chapter20 solow model

7/27/2019 Chapter20 Solow Model

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The McGraw-Hill Companies, 2012

Principles of Economics

Chapter 20

Economic Growth,

Productivity andLiving Standards


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The Remarkable Rise in Living

Standards: The Record

How might we measure changesin living standards?

Real GDP per person is a useful

measure, as it positively relates to a

number of variables, such as life

expectancy, infant health and

literacy.


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Real GDP per Person in FourIndustrialized Countries, 1870 - 2003


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Real GDP per Person in Selected

Countries, 1870-2003 (in US Dollars, 2000)


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Why Small Differences in

Growth Rates Matter

Compound interest

The payment of interest not only on

the original deposit but on all

previously accumulated interestSuppose a distant relative dies,

leaving you 10,000. How much will

this be worth in 40 years if you deposit

it in a saving account?


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At a 5% interest rate, your deposit in40 years will be worth:

If the interest rate is 6%, yourdeposit will be worth:

89.399,70)05,1(000,10 40

20.857,102)06,1(000,10 40


Growth Rates Matter


7/45 The McGraw-Hill Companies, 2012

The power of compound interest isthat, even at relatively low rates ofinterest, a small sum increases in

value. Very small differences in the

interest rate, over the long run,

imply large differences in theamount accumulated over time.


Growth Rates Matter



Government policies that affect the

long-term growth rate by a small amount

will have a major economic impact.


Growth Rates Matter



Why Nations Become Rich: the CrucialRole of Average Labour Productivity

What determines a nationseconomic growth rate?

Some definitions:

Y= real GDP

N= number of employed workers

POP= total population


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Real GDP per person

Real output/person depends on:

How much each worker can produce The percentage of the population that isworking

POP

Nx

N

Y

POP

Y



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Average labour productivity and theshare of population employed, Japan

(19602009)



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Average labour productivity and theshare of population employed, UnitedKingdom (1960-2009)



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Average labour productivity and theshare of population employed, UnitedStates (1960-2009)



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What determines a nationseconomic growth rate in thelong run?

average labour productivity!!



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The Solow Growth Model

The Solow Growth Model starts bypostulating a relationship betweenthe quantities of inputs used in the

production process and theeconomys total output (Y).

We assume there are only 2 inputs:

Physical capital, denoted as K

Labour, denoted as N


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The relationship between Y,K andN is known as a productionfunction, and can be written as:

Y = F(K,N)


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Assumption 1: Diminishing marginalproduct

If the amount of labour and other

inputs employed is held constant,then the greater the amount of

capital already in use, the less an

additional unit of capital adds to

production



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Y = the change in output

K = the change in the amount of

capital

Holding the labour input constant, themarginal product is defined as:

MPK =

K

Y



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Diminishing marginal product

Note: the labour is held constant.



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Assumption 2: Constant returns toscale (CRS)

If the labour and capital inputs are

both increased by equalproportions, then total output

increases by the same proportion.

We can write the CRS production

function as follows: zY = F(zK,zN)



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The y = f(k) curve is known as the production function and shows how average labour

productivity y = Y/N increases with the capital per worker or the capitallabour ratio k= K/N. For a constant labour force N the slope of this line measures the marginalproduct of capital MPK. Given the assumption of diminishing marginal product theslope will become smaller and the curve flatter as the capitallabour ratio increases.


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Investment and savingThe Solow Model assumes that

investment is financed by saving.

Saving is a constant fraction ofincome Y.

Let I denote investment in physicalcapital, S denote total saving & s

denote the savings rate.We have

I = S =sY



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In long-run equilibrium, investment perworker will just be sufficient to keep

the capital-labour ratio constant.

How muchinvestment is required tokeep the capital-labour ratio

constant?

The answer depends on two factors:

Depreciation rate

Population growth



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If capital depreciates at rate dper period then investment mustbe at least dk to keep the

capital-labour ratio from falling.

If the labour force grows at aconstant rate nper period, then

the economy will require anadditional investment nkto keepthe capital-labour ratio constant.



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So, the economy requiresinvestment per head to be

(d+n)k

to maintain a constant capital-labourratio.

E.g. If 3% of capital stock wears out each

year & the population grows by 2%,Then the required investment per

person employed is 5% to keep thecapital-labour ratio constant.



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Long-runequilibriumcondition is: k =i (d+n)k=0

A1 is the steadystate. At thispoint grossinvestment is

just sufficient to

maintain aconstant labourcapital ratio.



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The equilibriumcapital-labourratio [k1]determines theequilibriumvalue ofaverage labour

productivity[Y1] E1 becomes

steady state.



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An Increase in the Saving Rate



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Two important conclusions in explainingeconomic growth:

Average labour productivity depends onthe amount of physical capital per head in

the workforce. The more capital available to the workforce, the

higher the level of both labour productivity andincome per head of the population

In the long run, the economys steady stategrowth rate should equal the rate ofpopulation growth.

Why is the 2ndpoint less intuitive than the 1st?



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Over relatively long periods of time,growth in most industrializedeconomies tends to exceed the rateof population.

Between 1950 and 2003 the UKpopulation increased by about 20%(0.4% per year).

Real income increased by 2.1% peryear.

How do we explain the difference?



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We have assumed that toachieve higher average labourproductivity we need to increase

the amount of capital per worker. Is it possible that average labour

productivity can increase, even ifthe capital-labour ratio is

constant?Yes!



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Technical progress

An improvement in knowledge that

enables a higher output to be

produced from existing resourcesExample: the development of

personal computers over the last 20

years has made the labour force

more productive.



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To add technical progress, wemake a change to theproduction function.

Now rewrite as: y = Af(k)

Where A denotes technology

If technology improves by g percent per year then A = (1+g)



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Technical Processin the SolowModel


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Human capital

The accumulation of skills,

experience and knowledge by the

workforceWorkers with a large stock of human

capital are more productive than

workers with less training.

Let H denote the stock of human

capital: Y = AF(K,N,H)



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If the UK has a higher stock of human capital per workerthan India, its output per worker and living standards willbe higher, even if both countries have the samecapital-labour ratio.



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Total Factor Productivity

Total factor productivity

That part of growth in output which

is not accounted for by capital and

labour growth

TFP can be measured as follows:

1( )

A Y K N

A Y K N


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Total factor productivity can beinfluenced by factors, such as

entrepreneurship and management

skills

the political and legal environment


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Entrepreneurs are people whocreate new economicenterprises.

Because they introduce newproduction methods, they arecrucial to the economy.

How does a society fosterentrepreneurship?

How do you teachentrepreneurship?


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The political and legal environment

The establishment of well-definedproperty rights is crucial forinvestment.

Political instability and wars aredetrimental to investment.


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The Costs of Economic Growth

What are the costs of growth?The opportunity cost of increasing

the production of capitalgoods is

fewer consumergoods.

Reduced leisure time, worker safety

and health

The cost of research & development

The cost of education (humancapital)


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Promoting Economic Growth

How policymakers promotegrowthPolicies that support research and

developmentPolicies to increase human capital

Policies that promote saving andinvestment

Policies that attract foreigninvestment

The legal and political framework


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Promoting Economic Growth

The poorest countries: a special case?

Improve the legal and political framework

Corrupt legal systems create uncertainty aboutproperty rights.

Taxation and regulation discouragesentrepreneurship.

Markets are not allowed to function.

Lack of political stability discourages foreigninvestment.

Without political stability, foreign aid wontbe effective.

Is Economic Growth Always


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Is Economic Growth Always

Good for You?

Can economic growth continue withoutdepleting natural resources and damaging theglobal environment?

This limits to growth theory assumeseconomic growth will take the form of what

we have now. However, Growth can involve newer, more efficient goods and

services.

Increased wealth and productivity expands societyscapacity to safeguard the environment.

Environmental quality will not reach its optimallevel through market processes. Internationalmechanisms need to be established to dealwith global environmental problems.

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