/N,andthelevelofhumancapitalperworker,H/N,theproductionfunctionmaybewrittenas:

Y

Nf

K

N

H

N

,

( , )

Anincreaseincapitalperworkerortheaverageskillofworkersleadstoanincreaseinoutputperworker.

ExtendingtheProductionFunction

4.5 Physical versus Human Capital

Ex.Supposeaneconomyhas100workers,halfofthemunskilledandhalfofthemskilled.Therelativewageofskilledworkersistwicethatofunskilledworkers.Then:

HH

N [( ) ( )] .50 1 50 2 150

150

100 15


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B. Technological Progress and Growth

Technologyistheuseofscientificknowledgefor

improvingthewaytodothings.

GiventheamountofCapital(K)and Labor(L)Technologicalprogressleadsto

Increaseoutput

BetterproductsNewproductsAlargervarietyofproducts

5.1TechnologicalProgress andtheRateofGrowth


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TheProductionFunction

Y F K N A ( , , )(+ + +)

Y F K AN ( , )

ThePFwillbe:Amorerestrictivebutmoreconvenientformis

ANislaboraugmenting technology

Dividingboththesideofeq18byAN,weget

Redefineeq(19)


.(17)

.(18)

, 1Y K

FAN AN

.(19)

Y Kf

A N A N

.(20)

Inwords: Outputpereffectiveworkerisafunctionofcapitalpereffectiveworker.

Because of Decreasing

Returns of Capital (K),

K/AN=>Y/AN.

OutputperEffectiveWorkerversusCapitalperEffectiveWorker


TheProductionFunction


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1. The Relation between output per worker and capital per worker. I S sY

I

ANs

Y

AN

Dividing both sides byAN, we get

Interactions between Output and Capital

2. The Relation between investment per worker and capital per worker.

Given that Y

AN f

K

AN

I

ANsf

K

AN

then,

3. The Relation between depreciation per workerequivalently, the investment per

worker needed to maintain a constant level of capital per workerand capital per

worker.

K g g K A N

( ) ( ) g g KA Nor

( ) g gK

ANA N

The amount of investment per effective worker needed to maintain a constant level

of capital per effective worker is

5.1 Technological Progress and the Rate of Growth

1. Capital per effective worker and

output per effective worker

converge to constant values in the

long run.

2. Output per effective worker

increases with capital per effective

worker, but at a decreasing rate.

3. The relation between investment

per effective worker and capital

per effective worker is drawn as

the upper curve, multiplied by thesaving rate,s.

4. Finally, now that we allow for

technological progress (so A

increases over time), the number

of effective workers (AN) increases

over time.

TheDynamicsofCapitalperEffectiveWorkerandOutputperEffectiveWorker

InteractionsbetweenOutputandCapital



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In steady state, output (Y) grows at the same rate as effective

labor (AN); effective labor grows at a rate (gA+gN); therefore,

output growth in steady state equals (gA+gN). Capital per

effective worker also grows at a rate equal to (gA+gN).

The growth rate of output is independent of the saving rate.

Because output, capital, and effective labor all grow at the

same rate, (gA+gN), the steady state of the economy is also

called a state ofbalanced growth.


InteractionsbetweenOutputandCapital

Technologicalprogressinmoderneconomiesistheresultoffirmsresearchanddevelopment(R&D)activities. TheoutcomeofR&Disfundamentallyideas.SpendingonR&Ddependson:

1.Thefertilityoftheresearchprocess,orhowspendingonR&Dtranslatesintonewideasandnewproducts,dependsuponinteractionbetweenbasicresearchandappliedresearch

and

2.theappropriabilityofresearchresults,ortheextenttowhichfirmsbenefitfromtheresultsoftheirownR&D,whichdependsupondependsuponlegalprotectionsuchaspatents.

52 TheDeterminantsofTechnologicalProgress


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ThankYouAll

8_long run economic growth (1)

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