Macroeconomics Chapter 31 Introduction to Economic Growth C h a p t e r 3

Macroeconomics Chapter 32 Economic Growth and Standard of Living

Macroeconomics Chapter 33 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  Income Inequality.

Macroeconomics Chapter 34

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9 Long Term Economic Growth in OECD Countries

Macroeconomics Chapter 310 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.

Macroeconomics Chapter 311 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?

Macroeconomics Chapter 312 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?

Macroeconomics Chapter 313 Growth Questions  What can policymakers do to increase growth rates of real GDP per person?

Macroeconomics Chapter 314 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

Macroeconomics Chapter 315

Macroeconomics Chapter 316

Macroeconomics Chapter 317 Production Functions  MPL – Marginal Product of Labor Diminishing Marginal Product of labor  MPK – Marginal Product of Capital Diminishing Marginal Product of Capital

Macroeconomics Chapter 318 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)

Macroeconomics Chapter 319 Per Worker Production Function  y=f(k) y  output per worker k  capital per worker

Macroeconomics Chapter 320

Macroeconomics Chapter 321 An example: Cobb-Douglas Production Function

Macroeconomics Chapter 322 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

Macroeconomics Chapter 323 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

Macroeconomics Chapter 324 Solow Growth Model  Model ignores: Government  No taxes, public expenditures, debt, or money International Trade  No trade in goods or financial assets

Macroeconomics Chapter 325 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

Macroeconomics Chapter 326 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

Macroeconomics Chapter 327 Solow Growth Model

Macroeconomics Chapter 328 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.

Macroeconomics Chapter 329 Solow Growth Model  From the per worker production function ∆y/y = ∆Y/Y − ∆L/L ∆k/k = ∆K/K − ∆L/L

Macroeconomics Chapter 330 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)

Macroeconomics Chapter 331 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

Macroeconomics Chapter 332 Solow Growth Model  Real saving = s · (Y −δK)  Real saving = (saving rate) · (real income)

Macroeconomics Chapter 333 Solow Growth Model  Y−δK=C+s · (Y−δ K) Real income = consumption + real saving

Macroeconomics Chapter 334 Solow Growth Model  Y = C + I  Real GDP = consumption + gross investment  Y−δK = C + (I−δK)  Real NDP = consumption + net investment

Macroeconomics Chapter 335 Solow Growth Model  C+s · (Y−δK) = C+I−δK or  s · (Y−δK) = I−δK  Real saving = net investment

Macroeconomics Chapter 336 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

Macroeconomics Chapter 337 Solow Growth Model  Divide both sides by K  ∆K/K = s · Y/K − sδ

Macroeconomics Chapter 338 Solow Growth Model  ∆k/k = ∆K/K − ∆L/L  ∆k/k = s · (Y/K) − sδ − n

Macroeconomics Chapter 339 Solow Growth Model  Y/K =(Y/L) / (K/L)  Y/K = y/k

Macroeconomics Chapter 340 Solow Growth Model  ∆k/k = s · (y/k) − sδ − n  ∆y/y = α · (∆k/k)  ∆y/y = α · [ s · (y/k) − sδ − n]

Macroeconomics Chapter 341 Solow Growth Model

Macroeconomics Chapter 342 Solow Growth Model

Macroeconomics Chapter 343 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*)

Macroeconomics Chapter 344 Solow Growth Model

Macroeconomics Chapter 345 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