Introduction to Economic Growth

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C h a p t e r 3
Introduction to Economic Growth
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Economic Growth and Standard of Living
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World Distribution of Real GDP

• World Distribution of Per Capita income in 2000
• World Distribution of Per Capita Income in 1960
• Growth Rate in Per capita Income 1960-2000.
• Income Inequality.

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Long Term Economic Growth in OECD Countries
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Productivity Slowdown

• The decline in the growth rate of real GDP per
  person from 3.1 per year for 19601980 to 1.8
  per year for 19802000 is sometimes called the
  productivity slowdown.

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Growth Questions

• What factors caused some countries to grow fast
  and others to grow slow over periods such as 1960
  to 2000?
• In particular, why did the East Asian countries
  do so much better than the sub-Saharan African
  countries?

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Growth Questions

• How did countries such as the United States and
  other OECD members sustain growth rates of real
  GDP per person of around 2 per year for a
  century or more?

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Growth Questions

• What can policymakers do to increase growth rates
  of real GDP per person?

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Production Function

• Y A F(K, L)
• A ? Technology Level
• K ? Capital Stock machines and buildings used
  by business.
• L ? Labor Force number of workers

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Production Functions

• MPL Marginal Product of Labor
• Diminishing Marginal Product of labor
• MPK Marginal Product of Capital
• Diminishing Marginal Product of Capital

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Constant Returns to Scale

• Constant Returns to Scale
• Double K and L and Y will also double
• Therefore, if we multiply K and L by the quantity
  1/L we also multiply Y by 1/L to get
• Y/L A F(K/L, L/L)

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Per Worker Production Function

• yf(k)
• y ? output per worker
• k ? capital per worker

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An example Cobb-Douglas Production Function
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Contributions to GDP Growth

• ?Y/Y ?A/A a(?K/K) ß(?L/L)
• The growth rate of real GDP, ?Y/Y, equals the
  growth rate of technology, ?A/A, plus the
  contributions from the growth of capital,
  a(?K/K), and labor, ß(?L/L).
• Solow residual

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Contributions to GDP Growth

• a ß 1
• Share of capital income (a) share of labor
  income (ß) 1
• ?Y/Y ?A/A a(?K/K) ß(?L/L)
• 0 lt a lt 1
• 0 lt ß lt 1

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Solow Growth Model

• Model ignores
• Government
• No taxes, public expenditures, debt, or money
• International Trade
• No trade in goods or financial assets

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Solow Growth Model

• Labor force, L ( labor force/ population)
  population
• Labor-force participation rate
• Assume labor force participation rate is
  constant.
• Labor force growth rate is the population growth
  rate

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Solow Growth Model

• Growth rate in population
• We assume that population grows at a constant
  rate, denoted by n, where n is a positive number
  (n gt 0).
• ?L/L n

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Solow Growth Model
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Solow Growth Model

• Assume ?A/A 0
• ?Y/Y a(?K/K) (1-a)(?L/L)
• The growth rate of real GDP is a weighted average
  of the growth rates of capital and labor.

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Solow Growth Model

• From the per worker production function
• ?y/y ?Y/Y - ?L/L
• ?k/k ?K/K - ?L/L

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Solow Growth Model

• ?Y/Y a(?K/K) (1-a)(?L/L)
• ?Y/Y a(?K/K) - a(?L/ L) ?L/ L
• ?Y/Y - ?L/L a (?K/K - ?L/L)
• ?y/y a(?k/k)

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Solow Growth Model

• Each household divides up its real income in a
  fixed proportion s to saving and 1 - s to
  consumption ( C ).
• Capital depreciate at the same constant rate d
• dK is the amount of capital that depreciates each
  year

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Solow Growth Model

• Real saving s (Y -dK)
• Real saving (saving rate) (real income)

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Solow Growth Model

• Y-dKCs(Y-d K)
• Real income consumption real saving

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Solow Growth Model

• Y C I
• Real GDP consumption gross investment
• Y-dK C (I-dK)
• Real NDP consumption net investment

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Solow Growth Model

• Cs(Y-dK) CI-dK
• or
• s(Y-dK) I-dK
• Real saving net investment

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Solow Growth Model

• ?K I-dK
• Change in capital stock gross investment -
  depreciation,
• or
• Change in capital stock net investment
• ?K s(Y-dK)
• Change in capital stock real saving

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Solow Growth Model

• Divide both sides by K
• ?K/K sY/K - sd

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Solow Growth Model

• ?k/k ?K/K - ?L/L
• ?k/k s (Y/K) - sd - n

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Solow Growth Model

• Y/K (Y/L) / (K/L)
• Y/K y/k

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Solow Growth Model

• ?k/k s(y/k) - sd - n
• ?y/y a(?k/k)
• ?y/y a s(y/k) - sd - n

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Solow Growth Model
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Solow Growth Model
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Solow Growth Model

• steady state.
• When k k, ?k/k equals zero.
• ?k/k 0, k stays fixed at the value k.
• y f(k)

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Solow Growth Model
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Solow Growth Model

• In the steady state, ?k/k equals zero.
• s(y/k) - sd - n 0
• s(y -d k) nk
• Steady-state saving per worker steady-state
  capital provided for each new worker