Prof. Mathieu Taschereau-DumouchelSpring 2018

ECON 3040Intermediate Macroeconomic Theory

Lecture 22: Growth

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The Koreas are growing apart

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Big Questions• Why are some countries growing quickly while others

aren’t?• Do poor countries catch up?• What factors determine the rate of economic growth

over time?• What is the role of government when it comes to

growth?

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Today• International comparisons of income and growth

over time• Determinants of long-run economic growth– Solow model

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The Miracle of Compounding

• Small differences in average growth rates create huge differences in output per capita

• Example: output per capita growth 1820-1950– North America:• 1.58% per year => (1.0158)130 = 7.67

– Western Europe:• 1.06% per year => (1.0106)130 = 3.94

– Rest of the world:• 0.50% per year => (1.0050)130 = 1.91

• Small changes in policies can have huge effect

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Solow Growth Model• A broad and simple view of the economy– Useful to focus on a few basic ideas and isolate

the key drivers of economic growth in the long run

• Start with the basic goods market equationY= C + I + G + NX

– Assume• Close economy: NX = 0• No government purchases: G = 0

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Solow Growth Model• The behavior of the private sector– Household Consumption, C• Households save a constant fraction, s, of income every

year and consume the rest– Business Investment, I• Amount of capital expenditures undertaken

– The amount of new capital purchased

• Existing capital, K, depreciates at rate d– If I > d × K the stock of capital, K, will begin to increase– If I < d × K the less stock of capital, K, will begin to decline

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Solow Growth Model• Macroeconomic equilibrium– Since G = NX = 0 we get that

Y = C + IS = Y – C = I

– Where S is national saving• And also private saving since we have no government

• In equilibriumS = sY = sAF(K,N) = I

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Long Run Equilibrium• Focus on long-run or steady-state equilibrium– After the the economy reaches some stable point • At this stage GDP, capital, etc. will be constant• K reaches a constant level K*

– We reach a steady-state when investment is just enough to replace the capital that is depreciating

I = dK• In a long-run equilibrium we must have

sAF(K,N) = dK

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Long Run Equilibrium

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K* K

Investment Required to Leave K UnchangeddK

S,I

Convergence to the Long Run• What if we are not at the steady-state?– The economy will converge to the long-run

equilibrium over time– If we start with K below K*,• Actual investment (and savings) exceeds the

amount needed to replace the depreciating capital, so K rises

– If we start with K above K*, • Actual investment (and savings) is too low to

replace depreciating capital, so K falls

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Convergence to the Long Run

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K* K

Steady-State InvestmentdK

SavingsAF(K,N)

K1

dK1

sAF(K1,N)

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Example• Production Function

§ Population, N, is 25• Suppose

§ National saving rate, s, is 20%§ Depreciation rate on capital, d, is 12.5%

• Long run level of capital in the economy is

• Long run GDP

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€

2K 0.5N 0.5

€

0.2 × 2K 0.5250.5 = 0.125K⇒ K = 256

€

Y = 2 × 250.5 × 2560.5 =160

Saving and Productivity

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The Role of Saving• Higher saving rate, s, means – society can fund a higher stock of capital in the

long run– and thus attain a higher level of long run output

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Effect of Higher Saving on Long-Run Capital

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K* K

d×K

s×AF(K,N)

K**

Saving Rates and Per Capita Income

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The Role of Saving• Higher saving rate, s, means we can fund a higher

stock of capital and thus have a higher level of long run output

• However there are two problems– There is a trade-off between present and future

consumption• Cost of higher saving is lower consumption in the short run

– We cannot go on raising the saving rates forever to improve standards of living• The maximum saving rate is capped at 100% and we don’t

eat at this level!

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The Role of Productivity• The key factor in economic growth is

sustained productivity improvement, A– Productivity improvement directly increases the

level of output– This increases the available resources to fund both

current consumption and savings– Unlike the saving rate this process has no obvious

upper bound

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Effect of Higher Productivity on Long-Run Capital

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K* K

Investmentd×K

Savings×AF(K,N)

K**

Sources of Economic Growth in the U.S (Percent per Year)

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What Affects Productivity?• Level of technology and innovation• Quality of human capital• Business practices • Energy costs• Cost of doing business and levels of corruption

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Cost of Starting a Business

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Transparency and CorruptionEase of Access to Legal Documentation

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Demographics

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Population Growth• Suppose population, N, grows at rate n– Now want to focus on GDP per capita, y = Y/N

• Aggregate production function (Cobb Douglas)Y = AF(K,N) = AK0.3N0.7

• Per capita production function,y = Y/N =AK0.3N0.7/N

= AK0.3N-0.3

y = A(K/N)0.3 = Ak0.3

= Af(k)

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The Per-capita Production Function

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Steady-State with Population Growth• Now a long run equilibrium is reached when

GDP, y, and capital, k, per capita are constant• This means that steady-state investment must– Replace worn out capital, dK– Expand so the capital stock grows at the same rate

of population growth, nKI = (n + d)K

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Steady-State with Population Growth• Equating saving to investment implies

sY = (n + d)K• Putting this in per-worker terms yields

sAf(k) = (n + d)k• Note– This is almost identical to what we had before– But now we have one extra factor determining

long run GDP per capita: population growth, n

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The Steady-State Capital–Labor Ratio

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The Effects of Population Growth• Capital must increase faster to keep up with

growing population– We need to devote more resources to fund

investment• Implies a lower steady-state capital-labor ratio

and steady-state output per capita• Key implication– Slower population growth increases GDP per

capita– Major issue for economic development in Africa

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Population Growth and Long Run GDP per capita

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Population Growth and GDP Per CapitaCross-Country Evidence

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GDP and GDP per-capita• Population growth – Increases GDP since a higher labor force makes

more resources available for productionY = AF(K,N)

– But it lowers GDP per capita• At least if productivity is not increasing too• Output cannot keep up with the rise in the labor force• This is just a result of decreasing marginal productivity

of labor

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Convergence

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Will Poor Economies Catch Up?• It depends on the reason for poverty– It could be a temporary stage of development• The country has similar policies and institutions but

starts from a very low base• Capital per worker is initially very low

– These differences can be eliminated over time• Post war Germany and Japan • Southeast Asia after the 1950s• These countries will eventually catch up

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Temporary Differences in GDP per capita

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kAsia k

sAsia=sUS

kUS

iAsia=iUS

International Convergence

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0

10

20

30

40

50

60

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005Date

China

India

Korea

Thailand

Malaysia

Indonesia

Will Poor Economies Catch Up?• But poverty could also develop into a

permanent condition when a country faces serious structural problems– Low productivity or high population growth– Bad policies and institutions– Historical examples include Latin America and

much of Sub-Saharan Africa, at least until recently

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Permanent Differences in GDP per capita

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kAfrica k

sUS

kUS

sAfrica

iAfrica

iUS

International ConvergenceSub-Saharan Africa

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0

5

10

15

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Date

Congo

Ethiopia

Angola

Nigeria

Senegal

Zimbabwe

Income distribution across countries

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Income distribution across countries

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Income distribution over time

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Evolution of income per capita

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Evolution of income per capita

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Promoting Growth in Poor Countries• Developing good institutions– Reducing corruption and bureaucracy, improving law

and order, etc.– Improving education, family planning,– Developing markets and business culture

• International aid– Eliminating debts, extending cheap loans etc.. • Provide resources for more investment

S = I + Foreign Transfers

– Works best when right policies are in place

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GDP Per Capita in Advanced Economies

Growth Miracles and DisastersGDP per capita vs US

%US (1960) %US (2009)

Singapore 27.8% 112.3%

Ireland 44.2% 78.0%

Korea 10.8% 58.5%

US 100.0% 100.0%

Venezuela 37.5% 21.6%

Liberia 10.8% 0.9%

Zimbabwe 1.2% 0.4%

Application: The Growth of China• China is an economic juggernaut• Population 1.3 billion people• Starting with low level of GDP, but growing

rapidly

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Application: China• Fast output growth attributable to

– Huge increase in capital investment– Fast productivity growth (in part from changing to a market economy)– Increased trade

• Investment– Investment is huge in China; at the cost of current consumption, so saving is

high• Labor

– China has a huge labor force; comparative advantage!– As China grows, wages and standard of living will rise

• Problems China faces– Weak banking system– Increasing income inequality– Much unemployment in rural areas

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What Determines Long Term Economic Success?• Only productivity growth can generate

sustained growth in long run GDP

• Population growth increases GDP but not GDP per capita

• The key for poor economies to permanentlycatch-up with developed countries is to adopt the right growth policies

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