Economic Growth - Sciences

Economic Growth

Intermediate Macroeconomic TheoryMacroeconomic Analysis

University of North Texas

ECON 3560 / 5040 Economic Growth

Outline

1 Motivation

2 The Solow-Swan ModelModel I: no population growth & no technological progressModel II: population growth & no technological progressModel III: population growth & technological progress

3 Policies to Promote Growth


Outline

1 Motivation




The Lessons of Growth Theory

The lessons of growth theory can make a positive difference inthe lives of hundreds of millions of people

These lessons help us

1 Understand why poor countries are poor

2 Design policies that can help them grow

3 Learn how our own growth rate is affected by shocks and ourgovernment’s policies






























Huge effects from tiny differences

In rich countries like the U.S., if government policies or shockshave even a small impact on the long-run growth rate,

They will have a huge impact on our standard of living in thelong 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


Stylized Facts

Understand what causes differences in income over time andacross countries

Sources of economy’s output: factors of production (K, L) andproduction technology

The Solow-Swan model shows how saving, population growth,and technological progress affect the level of an economy’soutput and its growth over time


Stylized Facts


1 Sustained increase in Y

2 Sustained increase in y (= Y/L)

3 Differences in income across countries: yA 6= yB




Stylized Facts





Stylized Facts



→ Differences in income must come from differences in K, L,and technology



Stylized Facts





Outline

1 Motivation




Model IThe Accumulation of Capital

The supply of goods and the production function

Aggregate production function: Y = F(K, L)

CRS allows us to analyze all quantities relative to the size of thelabor force

→ per capita production function: y = f (k)

The demand for goods and the consumption function

No government and closed economy: y = c + i

Consumption per person: c = (1− s)y

→ saving (investment) per person: i = sy = sf (k)



















































































Growth in the capital stock and the steady state

Capital stock is a key determinant of the economy’s output

Investment per person: i = ∆k + δk

Law of motion: ∆k = sf (k)− δk

Steady-state (long-run equilibrium) level of capital (k∗):

→ ∆k = 0 or sf (k)− δk at k∗

Stability of a steady-state k∗

Investment (saving) > depreciation → k ↑

Investment (saving) < depreciation → k ↓

Investment (saving) = depreciation → k








→ ∆k = 0 or sf (k)− δk at k∗












→ ∆k = 0 or sf (k)− δk at k∗












→ ∆k = 0 or sf (k)− δk at k∗












→ ∆k = 0 or sf (k)− δk at k∗












→ ∆k = 0 or sf (k)− δk at k∗












→ ∆k = 0 or sf (k)− δk at k∗












→ ∆k = 0 or sf (k)− δk at k∗












→ ∆k = 0 or sf (k)− δk at k∗












→ ∆k = 0 or sf (k)− δk at k∗












→ ∆k = 0 or sf (k)− δk at k∗












→ ∆k = 0 or sf (k)− δk at k∗






Model IImplications

Can the model explain economic growth?

1 Sustained increase in Y: No

2 Sustained increase in y: No

3 yA 6= yB: Yes

How saving affects growth

Temporary effect on growth rate

→ High rate of saving leads to high growth temporarily, but theeconomy eventually approaches a steady state in which capitaland output are constant

Different saving rates ⇒ international differences in output


Model IImplications




3 yA 6= yB: Yes






Model IImplications




3 yA 6= yB: Yes






Model IImplications




3 yA 6= yB: Yes






Model IImplications




3 yA 6= yB: Yes






Model IImplications




3 yA 6= yB: Yes






Model IImplications




3 yA 6= yB: Yes






Model IImplications




3 yA 6= yB: Yes






Model IImplications




3 yA 6= yB: Yes






Model IImplications




3 yA 6= yB: Yes






Model IImplications




3 yA 6= yB: Yes






Model IImplications




3 yA 6= yB: Yes






Model IInternational Differences in Output

International evidence on investment (saving) rates and incomeper person


Model IInternational Differences in Output

International evidence on investment (saving) rates and incomeper person

Egypt

Chad

Pakistan

Indonesia

ZimbabweKenya

India

CameroonUganda

Mexico

IvoryCoast

Brazil

Peru

U.K.

U.S.Canada

FranceIsrael

GermanyDenmark

ItalySingapore

Japan

Finland

100,000

10,000

1,000

100

Income per person in 1992(logarithmic scale)

0 5 10 15Investment as percentage of output (average 1960 –1992)

20 25 30 35 40


Model IGolden Rule Level of Capital

Is higher saving always good?

An increase in k∗ has two opposing effects

1 More output (income)

2 Increase in replacement of capital that is wearing out

Optimal amount of capital accumulation from the standpoint ofeconomic well-being: Golden rule level of capital (kg)

→ k∗ with the highest level of consumption (c∗ = f (k∗)− δk∗)

→ MPK = δ at kg

Transition to the Golden Rule steady state









→ MPK = δ at kg










→ MPK = δ at kg










→ MPK = δ at kg










→ MPK = δ at kg










→ MPK = δ at kg










→ MPK = δ at kg










→ MPK = δ at kg










→ MPK = δ at kg










→ MPK = δ at kg



Model IIThe Steady State with Population Growth

Is population growth another possibility of the sustainedgrowth?

The steady state:Law of motion: ∆k = sf (k)− (δ + n)k

nk is the amount of investment necessary to provide newworkers with capital


1 Sustained increase in Y: Yes (n)


3 yA 6= yB: Yes

Golden Rule level of capital: MPK − δ = n









3 yA 6= yB: Yes










3 yA 6= yB: Yes










3 yA 6= yB: Yes










3 yA 6= yB: Yes










3 yA 6= yB: Yes










3 yA 6= yB: Yes










3 yA 6= yB: Yes










3 yA 6= yB: Yes










3 yA 6= yB: Yes










3 yA 6= yB: Yes










3 yA 6= yB: Yes



Model IIInternational Differences in Output

International evidence on population growth rates and incomeper person


Model IIInternational Differences in Output

International evidence on population growth rates and incomeper person

Chad

Kenya

Zimbabwe

Cameroon

Pakistan

Uganda

India

Indonesia

IsraelMexico

Brazil

Peru

Egypt

Singapore

U.S.

U.K.

Canada

FranceFinlandJapan

Denmark

IvoryCoast

Germany

Italy

100,000

10,000

1,000

1001 2 3 40

Income per person in 1992(logarithmic scale)

Population growth (percent per year) (average 1960 –1992)


Model IIITechnological Progress in the Solow-Swan Model

Introduce exogenous technological progress, which over timeexpands society’s ability to produce

Examples of technological progress

The Efficiency of Labor










1970: 50,000 computers in the world

2000: 51% of U.S. households have 1 or more computers






1981: 213 computers connected to the Internet

2000: 60 million computers connected to the Internet






The average car built in 1996 contained more computerprocessing power than the first lunar landing craft in 1969






Since 1980, semiconductor usage per unit of GDP hasincreased by a factor of 3500












Let A be the efficiency of labor or a society’s knowledge aboutproduction method and grows at some constant rate g

AL is the number of effective workers and grows at rate n + g

Labor-augmenting aggregate production function: Y = F(K, AL)

Per capita production function: y = f (k)


Model IIIThe Steady State with Technological Progress

The steady state:Law of motion: ∆k = sf (k)− (δ + n + g)k

gk is the amount of investment necessary to provide neweffective workers with capital


1 Sustained increase in Y: Yes (n + g)

2 Sustained increase in y: Yes (g)

3 yA 6= yB: Yes

Golden Rule level of capital: MPK − δ = n + g








3 yA 6= yB: Yes









3 yA 6= yB: Yes









3 yA 6= yB: Yes









3 yA 6= yB: Yes









3 yA 6= yB: Yes









3 yA 6= yB: Yes









3 yA 6= yB: Yes









3 yA 6= yB: Yes









3 yA 6= yB: Yes









3 yA 6= yB: Yes









3 yA 6= yB: Yes



Outline

1 Motivation




Policies to Promote GrowthEvaluating the Rate of Saving

Are we saving enough? Too much?

Use the Golden Rule to determine whether our saving rate andcapital stock are too high, too low, or about right

To do this, we need to compare (MPK − δ) to (n + g)

To estimate MPK − δ, we use three facts about the U.S.economy

1 The capital stock is about 2.5 times one year’s GDP: k = 2.5y

2 About 10% of GDP is used to replace depreciating capital:δk = 0.1y

3 Capital income is about 30% of GDP: MPK × k = 0.3y

⇒ MPK − δ = 0.08










⇒ MPK − δ = 0.08










⇒ MPK − δ = 0.08










⇒ MPK − δ = 0.08










⇒ MPK − δ = 0.08










⇒ MPK − δ = 0.08










⇒ MPK − δ = 0.08










⇒ MPK − δ = 0.08










⇒ MPK − δ = 0.08



From the last slide: MPK − δ = 0.08

U.S. real GDP grows an average of 3% per year, son + g = 0.03

Thus, in the U.S., MPK − δ = 0.08 > 0.03 = n + g

The U.S. is below the Golden Rule steady state:

⇒ if we increase our saving rate, we will have faster growth untilwe get to a new steady state with higher consumption perperson





































Policies to Promote GrowthPolicies to Increase the Saving Rate

Reduce the government budget deficit

Increase incentives for private saving:

1 Reduce capital gains tax, corporate income tax, estate tax asthey discourage saving

2 Replace federal income tax with a consumption tax

3 Expand tax incentives for IRAs (individual retirement accounts)and other retirement savings accounts





































Policies to Promote GrowthEncouraging Technological Progress

What policies might encourage faster technological progress?

1 Patent laws: encourage innovation by granting temporarymonopolies to inventors of new products

2 Tax incentives for R&D

3 Grants to fund basic research at universities

4 Industrial policy: encourage specific industries that are key forrapid tech. progress





































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Economic Growth - Sciences