chapter three quantity and quality chapter 3 compares and contrasts the theories of endogenous vs....

Chapter ThreeChapter ThreeChapter ThreeChapter Three

Quantity and QualityQuantity and QualityQuantity and QualityQuantity and Quality

Chapter 3Chapter 3

Compares and contrasts the theories of Compares and contrasts the theories of endogenous vs. exogenousendogenous vs. exogenous growthgrowthMain point: They differ less than you might thinkMain point: They differ less than you might think

Tells the whole story in words and picturesTells the whole story in words and picturesleaving all the mathematics to appendicesleaving all the mathematics to appendices

Discusses optimal saving and Discusses optimal saving and optimal optimal growthgrowthIt does not make sense, it turns out, to aim for It does not make sense, it turns out, to aim for

the highest possible rate of economic growththe highest possible rate of economic growth

Outline

Quantity and QualityQuantity and Quality

The practical question then for our consideration is,The practical question then for our consideration is,what are the most immediate and effectivewhat are the most immediate and effectivestimulants for the creation and progress of wealth.stimulants for the creation and progress of wealth.

THOMAS MALTHUSTHOMAS MALTHUS

Why did development economics fade away? … theWhy did development economics fade away? … theleading development economists failed to turn leading development economists failed to turn theirtheirintuitive insights into clear-cut models that could intuitive insights into clear-cut models that could serve as the core of an enduring discipline.serve as the core of an enduring discipline.

PAUL KRUGMANPAUL KRUGMAN

The practical question then for our consideration is,The practical question then for our consideration is,what are the most immediate and effectivewhat are the most immediate and effectivestimulants for the creation and progress of wealth.stimulants for the creation and progress of wealth.

THOMAS MALTHUSTHOMAS MALTHUS

Why did development economics fade away? … theWhy did development economics fade away? … theleading development economists failed to turn leading development economists failed to turn theirtheirintuitive insights into clear-cut models that could intuitive insights into clear-cut models that could serve as the core of an enduring discipline.serve as the core of an enduring discipline.

PAUL KRUGMANPAUL KRUGMAN


Saving behaviourSaving behaviour

EfficiencyEfficiency

Saving behaviourSaving behaviour


Invariably viewed as Invariably viewed as crucial determinants crucial determinants of economic growthof economic growth

Invariably viewed as Invariably viewed as crucial determinants crucial determinants of economic growthof economic growth

The Solow revolution: long-run per capita The Solow revolution: long-run per capita growth ultimately immune to all growth ultimately immune to all influences except influences except technological progresstechnological progress

The Solow revolution: long-run per capita The Solow revolution: long-run per capita growth ultimately immune to all growth ultimately immune to all influences except influences except technological progresstechnological progress

Technological change Technological change and economic growth and economic growth are both are both endogenousendogenous after allafter all

Growth is an exogenous Growth is an exogenous quantity from an economic quantity from an economic point of viewpoint of view

Growth is an exogenous Growth is an exogenous quantity from an economic quantity from an economic point of viewpoint of view


Two main theories of economic growthTwo main theories of economic growththe new theory of the new theory of endogenous growthendogenous growth

the neoclassical theory of the neoclassical theory of exogenous growthexogenous growth

Two main theories of economic growthTwo main theories of economic growththe new theory of the new theory of endogenous growthendogenous growth

the neoclassical theory of the neoclassical theory of exogenous growthexogenous growth

Let us compare their Let us compare their answers to some key answers to some key questions about growth, questions about growth, over time and across over time and across countriescountries

Let us compare their Let us compare their answers to some key answers to some key questions about growth, questions about growth, over time and across over time and across countriescountries

Endogenous growth:Endogenous growth:

Determination of economic Determination of economic growth and technological growth and technological progressprogress

G

T

Technological progressTechnological progress

EconomicEconomicgrowthgrowth


45°

Population growthPopulation growth

O

AC

Saving rate Saving rate times efficiency times efficiency minus minus depreciationdepreciation

Saving rate Saving rate times efficiency times efficiency minus minus depreciationdepreciation

B

Fig 3.1Fig 3.1

Endogenous growth and technology

Summarize the main implications of Summarize the main implications of endogenous-growth theory with the aid of a endogenous-growth theory with the aid of a simple diagramsimple diagram … … trace the effects of trace the effects of

certain certain exogenous exogenous eventsevents on on economic economic growthgrowth and and technological technological progressprogress, both of , both of which are which are endogenousendogenous

Experiment 1:Experiment 1: The saving rate The saving rate

Experiment 2:Experiment 2: Efficiency Efficiency

Experiment 3:Experiment 3: Depreciation Depreciation

Experiment 4:Experiment 4: Population growth Population growth

Experiment 1: The saving rateExperiment 1: The saving rate

What happens if the saving rate rises?What happens if the saving rate rises?What happens if the saving rate rises?What happens if the saving rate rises?

The G line shifts up to G’The G line shifts up to G’The G line shifts up to G’The G line shifts up to G’

The equilibrium point moves north-The equilibrium point moves north-east from A to B, at which east from A to B, at which economic growth is faster than economic growth is faster than before, as is before, as is technological technological progressprogress

The equilibrium point moves north-The equilibrium point moves north-east from A to B, at which east from A to B, at which economic growth is faster than economic growth is faster than before, as is before, as is technological technological progressprogress

The The population growth ratepopulation growth rate has not changed by has not changed by assumptionassumptionThe The population growth ratepopulation growth rate has not changed by has not changed by assumptionassumption

Hence, the growth of output per Hence, the growth of output per capita increases as much as capita increases as much as output growthoutput growth

Hence, the growth of output per Hence, the growth of output per capita increases as much as capita increases as much as output growthoutput growth

G

T




G’

Endogenous Growth:An Increase in the Saving Rate or in Efficiency Increases Economic Growth and Technological Progress

A

B

45°

Fig 3.2

Experiment 1

Experiment 1: The saving rate

Why does economic growth increase?Why does economic growth increase?Why does economic growth increase?Why does economic growth increase?

More capital is being accumulatedMore capital is being accumulatedMore capital is being accumulatedMore capital is being accumulated

Technological progress accelerates Technological progress accelerates through through learning by doinglearning by doingTechnological progress accelerates Technological progress accelerates through through learning by doinglearning by doing

With more capital to work with, With more capital to work with, people learn how to use it more people learn how to use it more efficientlyefficiently

With more capital to work with, With more capital to work with, people learn how to use it more people learn how to use it more efficientlyefficiently


How fast does the economy move from A How fast does the economy move from A to B?to B?

The endogenous-growth The endogenous-growth theory provides no answer theory provides no answer to this important questionto this important question

The endogenous-growth The endogenous-growth theory provides no answer theory provides no answer to this important questionto this important question

… … no dynamic no dynamic adjustment is involved adjustment is involved in the theoryin the theory

… … no dynamic no dynamic adjustment is involved adjustment is involved in the theoryin the theory

The dynamic deficiency of The dynamic deficiency of the endogenous-growth the endogenous-growth model actually has two model actually has two dimensionsdimensions

The dynamic deficiency of The dynamic deficiency of the endogenous-growth the endogenous-growth model actually has two model actually has two dimensionsdimensions

… … the model is the model is silent on the time it silent on the time it takes the economy takes the economy to move from one to move from one equilibrium to equilibrium to anotheranother

… … the model is the model is silent on the time it silent on the time it takes the economy takes the economy to move from one to move from one equilibrium to equilibrium to anotheranother

… … and about the and about the stability of the stability of the growth growth equilibriumequilibrium

… … and about the and about the stability of the stability of the growth growth equilibriumequilibrium

G

T




G’

Endogenous Growth:An Increase in the Saving Rate or in Efficiency Increases Economic Growth and Technological Progress

A

B

45°

Fig 3.2

Experiment 2

Experiment 2: EfficiencyExperiment 2: Efficiency

What happens if efficiency increases?What happens if efficiency increases?What happens if efficiency increases?What happens if efficiency increases?

… … shifts the G line up to G’shifts the G line up to G’

… … thereby increasing both thereby increasing both economic growth and technological economic growth and technological progressprogress

… … thereby increasing both thereby increasing both economic growth and technological economic growth and technological progressprogress

What does the interaction What does the interaction of saving and efficiency of saving and efficiency mean?mean?

What does the interaction What does the interaction of saving and efficiency of saving and efficiency mean?mean?

… … it means that a given level of it means that a given level of saving translates increased saving translates increased efficiency into more growthefficiency into more growth

… … it means that a given level of it means that a given level of saving translates increased saving translates increased efficiency into more growthefficiency into more growth

… … increased saving increased saving and increased and increased efficiency have efficiency have qualitatively the qualitatively the same effect on same effect on economic growth and economic growth and technological technological progressprogress

… … increased saving increased saving and increased and increased efficiency have efficiency have qualitatively the qualitatively the same effect on same effect on economic growth and economic growth and technological technological progressprogress

Fig 3.2 covers both Fig 3.2 covers both casescasesFig 3.2 covers both Fig 3.2 covers both casescases

G’

T

Technological progress

Economicgrowth

Economicgrowth

G

Endogenous Growth:An Increase in Depreciation Reduces Economic Growth and Technological Progress

B

A

45°

Fig 3.3

Experiment 3

Experiment 3: Experiment 3: DepreciationDepreciation

What happens if capital begins to What happens if capital begins to depreciate more rapidly than depreciate more rapidly than before?before?

What happens if capital begins to What happens if capital begins to depreciate more rapidly than depreciate more rapidly than before?before?

The productive part of the The productive part of the capital stock is, by capital stock is, by definition, the existing definition, the existing amount of machinery and amount of machinery and equipment available for use equipment available for use as inputs into production of as inputs into production of directly or indirectly saleable directly or indirectly saleable goods and servicesgoods and services

The productive part of the The productive part of the capital stock is, by capital stock is, by definition, the existing definition, the existing amount of machinery and amount of machinery and equipment available for use equipment available for use as inputs into production of as inputs into production of directly or indirectly saleable directly or indirectly saleable goods and servicesgoods and services

… … depends on whether more depends on whether more has been ‘added to it by the has been ‘added to it by the good conduct of some, than good conduct of some, than had been taken from it either had been taken from it either by the private misconduct of by the private misconduct of others, or by the publick others, or by the publick extravagance of government’ extravagance of government’ ((SmithSmith))

… … depends on whether more depends on whether more has been ‘added to it by the has been ‘added to it by the good conduct of some, than good conduct of some, than had been taken from it either had been taken from it either by the private misconduct of by the private misconduct of others, or by the publick others, or by the publick extravagance of government’ extravagance of government’ ((SmithSmith))

While gross investment is While gross investment is never negative, never negative, net net investment can be negativeinvestment can be negative, , if gross investment does not if gross investment does not suffice to make up for the suffice to make up for the wear and tear of existing wear and tear of existing capital capital

While gross investment is While gross investment is never negative, never negative, net net investment can be negativeinvestment can be negative, , if gross investment does not if gross investment does not suffice to make up for the suffice to make up for the wear and tear of existing wear and tear of existing capital capital

Therefore, if the depreciation of Therefore, if the depreciation of capital is sufficiently rapid, the capital is sufficiently rapid, the capital stock will decline, so capital stock will decline, so that output also declines: that output also declines: economic growth then becomes economic growth then becomes negativenegative

Therefore, if the depreciation of Therefore, if the depreciation of capital is sufficiently rapid, the capital is sufficiently rapid, the capital stock will decline, so capital stock will decline, so that output also declines: that output also declines: economic growth then becomes economic growth then becomes negativenegative

What does this mean? What does this mean? What does this mean? What does this mean?

Experiment 3: Depreciation

Let us return to the modelLet us return to the modelLet us return to the modelLet us return to the model

If the capital stock begins to If the capital stock begins to depreciate more rapidly than depreciate more rapidly than beforebefore

If the capital stock begins to If the capital stock begins to depreciate more rapidly than depreciate more rapidly than beforebefore

… … the G line shifts down to G’the G line shifts down to G’… … the G line shifts down to G’the G line shifts down to G’

… … the growth equilibrium the growth equilibrium moves south-west from A to moves south-west from A to BB

… … the growth equilibrium the growth equilibrium moves south-west from A to moves south-west from A to BB

Economic growth slows down, and so does Economic growth slows down, and so does technological progress, because it follows technological progress, because it follows per capita growth, and not vice versa, per capita growth, and not vice versa, through learning by doingthrough learning by doing

Economic growth slows down, and so does Economic growth slows down, and so does technological progress, because it follows technological progress, because it follows per capita growth, and not vice versa, per capita growth, and not vice versa, through learning by doingthrough learning by doing

More More depreciation depreciation means less means less growthgrowth

More More depreciation depreciation means less means less growthgrowth

Endogenous Growth:An Increase in Population Growth Reduces Technological Progress, but Leaves Economic Growth Unchanged

G

T’


Economicgrowth

Economicgrowth

45°

T

AB

OH

I

J

Fig 3.4

Experiment 4

Experiment 4: Population growthExperiment 4: Population growth

How does the economy react How does the economy react to an increase in population to an increase in population growth?growth?

The T line shifts upwards and to the left to T’The T line shifts upwards and to the left to T’

… … because with more population growth, a because with more population growth, a given rate of growth of output is consistent given rate of growth of output is consistent with less technological progress than beforewith less technological progress than before

The new T’ line cuts the vertical axis at point The new T’ line cuts the vertical axis at point I, which lies above point HI, which lies above point H


The rate of population The rate of population growth rises from OH to OIgrowth rises from OH to OIThe rate of population The rate of population growth rises from OH to OIgrowth rises from OH to OI

… … but economic growth remains but economic growth remains unchanged because the G line does not unchanged because the G line does not movemove

… … but economic growth remains but economic growth remains unchanged because the G line does not unchanged because the G line does not movemoveConsequently, the rate of growth of output Consequently, the rate of growth of output per capita decreases from JH to IJper capita decreases from JH to IJConsequently, the rate of growth of output Consequently, the rate of growth of output per capita decreases from JH to IJper capita decreases from JH to IJ

‘‘The slowest progress in wealth is often made where The slowest progress in wealth is often made where the stimulus arising from population alone is the the stimulus arising from population alone is the greatest.’greatest.’

‘‘The slowest progress in wealth is often made where The slowest progress in wealth is often made where the stimulus arising from population alone is the the stimulus arising from population alone is the greatest.’greatest.’

Recall Malthus:

Endogenous growth Endogenous growth accountingaccounting

Figures 3.1-3.3Figures 3.1-3.3

Qualitative reactions of Qualitative reactions of endogenous economic growth endogenous economic growth and technological progress to and technological progress to changes in the three key changes in the three key determinants of growthdeterminants of growth

Figures 3.1-3.3Figures 3.1-3.3

Qualitative reactions of Qualitative reactions of endogenous economic growth endogenous economic growth and technological progress to and technological progress to changes in the three key changes in the three key determinants of growthdeterminants of growth

Saving rateSaving rateSaving rateSaving rate

EfficiencEfficiencyyEfficiencEfficiencyyDepreciationDepreciationDepreciationDepreciation

What if we assign plausible What if we assign plausible values to the parameters of our values to the parameters of our simple model?simple model?

What if we assign plausible What if we assign plausible values to the parameters of our values to the parameters of our simple model?simple model?

We can get a glimpse We can get a glimpse of the likely of the likely quantitative quantitative responses of growth responses of growth and technological and technological progress to changes progress to changes in the parametersin the parameters

We can get a glimpse We can get a glimpse of the likely of the likely quantitative quantitative responses of growth responses of growth and technological and technological progress to changes progress to changes in the parametersin the parameters

This amounts to growth accounting This amounts to growth accounting that differs from the conventional that differs from the conventional kindkind

This amounts to growth accounting This amounts to growth accounting that differs from the conventional that differs from the conventional kindkind

What does that mean?What does that mean?


Rather than try to attribute economic Rather than try to attribute economic growth to changes in the quantity and growth to changes in the quantity and quality of labour, capital, and land ...quality of labour, capital, and land ...

Rather than try to attribute economic Rather than try to attribute economic growth to changes in the quantity and growth to changes in the quantity and quality of labour, capital, and land ...quality of labour, capital, and land ...

… … we now try to trace it to we now try to trace it to saving, efficiency, and saving, efficiency, and

depreciationdepreciation

… … we now try to trace it to we now try to trace it to saving, efficiency, and saving, efficiency, and

depreciationdepreciation

Depreciationrate 0.06

Efficiency0.30

Efficiency0.40

Efficiency0.50

Saving rate 0.10 -0.03 -0.02 -0.01

Saving rate 0.20 0.00 0.02 0.04

Saving rate 0.30 0.03 0.06 0.09

Saving rate 0.40 0.06 0.10 0.14

Economic GrowthTable 3.1

... as a Function of the Saving Rate,Efficiency, and Depreciation

... as a Function of the Saving Rate,Efficiency, and Depreciation

What does Table 3.1 show?What does Table 3.1 show?What does Table 3.1 show?What does Table 3.1 show?

Endogenous growth accountingEndogenous growth accounting

It shows It shows considerable sensitivity of the rate of considerable sensitivity of the rate of economic growth to variations in its economic growth to variations in its determinantsdeterminants

It shows It shows considerable sensitivity of the rate of considerable sensitivity of the rate of economic growth to variations in its economic growth to variations in its determinantsdeterminants

When the saving rate rises from 10% of GDP to 40% ...When the saving rate rises from 10% of GDP to 40% ...When the saving rate rises from 10% of GDP to 40% ...When the saving rate rises from 10% of GDP to 40% ...

… … annual output growth rises by 9 to 15 annual output growth rises by 9 to 15 percentage points, depending on percentage points, depending on efficiencyefficiency

… … annual output growth rises by 9 to 15 annual output growth rises by 9 to 15 percentage points, depending on percentage points, depending on efficiencyefficiency

An increase in efficiency from 0.3 to 0.5 ...An increase in efficiency from 0.3 to 0.5 ...An increase in efficiency from 0.3 to 0.5 ...An increase in efficiency from 0.3 to 0.5 ...

... increases annual growth by 2 to 8 ... increases annual growth by 2 to 8 percentage points, depending on the percentage points, depending on the saving ratesaving rate

... increases annual growth by 2 to 8 ... increases annual growth by 2 to 8 percentage points, depending on the percentage points, depending on the saving ratesaving rate

Endogenous growth accounting

An increase in the depreciation An increase in the depreciation rate from, say, 6% to 10% per rate from, say, 6% to 10% per yearyear

An increase in the depreciation An increase in the depreciation rate from, say, 6% to 10% per rate from, say, 6% to 10% per yearyear

… … would reduce each growth figure would reduce each growth figure in Table 3.1 by 4 percentage pointsin Table 3.1 by 4 percentage points

The annual rates of growth of The annual rates of growth of output per head can be found output per head can be found by subtracting the annual rate by subtracting the annual rate of population growth from the of population growth from the annual growth rates of output annual growth rates of output shown in the tableshown in the table

The usefulness of the The usefulness of the method behind Table method behind Table 3.1 as a growth-3.1 as a growth-accounting device is accounting device is understandably limited, understandably limited, since two of the since two of the parameters involved - parameters involved - efficiencyefficiency and and depreciationdepreciation - are - are unobservableunobservable

Examples: Examples:

TogoTogo NorwayNorway

Sub-SaharanAfrica

East Asiaand Pacific

World

Growth, 1980-1995 0.016 0.085 0.027

Saving rate, 1980-1995

0.22 0.34 0.24

Efficiency (assumed) 0.40 0.33 0.33

Depreciation (residual) 0.072 0.027 0.052

Decomposition of Growth

Table 3.2Table 3.2

in Sub-Saharan Africa, East Asia and Pacific,and the World, 1980-1995

in Sub-Saharan Africa, East Asia and Pacific,and the World, 1980-1995


Table 3.3Table 3.3 shows an example shows an example ofofconventional economic growth conventional economic growth accounting for comparisonaccounting for comparison

Table 3.3Table 3.3 shows an example shows an example ofofconventional economic growth conventional economic growth accounting for comparisonaccounting for comparison

We divide output growth We divide output growth between the between the contributions ofcontributions of

We divide output growth We divide output growth between the between the contributions ofcontributions of

1.1. Capital growth Capital growth through investmentthrough investment1.1. Capital growth Capital growth through investmentthrough investment

2.2. Labour-force Labour-force growth via population growth via population increaseincrease

2.2. Labour-force Labour-force growth via population growth via population increaseincrease3. A residual, which is attributed to total factor productivity growth

3. A residual, which is attributed to total factor productivity growth

Let’s look at Table 3.3Let’s look at Table 3.3Let’s look at Table 3.3Let’s look at Table 3.3

SevenOECD

Countries1960-1990

Four EastAsian

Countries1966-1990

Seven LatinAmericanCountries1940-1980

Growth of output 0.039 0.088 0.049

Contribution of capital 0.021 0.044 0.024

Contribution of labor 0.005 0.032 0.013

Contribution of totalfactor productivity(residual)

0.013 0.012 0.012

Traditional Growth AccountingTable 3.3Table 3.3

for OECD Countries, East Asian Countries, and Latin American Countries

for OECD Countries, East Asian Countries, and Latin American Countries


In all three regions, about a half of the In all three regions, about a half of the output growth is attributed to capital output growth is attributed to capital growthgrowth

In all three regions, about a half of the In all three regions, about a half of the output growth is attributed to capital output growth is attributed to capital growthgrowth

The residual is aboutThe residual is aboutthe same in all threethe same in all threeThe residual is aboutThe residual is aboutthe same in all threethe same in all three

This means an This means an increase in total factor increase in total factor productivity of about productivity of about 1.25% per year on 1.25% per year on averageaverage

This means an This means an increase in total factor increase in total factor productivity of about productivity of about 1.25% per year on 1.25% per year on averageaverage

This means that technological This means that technological progress has been relatively progress has been relatively most important in the OECD most important in the OECD region, accounting for a third region, accounting for a third of output growth compared of output growth compared with a fourth in Latin America with a fourth in Latin America and one-seventh in East Asiaand one-seventh in East Asia

This means that technological This means that technological progress has been relatively progress has been relatively most important in the OECD most important in the OECD region, accounting for a third region, accounting for a third of output growth compared of output growth compared with a fourth in Latin America with a fourth in Latin America and one-seventh in East Asiaand one-seventh in East Asia

Population growth has Population growth has mattered much more mattered much more in East Asia, where it in East Asia, where it has added more than has added more than 3 per-centage points 3 per-centage points to the annual growth to the annual growth rate of output on rate of output on averageaverage

Population growth has Population growth has mattered much more mattered much more in East Asia, where it in East Asia, where it has added more than has added more than 3 per-centage points 3 per-centage points to the annual growth to the annual growth rate of output on rate of output on averageaverage


What are the implications of the output-input What are the implications of the output-input approach?approach?

Let’s take an example of the spectacular Let’s take an example of the spectacular growth performance of the East Asian growth performance of the East Asian economieseconomies

… … achieved mostly through achieved mostly through the accumulation of more the accumulation of more capital and through more capital and through more labourlabour

… … achieved mostly through achieved mostly through the accumulation of more the accumulation of more capital and through more capital and through more labourlabour… … as opposed to better, or as opposed to better, or more efficient, labour and more efficient, labour and capitalcapital

… … as opposed to better, or as opposed to better, or more efficient, labour and more efficient, labour and capitalcapital

… … greater quantity, not better greater quantity, not better quality, the argument goesquality, the argument goes… … greater quantity, not better greater quantity, not better quality, the argument goesquality, the argument goes

The method of growth The method of growth decomposition decomposition suggested in Table 3.2 suggested in Table 3.2 shows this argument shows this argument in a different lightin a different light

… … even if it leads even if it leads to a similar to a similar conclusionconclusion


Nothing particularly Soviet about saving behaviour in Nothing particularly Soviet about saving behaviour in East Asia or about the way in which savings in the East-East Asia or about the way in which savings in the East-Asian countries generally have been channelled into Asian countries generally have been channelled into investmentinvestment

Nothing particularly Soviet about saving behaviour in Nothing particularly Soviet about saving behaviour in East Asia or about the way in which savings in the East-East Asia or about the way in which savings in the East-Asian countries generally have been channelled into Asian countries generally have been channelled into investmentinvestment

Saving rates in East Asia have Saving rates in East Asia have risen to their present level in risen to their present level in response to climate for saving response to climate for saving which has been ...which has been ...

Saving rates in East Asia have Saving rates in East Asia have risen to their present level in risen to their present level in response to climate for saving response to climate for saving which has been ...which has been ...

friendlyfriendlyfriendlyfriendly

stablestablestablestable

market-orientatedmarket-orientated

policy-policy-inducedinducedpolicy-policy-inducedinduced

This has meantThis has meant

modest inflationmodest inflation

positive real rates of interestpositive real rates of interest

realistic real exchange ratesrealistic real exchange rates

The level of income per headwith endogenous growth

Not interested Not interested mainly in economic mainly in economic growth as such … growth as such …

Not interested Not interested mainly in economic mainly in economic growth as such … growth as such …

… … but rather but rather in the in the fruits of fruits of growthgrowth

… … but rather but rather in the in the fruits of fruits of growthgrowth

Level of incomeLevel of incomeLevel of incomeLevel of income

Standard of lifeStandard of lifeStandard of lifeStandard of life

What does the theory of endogenous growth tell What does the theory of endogenous growth tell us about the level of output per head in the long us about the level of output per head in the long

run?run?

What does the theory of endogenous growth tell What does the theory of endogenous growth tell us about the level of output per head in the long us about the level of output per head in the long

run?run?

Endogenous Growth:Endogenous Growth:Determination of Capital Per Determination of Capital Per WorkerWorkerand Output Per Headand Output Per Head

OutputOutputper headper head


Capital per workerCapital per worker

P

C

Output/capital ratioOutput/capital ratio

Fig 3.5Fig 3.5

The level of income per headwith endogenous growth

Summarize the main implications of Summarize the main implications of endogenous-growth theory with the aid of a endogenous-growth theory with the aid of a simple diagramsimple diagram

… … trace the effects trace the effects of certain of certain exogenous eventsexogenous events on on output per headoutput per head and and capital per capital per workerworker, both of , both of which are which are endogenousendogenousExperiment 1:Experiment 1: Real interest rate Real interest rate


Experiment 3:Experiment 3: Static efficiency Static efficiency

Endogenous Growth:An Increase in the Real Interest Rate or in Depreciation Reduces Capital Per Worker and Output Per Head




BA

CC’

P

Fig 3.6Fig 3.6

Experiment 1

Experiment 1: The real interest rateExperiment 1: The real interest rate

Suppose, first, that the real interest rate Suppose, first, that the real interest rate goes upgoes upSuppose, first, that the real interest rate Suppose, first, that the real interest rate goes upgoes up

The capital/output ratio fallsThe capital/output ratio falls

Shifts the C line counter-Shifts the C line counter-clockwise to C’, so that clockwise to C’, so that its intersection with the its intersection with the production function production function moves from A to B in moves from A to B in Figure 3.6Figure 3.6

Shifts the C line counter-Shifts the C line counter-clockwise to C’, so that clockwise to C’, so that its intersection with the its intersection with the production function production function moves from A to B in moves from A to B in Figure 3.6Figure 3.6

This means less capital per This means less capital per worker and less output per headworker and less output per headThis means less capital per This means less capital per worker and less output per headworker and less output per head

Therefore, if we now allow for technological progress,Therefore, if we now allow for technological progress,output per head will grow less than it did originallyoutput per head will grow less than it did originallyTherefore, if we now allow for technological progress,Therefore, if we now allow for technological progress,output per head will grow less than it did originallyoutput per head will grow less than it did originally

… … at least as long as it takes the economy to at least as long as it takes the economy to move from the old equilibrium at A to the new move from the old equilibrium at A to the new

one at Bone at B

… … at least as long as it takes the economy to at least as long as it takes the economy to move from the old equilibrium at A to the new move from the old equilibrium at A to the new

one at Bone at B

Endogenous Growth:An Increase in the Real Interest Rate or in Depreciation Reduces Capital Per Worker and Output Per Head




BA

CC’

P

Fig 3.6Fig 3.6

Experiment 2


… … causes the cost of capital to risecauses the cost of capital to rise… … causes the cost of capital to risecauses the cost of capital to rise

… … qualitatively the same effect as qualitatively the same effect as thatthatof an increase in the interest rateof an increase in the interest rate

… … qualitatively the same effect as qualitatively the same effect as thatthatof an increase in the interest rateof an increase in the interest rate

… … the capital/output ratio falls, the capital/output ratio falls, and so do both capital per and so do both capital per worker and output per headworker and output per head

… … the capital/output ratio falls, the capital/output ratio falls, and so do both capital per and so do both capital per worker and output per headworker and output per head

Increased depreciation is likely Increased depreciation is likely to reflect, at least in part, a to reflect, at least in part, a deterioration in the quality deterioration in the quality and profitability of investment and profitability of investment decisionsdecisions

Increased depreciation is likely Increased depreciation is likely to reflect, at least in part, a to reflect, at least in part, a deterioration in the quality deterioration in the quality and profitability of investment and profitability of investment decisionsdecisions

… … reduces not only reduces not only the level of output per the level of output per head as in Figure 3.6head as in Figure 3.6

… … but also its rate of but also its rate of growth as in Figure growth as in Figure 3.33.3

This is a case where This is a case where the level and the rate the level and the rate of growth of output of growth of output per capita move in the per capita move in the same directionsame direction

Endogenous Growth:An Increase in Static Efficiency Increases Capital Per Worker and Output Per Head

Outputper head

Outputper head


A

B

P

P’C

Fig 3.7Fig 3.7

Experiment 3

Experiment 3: Efficiency

Static efficiency increasesStatic efficiency increasesStatic efficiency increasesStatic efficiency increases

The production function shifts The production function shifts upwards from P to P’ in Figure upwards from P to P’ in Figure 3.73.7

The production function shifts The production function shifts upwards from P to P’ in Figure upwards from P to P’ in Figure 3.73.7

This causes both capital per This causes both capital per worker and output per head worker and output per head to increaseto increase

This causes both capital per This causes both capital per worker and output per head worker and output per head to increaseto increase

The capital/output ratio remains The capital/output ratio remains unchanged because the C line does not unchanged because the C line does not movemove

The capital/output ratio remains The capital/output ratio remains unchanged because the C line does not unchanged because the C line does not movemove

Economic growth per capita Economic growth per capita must increase at least must increase at least temporarily as the economy temporarily as the economy moves from A to Bmoves from A to B

Economic growth per capita Economic growth per capita must increase at least must increase at least temporarily as the economy temporarily as the economy moves from A to Bmoves from A to B

The production The production function will be function will be drifting upwards more drifting upwards more rapidly than beforerapidly than before

The production The production function will be function will be drifting upwards more drifting upwards more rapidly than beforerapidly than before

Here we have a case Here we have a case where an external where an external event increases both event increases both the level and rate of the level and rate of growth of output per growth of output per capitacapita

Here we have a case Here we have a case where an external where an external event increases both event increases both the level and rate of the level and rate of growth of output per growth of output per capitacapita

Note: Increased static efficiency increases also dynamic efficiency

In sum

Three Three importantimportantdeterminants determinants ofofincome per income per headhead

Three Three importantimportantdeterminants determinants ofofincome per income per headhead

Income per Income per head is our head is our main measure main measure of the standard of the standard of livingof living

Income per Income per head is our head is our main measure main measure of the standard of the standard of livingof living

real interest ratereal interest ratereal interest ratereal interest ratedepreciationdepreciationdepreciationdepreciationefficiencyefficiencyefficiencyefficiency

What about the What about the saving rate?saving rate?

Does the saving rate not Does the saving rate not matter for the level of income matter for the level of income per head in this endogenous-per head in this endogenous-growth framework?growth framework?

The saving rate lies The saving rate lies buried below the buried below the surfacesurface

We have to look more We have to look more closely at the relationship closely at the relationship between the saving rate between the saving rate and the and the interest rateinterest rate

In sum

An increase in the An increase in the saving rate ...saving rate ...An increase in the An increase in the saving rate ...saving rate ...

... results in ... results in accumulation of accumulation of capital ...capital ...

... results in ... results in accumulation of accumulation of capital ...capital ...… … which tends to drive its which tends to drive its price - i.e. the real price - i.e. the real interest rate - downinterest rate - down

… … which tends to drive its which tends to drive its price - i.e. the real price - i.e. the real interest rate - downinterest rate - down

What if there is no learning by doing? The elimination What if there is no learning by doing? The elimination of learning by doing from the story without of learning by doing from the story without introducing some other mechanism, such as research introducing some other mechanism, such as research and development, that would preserve the and development, that would preserve the endogeneityendogeneity of technological progress ... of technological progress ...

What if there is no learning by doing? The elimination What if there is no learning by doing? The elimination of learning by doing from the story without of learning by doing from the story without introducing some other mechanism, such as research introducing some other mechanism, such as research and development, that would preserve the and development, that would preserve the endogeneityendogeneity of technological progress ... of technological progress ...

… … takes us back to the takes us back to the neoclassicalneoclassicalworld of world of exogenousexogenous growth growth

… … takes us back to the takes us back to the neoclassicalneoclassicalworld of world of exogenousexogenous growth growth

The neoclassical model again

Compare and contrast Compare and contrast endogenousendogenous growth with growth withthe neoclassical model of the neoclassical model of exogenousexogenous growth growthCompare and contrast Compare and contrast endogenousendogenous growth with growth withthe neoclassical model of the neoclassical model of exogenousexogenous growth growth

Let us now describe the Let us now describe the workings of the neoclassical workings of the neoclassical model in a few figures, model in a few figures, focusing first onfocusing first on

Let us now describe the Let us now describe the workings of the neoclassical workings of the neoclassical model in a few figures, model in a few figures, focusing first onfocusing first on

• the level of output per capitathe level of output per capita• the level of output per capitathe level of output per capita

• capital per workercapital per worker• capital per workercapital per worker

• rate of growth of output per headrate of growth of output per head• rate of growth of output per headrate of growth of output per head

• efficiencyefficiency• efficiencyefficiency

This will enable us to This will enable us to explore in more detail explore in more detail the qualitative and the qualitative and quantitative quantitative differences and differences and similarities between similarities between endogenous and endogenous and exogenous economic exogenous economic growthgrowth

This will enable us to This will enable us to explore in more detail explore in more detail the qualitative and the qualitative and quantitative quantitative differences and differences and similarities between similarities between endogenous and endogenous and exogenous economic exogenous economic growthgrowth

… … and then on theand then on the… … and then on theand then on the

Let’s take a glimpse at Let’s take a glimpse at Figure 3.8Figure 3.8Let’s take a glimpse at Let’s take a glimpse at Figure 3.8Figure 3.8

Exogenous Growth:Exogenous Growth:Determination of Capital Per Determination of Capital Per Worker and Output Per HeadWorker and Output Per Head

Outputper head

Outputper head


P

C

Output/capital ratio

Identical to Figure 3.5Identical to Figure 3.5

… shows a production function relating output per capita to capital per worker with diminishing returns

… shows a production function relating output per capita to capital per worker with diminishing returns

Fig 3.8Fig 3.8


Straight line represents the Straight line represents the capital/output ratiocapital/output ratioStraight line represents the Straight line represents the capital/output ratiocapital/output ratio

Harrod and Domar Harrod and Domar assumed the assumed the capital/output ratiocapital/output ratio to be fixed, without to be fixed, without an adequate an adequate explanationexplanation

Harrod and Domar Harrod and Domar assumed the assumed the capital/output ratiocapital/output ratio to be fixed, without to be fixed, without an adequate an adequate explanationexplanation

This made the This made the Harrod-Domar Harrod-Domar model model overdetermined: it overdetermined: it had two equations had two equations and only one and only one unknown or unknown or endogenous endogenous variablevariable

This made the This made the Harrod-Domar Harrod-Domar model model overdetermined: it overdetermined: it had two equations had two equations and only one and only one unknown or unknown or endogenous endogenous variablevariable

Then Solow came Then Solow came along and made along and made the the capital/output capital/output ratio ratio endogenous endogenous and found it to and found it to be fixed in the be fixed in the long runlong run

Then Solow came Then Solow came along and made along and made the the capital/output capital/output ratio ratio endogenous endogenous and found it to and found it to be fixed in the be fixed in the long runlong run


Solow showed that Solow showed that when the capital stock when the capital stock increases more than is increases more than is necessary for it to keep necessary for it to keep up with ...up with ...

Solow showed that Solow showed that when the capital stock when the capital stock increases more than is increases more than is necessary for it to keep necessary for it to keep up with ...up with ...

population growthpopulation growthpopulation growthpopulation growth

productivity gainsproductivity gainsproductivity gainsproductivity gains

depreciatiodepreciationndepreciatiodepreciationn

… … then the then the capital/outpucapital/outputtratio ratio increasesincreases

… … then the then the capital/outpucapital/outputtratio ratio increasesincreases

Diminishing returns to capitalDiminishing returns to capitalDiminishing returns to capitalDiminishing returns to capital Output increases more slowly than Output increases more slowly than capitalcapitalOutput increases more slowly than Output increases more slowly than capitalcapital

The The capital/output ratiocapital/output ratio slows down little by slows down little by littlelittleThe The capital/output ratiocapital/output ratio slows down little by slows down little by littlelittle… … until it stops when the until it stops when the long-run equilibrium growth pathlong-run equilibrium growth path has has been reachedbeen reached… … until it stops when the until it stops when the long-run equilibrium growth pathlong-run equilibrium growth path has has been reachedbeen reached

Along this path, output, capital, Along this path, output, capital, and labour in efficiency units all and labour in efficiency units all grow at the same rate, which is grow at the same rate, which is exogenously given by exogenously given by technological progresstechnological progress

Along this path, output, capital, Along this path, output, capital, and labour in efficiency units all and labour in efficiency units all grow at the same rate, which is grow at the same rate, which is exogenously given by exogenously given by technological progresstechnological progress

What does What does that mean?that mean?What does What does that mean?that mean?


This means that the level of This means that the level of savingsaving and and investmentinvestment forthcoming is just sufficient to forthcoming is just sufficient to keep capital growing at the same pace as keep capital growing at the same pace as output and quality-adjusted labour - i.e. to output and quality-adjusted labour - i.e. to keep up with ...keep up with ...

This means that the level of This means that the level of savingsaving and and investmentinvestment forthcoming is just sufficient to forthcoming is just sufficient to keep capital growing at the same pace as keep capital growing at the same pace as output and quality-adjusted labour - i.e. to output and quality-adjusted labour - i.e. to keep up with ...keep up with ...

population growthpopulation growthpopulation growthpopulation growth

productivity growthproductivity growthproductivity growthproductivity growth

depreciationdepreciationdepreciationdepreciation

In Figure 3.8, we In Figure 3.8, we assume that this assume that this adjustment process adjustment process has been completed, has been completed, so that the C line so that the C line reflects a constant reflects a constant capital/output ratio in capital/output ratio in long-run equilibrium long-run equilibrium

In Figure 3.8, we In Figure 3.8, we assume that this assume that this adjustment process adjustment process has been completed, has been completed, so that the C line so that the C line reflects a constant reflects a constant capital/output ratio in capital/output ratio in long-run equilibrium long-run equilibrium

The point of The point of intersection between intersection between the production function the production function and the C line shows and the C line shows the corresponding the corresponding long-run equilibrium long-run equilibrium values of output per values of output per head and capital per head and capital per headhead

The point of The point of intersection between intersection between the production function the production function and the C line shows and the C line shows the corresponding the corresponding long-run equilibrium long-run equilibrium values of output per values of output per head and capital per head and capital per headhead

By contrast, the By contrast, the equilibrium point in equilibrium point in Figure 3.5 reflects Figure 3.5 reflects both short-run and both short-run and long-run equilibriumlong-run equilibrium

By contrast, the By contrast, the equilibrium point in equilibrium point in Figure 3.5 reflects Figure 3.5 reflects both short-run and both short-run and long-run equilibriumlong-run equilibrium

Let us now experimentLet us now experiment

Exogenous Growth:Exogenous Growth:Determination of Capital Per Determination of Capital Per Worker and Output Per Head, AgainWorker and Output Per Head, Again

Outputper head

Outputper head


P

C

Output/capital ratio

Identical to Figure 3.5Identical to Figure 3.5

Fig 3.8Fig 3.8

The level of income per headwith exogenous growth

Summarize the main implications of Summarize the main implications of exogenous-growth theory with the aid of a exogenous-growth theory with the aid of a simple diagramsimple diagram … … trace the trace the

effects of certain effects of certain exogenous eventsexogenous events on on output per output per headhead and and capital capital per workerper worker, both , both of which are of which are endogenousendogenous

Experiment 1:Experiment 1: Saving rate Saving rate




Experiment 5: Technological progress

Exogenous Growth:An Increase in the Saving Rate Increases Capital Per Worker and Output Per Head

Outputper head

Outputper head


AB

C’C

P

The economy moves gradually The economy moves gradually from its initial long-run equilibrium from its initial long-run equilibrium point A to its new long-run point A to its new long-run equilibrium point Bequilibrium point B

The economy moves gradually The economy moves gradually from its initial long-run equilibrium from its initial long-run equilibrium point A to its new long-run point A to its new long-run equilibrium point Bequilibrium point B

Fig 3.9Fig 3.9

Experiment 1

Experiment 1: The saving Experiment 1: The saving raterate

How do output per head and capital per How do output per head and capital per worker react to an increase in the saving worker react to an increase in the saving rate?rate?

Saving equals investmentSaving equals investment

When the saving rate increases ...When the saving rate increases ...

… … the capital stock begins tothe capital stock begins to rise more rapidly than rise more rapidly than beforebefore

The capital/output ratio begins to The capital/output ratio begins to increase …increase …

… … clockwise rotationclockwise rotation of the C line to C’ of the C line to C’

Look at Figure 3.9Look at Figure 3.9

Experiment 1: The saving rateExperiment 1: The saving rate

This happens graduallyThis happens graduallyThis happens graduallyThis happens gradually

Important distinction Important distinction between the short run and between the short run and the long runthe long run

Important distinction Important distinction between the short run and between the short run and the long runthe long runWhen the new long-run When the new long-run equilibrium has been equilibrium has been reached, the growth of reached, the growth of output per headoutput per headis again equal to the rate of is again equal to the rate of technological progresstechnological progress

When the new long-run When the new long-run equilibrium has been equilibrium has been reached, the growth of reached, the growth of output per headoutput per headis again equal to the rate of is again equal to the rate of technological progresstechnological progress

The stimulating effect of an The stimulating effect of an increase in the saving rate increase in the saving rate on growth is, therefore, on growth is, therefore, temporarytemporary

The stimulating effect of an The stimulating effect of an increase in the saving rate increase in the saving rate on growth is, therefore, on growth is, therefore, temporarytemporary

Output grows more Output grows more rapidly than before as rapidly than before as long as it takes the long as it takes the economy to move from economy to move from the old to the new long-the old to the new long-run equilibrium, but run equilibrium, but thereafter economic thereafter economic growth will be the same growth will be the same as it was before the as it was before the increase in the saving increase in the saving rate, which started the rate, which started the processprocess

Output grows more Output grows more rapidly than before as rapidly than before as long as it takes the long as it takes the economy to move from economy to move from the old to the new long-the old to the new long-run equilibrium, but run equilibrium, but thereafter economic thereafter economic growth will be the same growth will be the same as it was before the as it was before the increase in the saving increase in the saving rate, which started the rate, which started the processprocess

Exogenous Growth:An Increase in Static Efficiency Increases Capital Per Worker and Output Per Head

Outputper head

Outputper head


A

B

P

P’C

Point B drifts north-Point B drifts north-easteastalong the C line at the along the C line at the rate of technological rate of technological progressprogress

Fig 3.10Fig 3.10

Experiment 2

Experiment 2: EfficiencyExperiment 2: Efficiency

Effects of an increaseEffects of an increasein static efficiencyin static efficiencyEffects of an increaseEffects of an increasein static efficiencyin static efficiency

… … shifts the production function upwardsshifts the production function upwards

… … increases saving and investmentincreases saving and investment

… … leads the capital stock to begin to rise leads the capital stock to begin to rise more rapidly than before - more rapidly more rapidly than before - more rapidly than is necessary for it just to keep up with than is necessary for it just to keep up with population, technical progress, and population, technical progress, and depreciationdepreciation

… … leads the capital stock to begin to rise leads the capital stock to begin to rise more rapidly than before - more rapidly more rapidly than before - more rapidly than is necessary for it just to keep up with than is necessary for it just to keep up with population, technical progress, and population, technical progress, and depreciationdepreciation

… … output per head and capital per worker output per head and capital per worker both increase from the original long-run both increase from the original long-run equilibrium A to the new long-run equilibrium A to the new long-run equilibrium Bequilibrium B

… … output per head and capital per worker output per head and capital per worker both increase from the original long-run both increase from the original long-run equilibrium A to the new long-run equilibrium A to the new long-run equilibrium Bequilibrium B

Increase in static Increase in static efficiency produces a efficiency produces a temporary boost to temporary boost to economic growtheconomic growth

Increase in static Increase in static efficiency produces a efficiency produces a temporary boost to temporary boost to economic growtheconomic growth

… … but once point B has but once point B has been reached, per been reached, per capita growth is again capita growth is again constrained by the constrained by the exogenously given rate exogenously given rate of technical progressof technical progress

… … but once point B has but once point B has been reached, per been reached, per capita growth is again capita growth is again constrained by the constrained by the exogenously given rate exogenously given rate of technical progressof technical progressPoint B drifts north-east Point B drifts north-east along the C line at the along the C line at the rate of technological rate of technological progressprogress

Point B drifts north-east Point B drifts north-east along the C line at the along the C line at the rate of technological rate of technological progressprogress

Exogenous Growth:An Increase in Population Growth or in Depreciation Reduces Capital Per Worker and Output Per Head

Outputper head

Outputper head


BA

CC’

P

The capital/labour ratio The capital/labour ratio begins to fall, so that output begins to fall, so that output per capita and capital per per capita and capital per worker also begin to fall worker also begin to fall towards point Btowards point B

The capital/labour ratio The capital/labour ratio begins to fall, so that output begins to fall, so that output per capita and capital per per capita and capital per worker also begin to fall worker also begin to fall towards point Btowards point B

But once the adjustment has been But once the adjustment has been completed, the rate of growth of output completed, the rate of growth of output

equals the rate of population growth equals the rate of population growth plus the exogenous rate of plus the exogenous rate of

technological progresstechnological progress

Fig 3.11Fig 3.11

Experiment 3


How do output per head and How do output per head and capital per worker react to capital per worker react to an increase in population an increase in population growth?growth?

How do output per head and How do output per head and capital per worker react to capital per worker react to an increase in population an increase in population growth?growth?

The economy is originally in long-The economy is originally in long-run equilibrium at point A in run equilibrium at point A in Figure 3.11Figure 3.11

Then the labour force begins Then the labour force begins to rise more rapidly than to rise more rapidly than beforebefore

Then the labour force begins Then the labour force begins to rise more rapidly than to rise more rapidly than beforebefore

This means that the current This means that the current level of saving and investment level of saving and investment is no longer enough to is no longer enough to maintain the same amount of maintain the same amount of capital per worker as at point capital per worker as at point AA

This means that the current This means that the current level of saving and investment level of saving and investment is no longer enough to is no longer enough to maintain the same amount of maintain the same amount of capital per worker as at point capital per worker as at point AA

The capital/labour ratio The capital/labour ratio begins to fall, so that begins to fall, so that output per capita and output per capita and capital per worker also capital per worker also begin to fall towards begin to fall towards point Bpoint B

The capital/labour ratio The capital/labour ratio begins to fall, so that begins to fall, so that output per capita and output per capita and capital per worker also capital per worker also begin to fall towards begin to fall towards point Bpoint B

Output per head falls less Output per head falls less than capital per worker, so than capital per worker, so that the capital/output ratio that the capital/output ratio increasesincreases

Output per head falls less Output per head falls less than capital per worker, so than capital per worker, so that the capital/output ratio that the capital/output ratio increasesincreases

This is shown by the This is shown by the counter-clockwise counter-clockwise rotation of the C line to rotation of the C line to C’C’

This is shown by the This is shown by the counter-clockwise counter-clockwise rotation of the C line to rotation of the C line to C’C’


The adjustment process takes timeThe adjustment process takes timeThe adjustment process takes timeThe adjustment process takes time

As long as it takes the economy to move from A to B, output has to As long as it takes the economy to move from A to B, output has to grow less rapidly than the labour force to make it possible for output grow less rapidly than the labour force to make it possible for output per worker to fallper worker to fall

As long as it takes the economy to move from A to B, output has to As long as it takes the economy to move from A to B, output has to grow less rapidly than the labour force to make it possible for output grow less rapidly than the labour force to make it possible for output per worker to fallper worker to fall

With technological progress, output With technological progress, output has to grow less rapidly than the has to grow less rapidly than the labour force in efficiency units to labour force in efficiency units to complete the process of adjustment complete the process of adjustment from A to Bfrom A to B

With technological progress, output With technological progress, output has to grow less rapidly than the has to grow less rapidly than the labour force in efficiency units to labour force in efficiency units to complete the process of adjustment complete the process of adjustment from A to Bfrom A to B

But once the adjustment has been But once the adjustment has been completed, the rate of completed, the rate of growth of growth of outputoutput equals the rate of equals the rate of population growthpopulation growth plus the plus the exogenous rate of exogenous rate of technological technological progressprogress

But once the adjustment has been But once the adjustment has been completed, the rate of completed, the rate of growth of growth of outputoutput equals the rate of equals the rate of population growthpopulation growth plus the plus the exogenous rate of exogenous rate of technological technological progressprogress

Output, therefore, grows Output, therefore, grows more rapidly than before more rapidly than before because population because population growth has increasedgrowth has increased

Output, therefore, grows Output, therefore, grows more rapidly than before more rapidly than before because population because population growth has increasedgrowth has increased

… … but the rate of but the rate of growth of output per growth of output per head is unchanged head is unchanged because technological because technological progress is givenprogress is given

… … but the rate of but the rate of growth of output per growth of output per head is unchanged head is unchanged because technological because technological progress is givenprogress is given

Exogenous Growth:An Increase in Population Growth or in Depreciation Reduces Capital Per Worker and Output Per Head

Output per

head

Output per

head


BA

CC’

P

The current level of saving and The current level of saving and investment is no longer enough to investment is no longer enough to keep the capital stock per worker keep the capital stock per worker intactintact

The capital/labour The capital/labour ratio begins to decline ratio begins to decline and output per head and output per head also fallsalso falls

Fig 3.11Fig 3.11

Experiment 4

Experiment 4: DepreciationExperiment 4: Depreciation

The capital stock begins to depreciate more rapidly than The capital stock begins to depreciate more rapidly than beforebeforeThe capital stock begins to depreciate more rapidly than The capital stock begins to depreciate more rapidly than beforebefore

The current level of The current level of saving and investment is saving and investment is no longer enough to keep no longer enough to keep the capital stock per the capital stock per worker intactworker intact

The current level of The current level of saving and investment is saving and investment is no longer enough to keep no longer enough to keep the capital stock per the capital stock per worker intactworker intact

More depreciation and more More depreciation and more population growth both population growth both render the current level of render the current level of capital formation insufficient capital formation insufficient to maintain the existing to maintain the existing capital/labour ratiocapital/labour ratio

More depreciation and more More depreciation and more population growth both population growth both render the current level of render the current level of capital formation insufficient capital formation insufficient to maintain the existing to maintain the existing capital/labour ratiocapital/labour ratio

More depreciation erodes More depreciation erodes the numerator of the the numerator of the ratio over time, while ratio over time, while more population growth more population growth accelerates the accelerates the denominatordenominator

More depreciation erodes More depreciation erodes the numerator of the the numerator of the ratio over time, while ratio over time, while more population growth more population growth accelerates the accelerates the denominatordenominator

The capital/labour ratio The capital/labour ratio begins to decline, and begins to decline, and output per head also output per head also fallsfalls

The capital/labour ratio The capital/labour ratio begins to decline, and begins to decline, and output per head also output per head also fallsfalls

Exogenous Growth:An Increase in Dynamic Efficiency (Technological Progress) Increases Capital Per Worker and Output Per Head

Outputper head

Outputper head


B

A

C

C’

P

P’

Capital per Capital per worker worker inin efficiency unitsefficiency units fallsfalls

Fig 3.12Fig 3.12

Experiment 5

Experiment 5: Experiment 5: Technological progressTechnological progress

Increased dynamic efficiencyIncreased dynamic efficiency… … increase in the rate of technological increase in the rate of technological progressprogress

Affects capital per worker Affects capital per worker and output per head in and output per head in two waystwo ways

1.1. The production function The production function begins to drift upwards at faster begins to drift upwards at faster pace than beforepace than before

1.1. The production function The production function begins to drift upwards at faster begins to drift upwards at faster pace than beforepace than before

2.2. The current level of saving The current level of saving and investment no longer and investment no longer suffices to maintain capital in suffices to maintain capital in its original equilibrium its original equilibrium proportion to labour in proportion to labour in efficiency unitsefficiency units

2.2. The current level of saving The current level of saving and investment no longer and investment no longer suffices to maintain capital in suffices to maintain capital in its original equilibrium its original equilibrium proportion to labour in proportion to labour in efficiency unitsefficiency units

… … because the because the quality, i.e. quality, i.e. efficiency, of labour efficiency, of labour is now improving is now improving more rapidly than more rapidly than beforebefore

… … because the because the quality, i.e. quality, i.e. efficiency, of labour efficiency, of labour is now improving is now improving more rapidly than more rapidly than beforebeforeCapital per worker Capital per worker in efficiency units in efficiency units fallsfalls

Capital per worker Capital per worker in efficiency units in efficiency units fallsfalls

Experiment 5: Experiment 5: Technological progressTechnological progress

Notice the Notice the symmetrysymmetryNotice the Notice the symmetrysymmetry

If population growth, If population growth, depreciation, or depreciation, or technological progress technological progress increase, then the current increase, then the current amount of saving and amount of saving and investment needed to investment needed to maintain capital in its maintain capital in its original equilibrium original equilibrium proportion to labour in proportion to labour in efficiency units increases, efficiency units increases, leaving less for the leaving less for the accumulation of fresh accumulation of fresh capital, which means that capital, which means that the capital/output ratio the capital/output ratio declinesdeclines

If population growth, If population growth, depreciation, or depreciation, or technological progress technological progress increase, then the current increase, then the current amount of saving and amount of saving and investment needed to investment needed to maintain capital in its maintain capital in its original equilibrium original equilibrium proportion to labour in proportion to labour in efficiency units increases, efficiency units increases, leaving less for the leaving less for the accumulation of fresh accumulation of fresh capital, which means that capital, which means that the capital/output ratio the capital/output ratio declinesdeclines

The C line rotates counter-The C line rotates counter-clockwise to C’clockwise to C’The C line rotates counter-The C line rotates counter-clockwise to C’clockwise to C’

Increased technological progressIncreased technological progressIncreased technological progressIncreased technological progress

The production function The production function shifts from P to P’shifts from P to P’The production function The production function shifts from P to P’shifts from P to P’

… … so that a new so that a new equilibrium is ultimately equilibrium is ultimately reached at B, which then reached at B, which then continues to drift north-continues to drift north-east along the new C’ lineeast along the new C’ line

… … so that a new so that a new equilibrium is ultimately equilibrium is ultimately reached at B, which then reached at B, which then continues to drift north-continues to drift north-east along the new C’ lineeast along the new C’ line

Increased dynamic Increased dynamic efficiency increases both efficiency increases both capital per worker and capital per worker and output per headoutput per head

Increased dynamic Increased dynamic efficiency increases both efficiency increases both capital per worker and capital per worker and output per headoutput per head

Summary of experiments

An increase in theAn increase in the saving ratesaving rate

increases output per headincreases output per head

An increase inAn increase in static efficiencystatic efficiency


IncreasedIncreased depreciationdepreciation reducesreduces

output per headoutput per head

IncreasedIncreased population growthpopulation growth

reduces output per headreduces output per head

An increase inAn increase in dynamic efficiencydynamic efficiency


An increase in theAn increase in the saving ratesaving rate


An increase inAn increase in static efficiencystatic efficiency


IncreasedIncreased depreciationdepreciation reducesreduces

output per headoutput per head

IncreasedIncreased population growthpopulation growth

reduces output per headreduces output per head

An increase inAn increase in dynamic efficiencydynamic efficiency


(Fig 3.9)

(Fig 3.10)

(Fig 3.11)

(Fig 3.11)

(Fig 3.12)

(Fig 3.9)

(Fig 3.10)

(Fig 3.11)

(Fig 3.11)

(Fig 3.12)


The long-run equilibrium level of output per capita The long-run equilibrium level of output per capita depends on depends on The long-run equilibrium level of output per capita The long-run equilibrium level of output per capita depends on depends on Saving rateSaving rateSaving rateSaving rate Static efficiencyStatic efficiencyStatic efficiencyStatic efficiency DepreciatioDepreciatio

nnDepreciatioDepreciationn

Population growthPopulation growthPopulation growthPopulation growth

… … as well as onas well as on… … as well as onas well as on

Dynamic efficiency Dynamic efficiency Dynamic efficiency Dynamic efficiency

… … even if the long-run even if the long-run equilibrium rate of growth of equilibrium rate of growth of output per head depends output per head depends solely on dynamic efficiency solely on dynamic efficiency - i.e. technological progress- i.e. technological progress

… … even if the long-run even if the long-run equilibrium rate of growth of equilibrium rate of growth of output per head depends output per head depends solely on dynamic efficiency solely on dynamic efficiency - i.e. technological progress- i.e. technological progress

So, even if a higher saving So, even if a higher saving rate and so on has no effect rate and so on has no effect on the long-run rate of on the long-run rate of growth of output, it does growth of output, it does affect the affect the level of outputlevel of output in in the long runthe long run

So, even if a higher saving So, even if a higher saving rate and so on has no effect rate and so on has no effect on the long-run rate of on the long-run rate of growth of output, it does growth of output, it does affect the affect the level of outputlevel of output in in the long runthe long run

This raises two questionsThis raises two questionsThis raises two questionsThis raises two questions


FirstFirstFirstFirst

How sensitive is the level of output per head?How sensitive is the level of output per head?- to variations in ...- to variations in ...How sensitive is the level of output per head?How sensitive is the level of output per head?- to variations in ...- to variations in ...

Saving rateSaving rateSaving rateSaving rate Static efficiencyStatic efficiency DepreciationDepreciation Population growthPopulation growthPopulation growthPopulation growth

Is it, in particular, Is it, in particular, sensitive enough for sensitive enough for us to be able on that us to be able on that basis to account for basis to account for the observed the observed differences in living differences in living standards across standards across countries?countries?

Is it, in particular, Is it, in particular, sensitive enough for sensitive enough for us to be able on that us to be able on that basis to account for basis to account for the observed the observed differences in living differences in living standards across standards across countries?countries?

That would mean That would mean that economic that economic performance over performance over long periods long periods depends after all on depends after all on economic variables economic variables in addition to in addition to techno-logical techno-logical progressprogress

That would mean That would mean that economic that economic performance over performance over long periods long periods depends after all on depends after all on economic variables economic variables in addition to in addition to techno-logical techno-logical progressprogress

Which, if true, makes Which, if true, makes the exogeneity of the exogeneity of economic growth in economic growth in the long run the long run according to the according to the Solow model less Solow model less binding than it binding than it otherwise would beotherwise would be

Which, if true, makes Which, if true, makes the exogeneity of the exogeneity of economic growth in economic growth in the long run the long run according to the according to the Solow model less Solow model less binding than it binding than it otherwise would beotherwise would be


SecondSecondSecondSecondIf an increase in the If an increase in the saving rate or in static saving rate or in static efficiency or a decrease efficiency or a decrease in depreciation provides in depreciation provides only a temporary boost only a temporary boost to economic growthto economic growth

If an increase in the If an increase in the saving rate or in static saving rate or in static efficiency or a decrease efficiency or a decrease in depreciation provides in depreciation provides only a temporary boost only a temporary boost to economic growthto economic growth

… … and thus increases and thus increases eco-nomic growth per eco-nomic growth per capita only in the capita only in the medium term ...medium term ...

… … and thus increases and thus increases eco-nomic growth per eco-nomic growth per capita only in the capita only in the medium term ...medium term ...

… … then how then how long does it long does it take?take? How How long is the long is the medium term?medium term?

… … then how then how long does it long does it take?take? How How long is the long is the medium term?medium term?

If the medium term proves If the medium term proves totolast long, then the last long, then the neoclassical conclusion neoclassical conclusion that economic growth is that economic growth is independent of the saving independent of the saving rate, static efficiency, and rate, static efficiency, and depreciation in the long depreciation in the long run becomes less arresting run becomes less arresting than otherwisethan otherwise

If the medium term proves If the medium term proves totolast long, then the last long, then the neoclassical conclusion neoclassical conclusion that economic growth is that economic growth is independent of the saving independent of the saving rate, static efficiency, and rate, static efficiency, and depreciation in the long depreciation in the long run becomes less arresting run becomes less arresting than otherwisethan otherwise

For the concept of For the concept of long-run equilibrium long-run equilibrium to be interesting and to be interesting and relevant from an relevant from an economic point of economic point of view, it must not be view, it must not be too remotetoo remote

For the concept of For the concept of long-run equilibrium long-run equilibrium to be interesting and to be interesting and relevant from an relevant from an economic point of economic point of view, it must not be view, it must not be too remotetoo remote

The longer the The longer the road to the road to the long run, the long run, the more it more it matters what matters what happens along happens along the way at a the way at a given speedgiven speed

The longer the The longer the road to the road to the long run, the long run, the more it more it matters what matters what happens along happens along the way at a the way at a given speedgiven speed

How strong? How long?

How large are the effects of more How large are the effects of more savingsaving, more , more efficiencyefficiency, and less , and less depreciationdepreciation on output per capita on output per capita likely to be?likely to be?

How large are the effects of more How large are the effects of more savingsaving, more , more efficiencyefficiency, and less , and less depreciationdepreciation on output per capita on output per capita likely to be?likely to be?

How far can the SHow far can the S olow model take olow model take us towards a full accounting for the us towards a full accounting for the differences in income per head that can differences in income per head that can be observed in the world?be observed in the world?

How far can the SHow far can the S olow model take olow model take us towards a full accounting for the us towards a full accounting for the differences in income per head that can differences in income per head that can be observed in the world?be observed in the world?We must establish the observed We must establish the observed income differences that we want to income differences that we want to explainexplain

We must establish the observed We must establish the observed income differences that we want to income differences that we want to explainexplainWe want our model to be able to explain, say, 30-fold to We want our model to be able to explain, say, 30-fold to 60-fold differences in the level of output per capita 60-fold differences in the level of output per capita across countriesacross countries

We want our model to be able to explain, say, 30-fold to We want our model to be able to explain, say, 30-fold to 60-fold differences in the level of output per capita 60-fold differences in the level of output per capita across countriesacross countries

Can the Solow model do this?Can the Solow model do this?

SwitzerlandSwitzerlandSwitzerlandSwitzerland

MozambiqueMozambiqueMozambiqueMozambique

United StatesUnited StatesUnited StatesUnited States

EthiopiaEthiopiaEthiopiaEthiopia

Depreciationrate = 0.08

Saving rate0.1

Saving rate0.2

Saving rate0.3

Saving rate0.4

Generalefficiency 1

1.00 1.41 1.73 2.00

Generalefficiency 2

2.83 4.00 4.90 5.66

Generalefficiency 3

5.20 7.35 9.00 10.39

Generalefficiency 4

8.00 11.31 13.86 16.00

How Output Per Head Varies with the Saving Rate and General EfficiencyTable 3.4Table 3.4


The Solow model is The Solow model is versatile enough to be versatile enough to be able to account for at able to account for at least a good deal of the least a good deal of the income differencesincome differences that that we observe around the we observe around the worldworld

The Solow model is The Solow model is versatile enough to be versatile enough to be able to account for at able to account for at least a good deal of the least a good deal of the income differencesincome differences that that we observe around the we observe around the worldworld

Notice that the figures Notice that the figures in Table 3.4 refer to in Table 3.4 refer to long-run equilibrium long-run equilibrium levelslevels of output per of output per capitacapita

Notice that the figures Notice that the figures in Table 3.4 refer to in Table 3.4 refer to long-run equilibrium long-run equilibrium levelslevels of output per of output per capitacapita

Insofar as individual countries have yet to reach their Insofar as individual countries have yet to reach their long-run equilibrium, their current income differences long-run equilibrium, their current income differences may be larger than those which ultimately will emerge may be larger than those which ultimately will emerge in the in the long runlong run

Insofar as individual countries have yet to reach their Insofar as individual countries have yet to reach their long-run equilibrium, their current income differences long-run equilibrium, their current income differences may be larger than those which ultimately will emerge may be larger than those which ultimately will emerge in the in the long runlong run

Which brings us to the next questionWhich brings us to the next question


How long does it take a How long does it take a country to reach its long-run country to reach its long-run equilibrium?equilibrium?

How long does it take a How long does it take a country to reach its long-run country to reach its long-run equilibrium?equilibrium?

How long does it take the How long does it take the capital stockcapital stock, and , and hencehencealso output and the also output and the capital/output ratiocapital/output ratio, to , to move tomove tothe long-run equilibrium identified by Solow?the long-run equilibrium identified by Solow?

How long does it take the How long does it take the capital stockcapital stock, and , and hencehencealso output and the also output and the capital/output ratiocapital/output ratio, to , to move tomove tothe long-run equilibrium identified by Solow?the long-run equilibrium identified by Solow?If the economy happens initially to be out of If the economy happens initially to be out of equilibrium or it is thrown out of pre-existing equilibrium or it is thrown out of pre-existing equilibrium by some exogenous event, say, a equilibrium by some exogenous event, say, a change in the saving rate or a technological change in the saving rate or a technological innovation ...innovation ...

If the economy happens initially to be out of If the economy happens initially to be out of equilibrium or it is thrown out of pre-existing equilibrium or it is thrown out of pre-existing equilibrium by some exogenous event, say, a equilibrium by some exogenous event, say, a change in the saving rate or a technological change in the saving rate or a technological innovation ...innovation ...

... what then?... what then?... what then?... what then?


It turns out that the It turns out that the adjustment mechanism is adjustment mechanism is rather slow. It takes a long rather slow. It takes a long time - decades! - for the time - decades! - for the economy to travel to its new economy to travel to its new long-run equilibriumlong-run equilibrium

It turns out that the It turns out that the adjustment mechanism is adjustment mechanism is rather slow. It takes a long rather slow. It takes a long time - decades! - for the time - decades! - for the economy to travel to its new economy to travel to its new long-run equilibriumlong-run equilibrium

This result holds for a This result holds for a wide range of wide range of reasonable estimates reasonable estimates of the exogenous of the exogenous parameters of the parameters of the Solow modelSolow model

This result holds for a This result holds for a wide range of wide range of reasonable estimates reasonable estimates of the exogenous of the exogenous parameters of the parameters of the Solow modelSolow model

Fundamental implication:Fundamental implication:Fundamental implication:Fundamental implication:

Saving rate risesSaving rate risesSaving rate risesSaving rate rises … … and the capital stock and the capital stock accordingly begins to rise to a new, accordingly begins to rise to a new, higher equilibrium levelhigher equilibrium level

… … and the capital stock and the capital stock accordingly begins to rise to a new, accordingly begins to rise to a new, higher equilibrium levelhigher equilibrium level

… … output also begins to riseoutput also begins to rise… … output also begins to riseoutput also begins to rise

Output and capital keep rising as long as it Output and capital keep rising as long as it takes the adjustment mechanism to be takes the adjustment mechanism to be completed completed

Output and capital keep rising as long as it Output and capital keep rising as long as it takes the adjustment mechanism to be takes the adjustment mechanism to be completed completed Decades!Decades!Decades!Decades!


This means that, after all, This means that, after all, increased increased savingsaving is capable of is capable of stimulating economic growth stimulating economic growth for a long time, even if, for a long time, even if, ultimately, per capita growth ultimately, per capita growth depends solely on technological depends solely on technological progressprogress

This means that, after all, This means that, after all, increased increased savingsaving is capable of is capable of stimulating economic growth stimulating economic growth for a long time, even if, for a long time, even if, ultimately, per capita growth ultimately, per capita growth depends solely on technological depends solely on technological progressprogress

The same applies to an The same applies to an increase in increase in static efficiencystatic efficiency or a decrease in or a decrease in depreciationdepreciation: their effects on : their effects on economic growth can last a economic growth can last a long time, even if they peter long time, even if they peter out in the endout in the end

The same applies to an The same applies to an increase in increase in static efficiencystatic efficiency or a decrease in or a decrease in depreciationdepreciation: their effects on : their effects on economic growth can last a economic growth can last a long time, even if they peter long time, even if they peter out in the endout in the end

The almost exclusive focus on The almost exclusive focus on technological changetechnological change as the as the solesoledriving force of economic growth in the long run was driving force of economic growth in the long run was misplacedmisplaced

The almost exclusive focus on The almost exclusive focus on technological changetechnological change as the as the solesoledriving force of economic growth in the long run was driving force of economic growth in the long run was misplacedmisplacedSaving behaviourSaving behaviour, , efficiencyefficiency, and , and depreciationdepreciation can can matter greatly for economic growth and for the matter greatly for economic growth and for the consequent income differences across countries around consequent income differences across countries around the world over long periods, once the Solow model is the world over long periods, once the Solow model is viewed in this lightviewed in this light

Saving behaviourSaving behaviour, , efficiencyefficiency, and , and depreciationdepreciation can can matter greatly for economic growth and for the matter greatly for economic growth and for the consequent income differences across countries around consequent income differences across countries around the world over long periods, once the Solow model is the world over long periods, once the Solow model is viewed in this lightviewed in this light

It takes a long time: The evolution of the capital/output ratio in the Solow model

2,50

2,75

3,00

3,25

3,50

3,75

4,00

0 7 14 21 28 35 42 49 56 63 70 77 84 91 98

Years

Ca

pita

l/out

pu

t ra

tio

Fig 3.13

In this example it takes the capital/output ratio over 100 years to rise from its initial disequilibrium value of 2.5 to its long-run equilibrium value of 4

Exogenous Growth:Exogenous Growth:Determination of Economic Growth and Determination of Economic Growth and EfficiencyEfficiency

It remains to describe the It remains to describe the determination of economic growth determination of economic growth in the Solow model in a few in the Solow model in a few figures ...figures ...

It remains to describe the It remains to describe the determination of economic growth determination of economic growth in the Solow model in a few in the Solow model in a few figures ...figures ...

… just as we described the endogenous-growth model in Figures 3.1-3.12

Exogenous Growth:Exogenous Growth:Determination of Economic Growth and Determination of Economic Growth and EfficiencyEfficiency

S

G

Efficiency

Economicgrowth

Economicgrowth

Saving rate

Depreciation

E

Population growth plus Population growth plus technical progresstechnical progress

Fig 3.14Fig 3.14

Exogenous growth and technology

Summarize the main implications Summarize the main implications of exogenous-growth theory with of exogenous-growth theory with the aid of a simple diagramthe aid of a simple diagram

… … trace the effects trace the effects of certain of certain exogenous eventsexogenous events on the rate of on the rate of economic growtheconomic growth and and efficiencyefficiency, both , both of which are of which are endogenousendogenous

Experiment 1:Experiment 1: The saving rate The saving rate




Experiment 5: Technological progress


Exogenous Growth:Exogenous Growth:An Increase in the An Increase in the Saving RateSaving Rate Increases Increases Economic Growth for a Long Time, but Not Economic Growth for a Long Time, but Not ForeverForever

S

G


Economicgrowth

Economicgrowth

G’E’

A

B

C

E

Fig 3.15Fig 3.15

Exogenous Growth:Exogenous Growth:An Increase in An Increase in DepreciationDepreciation Reduces ReducesEconomic Growth for a Long Time, but Not Economic Growth for a Long Time, but Not ForeverForever

EG

Efficiency

Economicgrowth

Economicgrowth

G’

A

B

C

E’

S


Fig 3.16Fig 3.16

Exogenous Growth:Exogenous Growth:An Increase in An Increase in Static EfficiencyStatic Efficiency Increases IncreasesEconomic Growth for a Long Time, but Not Economic Growth for a Long Time, but Not ForeverForever

E’G

Efficiency

E

B

AS

Experiment 3: Static efficiency

Economicgrowth

Economicgrowth

Fig 3.17Fig 3.17

Exogenous Growth:Exogenous Growth:Increased Increased Population GrowthPopulation Growth or or Dynamic Efficiency Dynamic Efficiency (Technological Progress)(Technological Progress) Increases Economic Growth Increases Economic Growth ForeverForever

E’


Economicgrowth

Economicgrowth

GE

B

AS

S’

Experiment 4: Population growthExperiment 5: Technological progress

Fig 3.18Fig 3.18

How much How much should a country should a country save?save?

How much How much should a country should a country save?save?

The optimal share of saving in The optimal share of saving in national income is that which national income is that which allows people as much allows people as much consumption as possible in the consumption as possible in the long runlong run

The optimal share of saving in The optimal share of saving in national income is that which national income is that which allows people as much allows people as much consumption as possible in the consumption as possible in the long runlong runWe must look for an optimum We must look for an optimum somewhere between too little somewhere between too little saving and too muchsaving and too much

We must look for an optimum We must look for an optimum somewhere between too little somewhere between too little saving and too muchsaving and too much

The quest for the optimal The quest for the optimal amount of saving involves amount of saving involves choosing the optimal path choosing the optimal path of consumption over timeof consumption over time

The quest for the optimal The quest for the optimal amount of saving involves amount of saving involves choosing the optimal path choosing the optimal path of consumption over timeof consumption over time

What should the What should the optimal path of a optimal path of a nation’s consumption nation’s consumption look like?look like?

What should the What should the optimal path of a optimal path of a nation’s consumption nation’s consumption look like?look like?One should not accept One should not accept growth that does not at growth that does not at least keep up with the real least keep up with the real interest rateinterest rate

One should not accept One should not accept growth that does not at growth that does not at least keep up with the real least keep up with the real interest rateinterest rate

The appropriate benchmark The appropriate benchmark for optimal growth is not the for optimal growth is not the real interest stripped bare, real interest stripped bare, but rather the real interest but rather the real interest rate net of the subjective rate net of the subjective rate of time preferencerate of time preference

The appropriate benchmark The appropriate benchmark for optimal growth is not the for optimal growth is not the real interest stripped bare, real interest stripped bare, but rather the real interest but rather the real interest rate net of the subjective rate net of the subjective rate of time preferencerate of time preference

How much to save?

How much to save?

Consumption and consumer Consumption and consumer welfare reach a sustainable welfare reach a sustainable maximum over the long runmaximum over the long run

Consumption and consumer Consumption and consumer welfare reach a sustainable welfare reach a sustainable maximum over the long runmaximum over the long run

... when the rate of growth of ... when the rate of growth of consumption and output per consumption and output per capita equals, or is at least capita equals, or is at least proportional to, the real proportional to, the real interest rate adjusted for interest rate adjusted for impatienceimpatience

... when the rate of growth of ... when the rate of growth of consumption and output per consumption and output per capita equals, or is at least capita equals, or is at least proportional to, the real proportional to, the real interest rate adjusted for interest rate adjusted for impatienceimpatienceThis condition for optimal growth This condition for optimal growth actually makes saving directly actually makes saving directly proportional to output, as we have proportional to output, as we have assumed throughoutassumed throughout

This condition for optimal growth This condition for optimal growth actually makes saving directly actually makes saving directly proportional to output, as we have proportional to output, as we have assumed throughoutassumed throughout

It follows that It follows that consumption is also consumption is also proportional to output ...proportional to output ...

It follows that It follows that consumption is also consumption is also proportional to output ...proportional to output ...

… … because consumption because consumption plus saving equals outputplus saving equals output… … because consumption because consumption plus saving equals outputplus saving equals output

This means that This means that consumption, output, and consumption, output, and capital must all grow at the capital must all grow at the same rate in equilibriumsame rate in equilibrium

This means that This means that consumption, output, and consumption, output, and capital must all grow at the capital must all grow at the same rate in equilibriumsame rate in equilibrium

In sum, then, it is in the In sum, then, it is in the interest of consumers to interest of consumers to save that proportion of their save that proportion of their income that maximizes their income that maximizes their consumption over timeconsumption over time

In sum, then, it is in the In sum, then, it is in the interest of consumers to interest of consumers to save that proportion of their save that proportion of their income that maximizes their income that maximizes their consumption over timeconsumption over time

What does What does thisthis mean? mean?

How much to save?

The optimal saving rate thus The optimal saving rate thus chosen from a wide range of chosen from a wide range of available possibilities available possibilities influences capital accumulation influences capital accumulation and hence also the equilibrium and hence also the equilibrium levels of capital per worker and levels of capital per worker and output per headoutput per head

The optimal saving rate thus The optimal saving rate thus chosen from a wide range of chosen from a wide range of available possibilities available possibilities influences capital accumulation influences capital accumulation and hence also the equilibrium and hence also the equilibrium levels of capital per worker and levels of capital per worker and output per headoutput per head

If the optimal saving rate If the optimal saving rate exceeds the current saving exceeds the current saving rate, then the increase in the rate, then the increase in the saving rate necessary to reach saving rate necessary to reach the optimal level affects the optimal level affects economic growth as in Figures economic growth as in Figures 3.2 and 3.153.2 and 3.15

If the optimal saving rate If the optimal saving rate exceeds the current saving exceeds the current saving rate, then the increase in the rate, then the increase in the saving rate necessary to reach saving rate necessary to reach the optimal level affects the optimal level affects economic growth as in Figures economic growth as in Figures 3.2 and 3.153.2 and 3.15

The result that maximum The result that maximum saving is not a sensible saving is not a sensible economic objective economic objective means that maximal means that maximal economic growth is not a economic growth is not a desirable or sensible desirable or sensible objective eitherobjective either

The result that maximum The result that maximum saving is not a sensible saving is not a sensible economic objective economic objective means that maximal means that maximal economic growth is not a economic growth is not a desirable or sensible desirable or sensible objective eitherobjective either

Rather, economic growth Rather, economic growth should be sustained at should be sustained at that rate which permits that rate which permits maximal consumptionmaximal consumption in in the long runthe long run

Rather, economic growth Rather, economic growth should be sustained at should be sustained at that rate which permits that rate which permits maximal consumptionmaximal consumption in in the long runthe long run

This can be achieved by This can be achieved by setting the saving rate setting the saving rate rightright

This can be achieved by This can be achieved by setting the saving rate setting the saving rate rightright

How much to save?

The golden rule ofThe golden rule ofcapital accumulationcapital accumulationThe golden rule ofThe golden rule ofcapital accumulationcapital accumulation

Maximum sustainable consumption Maximum sustainable consumption is achieved by saving capital income is achieved by saving capital income and consuming labour incomeand consuming labour income

Maximum sustainable consumption Maximum sustainable consumption is achieved by saving capital income is achieved by saving capital income and consuming labour incomeand consuming labour income

How high does the How high does the saving rate have to be saving rate have to be for growth to be for growth to be optimal?optimal?

How high does the How high does the saving rate have to be saving rate have to be for growth to be for growth to be optimal?optimal?

a) the share of capital in national a) the share of capital in national income is one-thirdincome is one-thirda) the share of capital in national a) the share of capital in national income is one-thirdincome is one-third

b) output growth equals the real b) output growth equals the real interest rateinterest rateb) output growth equals the real b) output growth equals the real interest rateinterest rate

c) the discount rate equals the c) the discount rate equals the rate of population growthrate of population growthc) the discount rate equals the c) the discount rate equals the rate of population growthrate of population growth

What then?What then?

Let’s suppose:Let’s suppose:Let’s suppose:Let’s suppose:

How much to save?

Then output per head Then output per head grows at the rate of grows at the rate of real interest adjusted real interest adjusted for impatience, as for impatience, as optimal growth optimal growth requiresrequires

Then output per head Then output per head grows at the rate of grows at the rate of real interest adjusted real interest adjusted for impatience, as for impatience, as optimal growth optimal growth requiresrequires

In this case, the optimal In this case, the optimal saving rate equals the saving rate equals the share of capital in share of capital in national income and is, national income and is, therefore, one-third therefore, one-third according to the golden according to the golden rulerule

In this case, the optimal In this case, the optimal saving rate equals the saving rate equals the share of capital in share of capital in national income and is, national income and is, therefore, one-third therefore, one-third according to the golden according to the golden rulerule

How much to save?

Very few countries actually save Very few countries actually save and invest that much of their and invest that much of their incomeincome

Gross domestic investment in 1995:Gross domestic investment in 1995:

Thailand (43% of GNP)Thailand (43% of GNP)

China (40%)China (40%)

Indonesia (38%)Indonesia (38%)

Hong Kong (35%)Hong Kong (35%)

Singapore (33%)Singapore (33%)

Does this mean that consumersDoes this mean that consumersdo not maximize their do not maximize their consumption over time?consumption over time?

On average nations save and invest about 20% of their income

Optimal growth in figures:Experiments

1. The real interest rate1. The real interest rate1. The real interest rate1. The real interest rate

2. Technological progress2. Technological progress2. Technological progress2. Technological progress

3. Population growth3. Population growth3. Population growth3. Population growth

4. Depreciation4. Depreciation4. Depreciation4. Depreciation

5. Impatience5. Impatience5. Impatience5. Impatience

6. Static efficiency6. Static efficiency6. Static efficiency6. Static efficiency

7. Depreciation again7. Depreciation again7. Depreciation again7. Depreciation again

8. Impatience again8. Impatience again8. Impatience again8. Impatience again

9. Population growth again9. Population growth again9. Population growth again9. Population growth again

Exogenous Growth with Optimal Saving:Exogenous Growth with Optimal Saving: Determination of EconomicDetermination of EconomicGrowth and the Growth and the Real Interest RateReal Interest Rate

Real interest rateReal interest rate

Economicgrowth

Economicgrowth

G

S

Impatience minuspopulation growthImpatience minuspopulation growth

Population growthPopulation growthplus technical progressplus technical progressPopulation growthPopulation growthplus technical progressplus technical progress

45°

Fig 3.19Fig 3.19Fig 3.19Fig 3.19

Exogenous Growth with Optimal Saving:Exogenous Growth with Optimal Saving:Increased Increased Technological ProgressTechnological Progress Increases IncreasesEconomic Growth and the Real Interest RateEconomic Growth and the Real Interest Rate


Economicgrowth

Economicgrowth

G

A

B

S

S’

45°

Fig 3.20Fig 3.20Fig 3.20Fig 3.20

Experiment 1

Exogenous Growth with Optimal Saving:Exogenous Growth with Optimal Saving:An Increase in An Increase in Population GrowthPopulation Growth Increases Increases Economic Growth, but Leaves the Real Interest Economic Growth, but Leaves the Real Interest Rate UnchangedRate Unchanged


Economicgrowth

Economicgrowth

G

A

B

S

S’

45°

G’

Fig 3.21Fig 3.21

Experiment 2

Exogenous Growth with Optimal Saving:Exogenous Growth with Optimal Saving:

Increased Increased DepreciationDepreciation Reduces Economic Reduces EconomicGrowth for a Time, but Not ForeverGrowth for a Time, but Not Forever

RG


R’

A

B

S

Economicgrowth

Economicgrowth

Fig 3.22Fig 3.22

Experiment 3

Exogenous Growth with Optimal Saving:Exogenous Growth with Optimal Saving:IncreasedIncreased Patience Patience Increases Economic Growth for Increases Economic Growth fora Time, Reduces the Real Interest Rate, and Leavesa Time, Reduces the Real Interest Rate, and LeavesGrowth Ultimately UnchangedGrowth Ultimately Unchanged


G’

C AS

G

45°

B

RR’

Economicgrowth

Economicgrowth

Fig 3.23Fig 3.23Fig 3.23Fig 3.23

Experiment 4

Endogenous Growth with Optimal Saving:Endogenous Growth with Optimal Saving: Determination of Economic GrowthDetermination of Economic Growthand the and the Real Interest RateReal Interest Rate


Economicgrowth

Economicgrowth

GR

Impatience minuspopulation growthImpatience minuspopulation growth

45°

Fig 3.24Fig 3.24Fig 3.24Fig 3.24

Endogenous Growth with Optimal Endogenous Growth with Optimal Saving:Saving:An Increase in An Increase in EfficiencyEfficiency Increases Economic Increases EconomicGrowth and the Real Interest RateGrowth and the Real Interest Rate


Economicgrowth

Economicgrowth

GR R’

A

B

45°

Fig 3.25Fig 3.25Fig 3.25Fig 3.25

Experiment 5

Endogenous Growth with Optimal Saving:Endogenous Growth with Optimal Saving:An An Increase in DepreciationIncrease in Depreciation Reduces Economic Reduces EconomicGrowth and the Real Interest RateGrowth and the Real Interest Rate


Economicgrowth

Economicgrowth

GR’ R

B

A

45°

Depreciation again

Fig 3.26Fig 3.26Fig 3.26Fig 3.26

Experiment 6

Endogenous Growth with Optimal Saving:Endogenous Growth with Optimal Saving:IncreasedIncreased Patience Patience oror Population Growth Population Growth Increases Increases Economic Growth, but Leaves the Real Interest Rate Economic Growth, but Leaves the Real Interest Rate UnchangedUnchanged


Economicgrowth

Economicgrowth

G’R

A

B G

45°

Impatience again

Population growth again

Fig 3.27Fig 3.27Fig 3.27Fig 3.27

Experiment 7

Experiment 8

Optimal growth in figures

The medium-term effects with The medium-term effects with exogenous growth are exogenous growth are qualitatively the same qualitatively the same throughout as the long-run throughout as the long-run effects with endogenous growtheffects with endogenous growth

The medium-term effects with The medium-term effects with exogenous growth are exogenous growth are qualitatively the same qualitatively the same throughout as the long-run throughout as the long-run effects with endogenous growtheffects with endogenous growth

But quantitatively But quantitatively theytheyare quite differentare quite different

But quantitatively But quantitatively theytheyare quite differentare quite different

The constancy of efficiency gives increased The constancy of efficiency gives increased savingsavingits great power to increase economic growthits great power to increase economic growth

The constancy of efficiency gives increased The constancy of efficiency gives increased savingsavingits great power to increase economic growthits great power to increase economic growth

The effect of increased saving on growth is The effect of increased saving on growth is weakenedweakenedby the consequent increase in the capital/output by the consequent increase in the capital/output ratio, which entails reduced efficiencyratio, which entails reduced efficiency

The effect of increased saving on growth is The effect of increased saving on growth is weakenedweakenedby the consequent increase in the capital/output by the consequent increase in the capital/output ratio, which entails reduced efficiencyratio, which entails reduced efficiency

The The endogenousendogenous-growth model:-growth model:The The endogenousendogenous-growth model:-growth model:

The The exogenousexogenous-growth model:-growth model:The The exogenousexogenous-growth model:-growth model:

Fig 3.28Fig 3.28

0

50

100

150

200

250

300

350

400

450

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Years

Ou

tpu

t p

er

cap

ita

Before

After (Exogenous growth)

After (Endogenous growth)

The first twenty years: The path of output per capita before and after an increase in the saving rate from 15% to 30%

Optimal Economic Growth: Overview of Results

Table 3.5

Economic growthReal interest rateReference

Exogenous growthExogenous growth

Saving rate Zero/plus Minus/zero Fig 3.23

Efficiency (dynamic) Plus Plus Fig 3.20

Depreciation Zero/minus Zero/minus Fig 3.22

Population growth Plus Zero Fig 3.21

Endogenous growthEndogenous growth

Saving rate Plus Zero Fig 3.27

Efficiency (static) Plus Plus Fig 3.25

Depreciation Minus Minus Fig 3.26

Population growth Plus Zero Fig 3.27

Summary

Main messageMain messageMain messageMain message

Not much qualitative difference Not much qualitative difference between endogenous and between endogenous and exogenous growthexogenous growth

Not much qualitative difference Not much qualitative difference between endogenous and between endogenous and exogenous growthexogenous growth

Economic growth depends crucially onEconomic growth depends crucially onEconomic growth depends crucially onEconomic growth depends crucially on

savingsavingsavingsaving efficiencyefficiencyefficiencyefficiency depreciationdepreciationdepreciationdepreciation

Explicit in the theory Explicit in the theory of endogenous of endogenous growthgrowth

Explicit in the theory Explicit in the theory of endogenous of endogenous growthgrowth

Implicit in the theory Implicit in the theory of exogenous growthof exogenous growthImplicit in the theory Implicit in the theory of exogenous growthof exogenous growth

Summary

The time span over which saving and The time span over which saving and efficiency exert a potentiallyefficiency exert a potentiallystrong influence on economic growth ...strong influence on economic growth ...

The time span over which saving and The time span over which saving and efficiency exert a potentiallyefficiency exert a potentiallystrong influence on economic growth ...strong influence on economic growth ...

… … seems long enough toseems long enough tobe interesting and relevantbe interesting and relevantfrom an economic point of from an economic point of

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… … seems long enough toseems long enough tobe interesting and relevantbe interesting and relevantfrom an economic point of from an economic point of

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Questions for reviewQuestions for review

1.1. Does the rate of growth of output per head depend on population Does the rate of growth of output per head depend on population growth? Does the answer to this question depend on whether economic growth? Does the answer to this question depend on whether economic growth is exogenous or endogenous? How? Illustrate your answers with growth is exogenous or endogenous? How? Illustrate your answers with diagrams. Does your analysis imply that countries with small diagrams. Does your analysis imply that countries with small populations ultimately become more - or less? - affluent per capita than populations ultimately become more - or less? - affluent per capita than large (i.e. populous) countries?large (i.e. populous) countries?

2.2. Consider a country that is exposed to an adverse external shock - a Consider a country that is exposed to an adverse external shock - a lasting decline in the price of its main exports, for example. This shock lasting decline in the price of its main exports, for example. This shock lowers the standard of living, and people decide to consume more and lowers the standard of living, and people decide to consume more and save less out of current income, other things being equal. If this change save less out of current income, other things being equal. If this change is permanent, how would you expect it to influence is permanent, how would you expect it to influence

I.I. the rate of growth of output per capita in the long run and the rate of growth of output per capita in the long run and

II.II. the level of income per capita in the long run? the level of income per capita in the long run?

1.1. Does the rate of growth of output per head depend on population Does the rate of growth of output per head depend on population growth? Does the answer to this question depend on whether economic growth? Does the answer to this question depend on whether economic growth is exogenous or endogenous? How? Illustrate your answers with growth is exogenous or endogenous? How? Illustrate your answers with diagrams. Does your analysis imply that countries with small diagrams. Does your analysis imply that countries with small populations ultimately become more - or less? - affluent per capita than populations ultimately become more - or less? - affluent per capita than large (i.e. populous) countries?large (i.e. populous) countries?

2.2. Consider a country that is exposed to an adverse external shock - a Consider a country that is exposed to an adverse external shock - a lasting decline in the price of its main exports, for example. This shock lasting decline in the price of its main exports, for example. This shock lowers the standard of living, and people decide to consume more and lowers the standard of living, and people decide to consume more and save less out of current income, other things being equal. If this change save less out of current income, other things being equal. If this change is permanent, how would you expect it to influence is permanent, how would you expect it to influence

I.I. the rate of growth of output per capita in the long run and the rate of growth of output per capita in the long run and

II.II. the level of income per capita in the long run? the level of income per capita in the long run?

Questions for reviewQuestions for review

3.3. Consider a country whose capital stock is greatly reduced because of a Consider a country whose capital stock is greatly reduced because of a natural calamity or war, for example. What additional information do natural calamity or war, for example. What additional information do you need in order to be able to assess the likely consequences of the you need in order to be able to assess the likely consequences of the reduction in the capital stock for the level and rate of growth of per reduction in the capital stock for the level and rate of growth of per capita GNP in the long run?capita GNP in the long run?

4.4. ‘An increase in the propensity to save increases economic growth only ‘An increase in the propensity to save increases economic growth only temporarily. Therefore, government policies aimed at stimulating temporarily. Therefore, government policies aimed at stimulating saving are not well suited to improving the standard of living in the saving are not well suited to improving the standard of living in the long run.’ Evaluate this statement in view of the theories of long run.’ Evaluate this statement in view of the theories of A.A. Exogenous economic growth Exogenous economic growth B.B. Endogenous growth. Endogenous growth.

5.5. ‘A nation dedicated to the maximum welfare of its citizens should aim ‘A nation dedicated to the maximum welfare of its citizens should aim for as rapid economic growth as possible.’ True or false? Why? for as rapid economic growth as possible.’ True or false? Why?

Classroom discussion

chapter three quantity and quality chapter 3 compares and contrasts the theories of endogenous vs....

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