macroeconomics chapter 31 introduction to economic growth c h a p t e r 3

Macroeconomics Chapter 3 1

Introduction to Economic Growth

C h a p t e r 3


Economic Growth and Standard of Living


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.


Long Term Economic Growth in OECD Countries


Productivity Slowdown

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.


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?


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?


Growth Questions

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


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


Production Functions

MPL – Marginal Product of Labor Diminishing Marginal Product of labor

MPK – Marginal Product of Capital Diminishing Marginal Product of Capital


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)


Per Worker Production Function

y=f(k) y output per worker k capital per worker


An example: Cobb-Douglas Production Function

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Contributions to GDP Growth

∆ 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


Contributions to GDP Growth

α + β = 1 Share of capital income (α) + share of labor income (β) = 1

∆ Y/Y = ∆A/A + α·(∆K/K) + β·(∆L/L) 0 < α < 1 0 < β < 1


Solow Growth Model

Model ignores: Government

No taxes, public expenditures, debt, or money

International Trade No trade in goods or financial assets


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


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 > 0).

∆L/L = n


Solow Growth Model


Solow Growth Model

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.


Solow Growth Model

From the per worker production function ∆y/y = ∆Y/Y − ∆L/L

∆k/k = ∆K/K − ∆L/L


Solow Growth Model

∆ Y/Y= α·(∆K/K) + (1−α)·(∆L/L)

∆Y/Y= α·(∆K/K) − α·(∆L/ L) + ∆L/ L

∆Y/Y − ∆L/L = α · (∆K/K − ∆L/L)

∆y/y = α·(∆k/k)


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 δ

δK is the amount of capital that depreciates each year


Solow Growth Model

Real saving = s · (Y −δK)

Real saving = (saving rate) · (real income)


Solow Growth Model

Y−δK=C+s·(Y−δ K) Real income = consumption + real saving


Solow Growth Model Y = C + I Real GDP = consumption + gross

investment

Y−δK = C + (I−δK) Real NDP = consumption + net

investment


Solow Growth Model

C+s·(Y−δK) = C+I−δK

or

s·(Y−δK) = I−δK Real saving = net investment


Solow Growth Model

∆ K = I−δK Change in capital stock = gross investment

− depreciation, or Change in capital stock = net investment

∆K = s·(Y−δK) Change in capital stock = real saving


Solow Growth Model

Divide both sides by K

∆K/K = s·Y/K − sδ


Solow Growth Model

∆ k/k = ∆K/K − ∆L/L

∆k/k = s· (Y/K) − sδ − n


Solow Growth Model

Y/K =(Y/L) / (K/L)

Y/K = y/k


Solow Growth Model

∆ k/k = s·(y/k) − sδ − n

∆y/y = α·(∆k/k)

∆y/y = α·[ s·(y/k) − sδ − n]


Solow Growth Model


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*)


Solow Growth Model


Solow Growth Model

In the steady state, ∆k/k equals zero. s·(y*/k*) − sδ − n= 0

s·(y* −δ k*) = nk*

Steady-state saving per worker = steady-state capital provided for each new worker

macroeconomics chapter 31 introduction to economic growth c h a p t e r 3

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