巴罗宏观经济学课件 (6)

Solow Growth Model
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Real saving = s · (Y −δK) Real saving = (saving rate) · (real income)
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Solow Growth Model
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Y−δK=C+s·(Y−δ K) Real income = consumption + real saving
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Solow Growth Model
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From the per worker production function
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∆y/y = ∆Y/Y − ∆L/L ∆k/k = ∆K/K − ∆L/L
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Solow Growth Model
¡ ∆Y/Y= α·(∆K/K) + (1−α)·(∆L/L)
¡ + ∆L/ L ∆Y/Y − ∆L/L = α · (∆K/K − ∆L/L) ∆y/y = α·(∆k/k)
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Solow Growth Model
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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 δ δK is the amount of capital that depreciates each year
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Contributions to GDP Growth
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α+β=1
Share of capital income (α) + share of labor income (β) = 1
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∆Y/Y = ∆A/A + α·(∆K/K) + β·(∆L/L) l 0 < α < 1 l 0 < β < 1
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Solow Growth Model
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Y/K =(Y/L) / (K/L) Y/K = y/k
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Solow Growth Model
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∆k/k = s·(y/k) − sδ − n ∆y/y = α·(∆k/k) ∆y/y = α·[ s·(y/k) − sδ − n]
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Solow Growth Model
C+s·(Y−δK) = C+I−δK
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s·(Y−δK) = I−δK Real saving = net investment
Solow Growth Model
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∆K = I−δK
Change in capital stock = gross investment − depreciation, or Change in capital stock = net investment
Solow Growth Model
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Labor force, L = ( labor force/ population) · population
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Labor-force participation rate Assume labor force participation rate is constant. Labor force growth rate is the population growth rate
Solow Growth Model
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Model ignores:
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Government
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No taxes, public expenditures, debt, or money No trade in goods or financial assets
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International Trade
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Growth Questions
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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 subSaharan African countries?
∆L/L = n
Solow Growth Model
Solow Growth Model
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Assume ∆A/A = 0 ∆Y/Y= α·(∆K/K) + (1−α)·(∆L/L) The growth rate of real GDP is a weighted average of the growth rates of capital and labor.
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Change in capital stock = real saving
∆K = s·(Y−δK)
Solow Growth Model
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Divide both sides by K ∆K/K = s·Y/K − sδ
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Solow Growth Model
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∆k/k = ∆K/K − ∆L/L ∆k/k = s· (Y/K) − sδ − n
Solow Growth Model
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In the steady state, ∆k/k equals zero. s·(y*/k*) − sδ − n= 0 s·(y* −δ k*) = nk* Steady-state saving per worker = steadystate capital provided for each new worker
Introduction to Economic Growth
Economic Growth and Standard of Living
World Distribution of Real GDP
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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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Growth Questions
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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?
Contributions to GDP Growth
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∆Y/Y = ∆A/A + α·(∆K/K) + β·(∆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, α·(∆K/K), and labor, β·(∆L/L). Solow residual
Long Term Economic Growth in OECD Countries
Productivity Slowdown
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The decline in the growth rate of real GDP per person from 3.1% per year for 1960–1980 to 1.8% per year for 1980–2000 is sometimes called the productivity slowdown.
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Production Functions
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MPL – Marginal Product of Labor
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Diminishing Marginal Product of labor Diminishing Marginal Product of Capital
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MPK – Marginal Product of Capital
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Growth Questions
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What can policymakers do to increase growth rates of real GDP per person?
Production Function
Y = A· F(K, L)
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A Technology Level K Capital Stock – machines and buildings used by business. L Labor Force – number of workers
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Constant Returns to Scale
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Constant Returns to Scale
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Double K and L and Y will also double
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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)
Solow Growth Model
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