National Income & Business Cycles

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Ohio Wesleyan UniversityGoran Skosples

7. Long-Run Growth

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Objectives

Why growth matters? Learn the closed economy Solow model See how a country’s standard of living depends

on its saving and population growth rates Importance of productivity growth Policies to promote growth

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Key Concepts Solow growth model Steady state Break-even investment Rule of 70 Depreciation Dilution

Productivity Sustainable growth

rate Capital flows Foreign Direct

Investment (FDI)

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QuestionShall we play a game?

• Life expectancy is less than 50 years• 1 out every 10 infants dies before the age of one• More than 90% of households have no electricity,

refrigerator, telephone, or car• Fewer than 10% of adults have completed high

school.

What country is it?

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Why growth matters

Data on infant mortality rates:• 20% in the poorest 1/5 of all countries• 0.4% in the richest 1/5

In Bangladesh, about 80% of people live on less than $2/day.

One-fourth of the poorest countries have had famines during the past 3 decades.

Poverty is associated with oppression of women and minorities.Economic growth raises living standards and reduces poverty….

…for poor countries

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Income and poverty in the world selected countries, 2000

0

10

20

30

40

50

60

70

80

90

100

$0 $5,000 $10,000 $15,000 $20,000

Income per capita in dollars

% o

f pop

ulat

ion

livin

g on

$2

per

day

or le

ss

Madagascar

India

BangladeshNepal

Botswana

Mexico

ChileS. Korea

Brazil Russian Federation

Thailand

Peru

ChinaKenya

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Why growth matters

Anything that effects the long-run rate of economic growth – even by a tiny amount – will have huge effects on living standards in the long run.

1,081.4%243.7%85.4%

624.5%169.2%64.0%

2.5%

2.0%

…100 years…50 years…25 years

percentage increase in standard of living after…

annual growth rate of

income per capita

…for rich countries

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The lessons of growth theory

These lessons help us understand why poor

countries are poor design policies that

can help them grow learn how our own

growth rate is affected by shocks and our government’s policies

…can make a positive difference in the lives of hundreds of millions of people.

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Int’l Differences in the Standard of LivingGDP GDP

Country per capita Country per capitaQatar $179,000 France $33,100 Singapore $62,100 Israel $29,800 Norway $54,600 Argentina $14,700 United States $47,200 Brazil $10,800 Hong Kong $45,900 China $7,600 Australia $41,000 India $3,500 Netherlands $40,300 Nigeria $2,500 Canada $39,400 Ghana $2,500 Sweden $39,100 Bangladesh $1,700 Germany $35,700 Somalia $600 United Kingdom $34,800 Zimbabwe $500 Japan $34,000 Congo, DR $300 data is in PPP

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Historical GDP per capita

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US GDP per capita

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Growth of US GDP per capita

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Sources of Economic Growth Given what you have learned so far, what causes

differences in incomes?

Y = A K L1-

1.

2.

3.

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The Solow Model due to Robert Solow,

won Nobel Prize for contributions to the study of economic growth

a major paradigm:• widely used in policy making• benchmark against which most

recent growth theories are compared

looks at the determinants of economic growth and the standard of living in the long run

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How Solow model is different from Chapter 3’s model

1. K is no longer fixed:investment causes it to grow, depreciation causes it to shrink.

2. L is no longer fixed:population growth causes it to grow.

3. The consumption function is simpler.

4. No G or T(only to simplify presentation; we can still do fiscal policy experiments)

5. Cosmetic differences.

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The production function In aggregate terms: Y = F (K, L ) Define: _______ = ______________

_______ = ______________ Assume constant returns to scale Divide through by L:

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The production functionOutput per worker, y

Capital per worker, k

f(k)

Note: this production function exhibits ___________MPK.

1MPK

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The national income identity Y = _______

In “per worker” terms: y = _____ , where c = _____ and i =_____

s = the saving rate (an exogenous parameter)Note: s is the only lowercase variable that is not equal to its uppercase version divided by L

Consumption function: (per worker)

(remember, no G )

The consumption function

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Saving and investment saving (per worker) =

= =

National income identity is

Rearrange to get: (investment = saving, like in chap. 3!)

Using the results above, i =

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Output, consumption, and investment

Output per worker, y

Capital per worker, k

f(k)

sf(k)

k1

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Population Growth Assume that the population--and labor force--

grow at rate n. (n is exogenous)

EX: Suppose L = 1000 in year 1 and the population is growing at 2%/year ( ________ ).

Then L =

so L = in year 2.

L nL

n L

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Capital accumulationThe basic idea: _________ increases the capital

stock, ___________ and_______ reduces it.

Change in capital stock = investment – depreciation – dilution

k

Since _________ , this becomes:

k = s f(k) – (+n )k

The equation of motion for k

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Break-even investment ( + n)k = ,

the amount of investment necessary to keep ___ constant.

Break-even investment includes:• ____ to replace capital as it wears out

• ____ to equip new workers with capital

(otherwise, k would fall as the existing capital stock would be spread more thinly over a larger population of workers)

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Break-even investmentBreak-even investment, (+n)k

Capital per worker, k

δ = the rate of depreciationn = population growth rate

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The steady state

If investment is just enough to cover depreciation (s f(k) – (+n)k ) then capital per worker will remain ________:

k = ____.

This constant value, denoted k*, is called the _______ ______________________.

k = s f(k) – (+n)k

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The steady state

Investment and

depreciation

Capital per worker, k

sf(k)

(+n)k

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Moving toward the steady state

Investment and

depreciation

Capital per worker, k

sf(k)

(+n)k

k*

k = sf(k) (+n)k

k1

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An increase in the saving rate

Investment and

depreciation

k

(+n)k

s1 f(k)

*k1

An increase in the saving rate ______ investment ……causing k to ____________________________:

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Prediction: Higher s _______ k*. And since y = _____ ,

______ k* _______ y* .

Thus, the Solow model predicts that countries with higher rates of saving and investment will have _________ levels of capital and income per worker in the long run.

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International Evidence on Investment Rates and Income per Person

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The impact of population growth

Investment, break-even investment

Capital per worker, k

sf(k)

( +n1) k

k1*

An increase in n causes an _______ in break-even investment,leading to a ____ steady-state level of k.

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Prediction:

Higher n _______ k*. And since y = ,

_______ k* _______ y* .

Thus, the Solow model predicts that countries with higher population growth rates will have _________ levels of capital and income per worker in the long run.

f(k)

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International Evidence on Population Growth and Income

per PersonIn

com

e pe

r per

son

in 2

000

(log

scal

e)

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The impact of population growth

Population growth = 0 Population growth = n

L:

K:

Y:

k:

y:

L:

K:

Y:

k:

y:

Determine what happens to each variable when population growth is 0 and when it is n? Fill in whether at the steady-state the variable is constant or whether it grows or declines and at which rate:

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Productivity GrowthOutput and Investment

k

(+n)k

s1 f(k)

*k1

f1(k)Productivity growth _______ investment which leads to a _____ steady-state level of income per capita

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Implications of the Solow Model Countries below the steady-state level of capital

per worker will _____ and countries above the steady-state level of capital per worker will _____

The further below its steady-state level of capital per worker a country is, the _______ it will grow• After a war or a natural disaster, a country will

grow _______

Capital should flow from rich to poor countries• Why?• Is that happening?

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Growth Rates in the OECD

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Growth Rates Around the World

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Implications of the Solow Model What can cause growth in the Solow model?

• • • •

However, in a new steady-state: Can the above sources of growth continuously

rise? In the long run, the rate of ______________

_____________ is the dominant factor determining how quickly living standards rise

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Examples of technological progress From 1950 to 2000, U.S. farm sector productivity

nearly tripled. The real price of computer power has fallen an

average of 30% per year over the past three decades.

Percentage of U.S. households with ≥ 1 computers: 8% in 1984, 62% in 2003

2000: 361m Internet users, 740m cell phone users 2011: 2.4b Internet users, 5.9b cell phone users

2001: iPod capacity = 5gb, 1000 songs. Not capable of playing episodes of Entourage. 2009: iPod capacity = 120gb, 30,000 songs. Can play episodes of Entourage.

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Total Factor Productivity Differences in income per capita: y = Ak

Both capital per worker (k) and total factor productivity (A) explain differences in incomes per capita around the world

Richer countries have both more capital per worker and higher total factor productivity• capital per worker explains about ____ of the

difference in incomes per capita• TFP explain about ____ of the difference in

incomes per capita

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The US and China

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Policies to Raise Living Standards

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Measures of Living Standards Is GDP per capita a good measure of the living

standards? What are some other measures?

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Happiness and GDP per capita

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Summary

1. The Solow growth model shows that, in the long run, a country’s standard of living depends• positively on its saving rate.• negatively on its population growth rate.• positively on total factor productivity

2. An increase in the saving rate leads to • higher output in the long run• faster growth temporarily • but not faster steady state growth.

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3. In the long run, only a continuous increase in productivity growth can lead to sustained increase in the standard of living

4. Both capital per worker and total factor productivity explain income differences around the world

Summary