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

Macroeconomics Chapter 32 Fact 1 on Economic Growth  Large variations in per capita income across countries.  Real GDP in 2000, PPP-adjusted, in 1996 US$

Macroeconomics Chapter 33 Rise in Income Inequality

Macroeconomics Chapter 34 Fact 2 – Cont’  Large variations in growth rates of income across countries.

Macroeconomics Chapter 35

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7 Fact 3 – Cont’  A country ’ s relative position in the world distribution of per capita incomes may experience large changes over time. Countries can move from "poor" to "rich", and vice versa.

Macroeconomics Chapter 38

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Macroeconomics Chapter 311 Fact 4 – Cont’ In the Unites States over the last century:  the real rate of return to capital, r, shows no trend upward or downward;  the share of income devoted to capital, rK/Y, and labor, wL/Y, show no trend;  the average growth rate of output per person has been positive and relatively constant over time - i.e., the Unites States exhibited steady, sustained per capita income growth (or, the U.S. economy is on the balanced growth path). The above three features of the United States are also called Kaldor facts (balanced growth).

Macroeconomics Chapter 312

Macroeconomics Chapter 313 Long Term Economic Growth in OECD Countries

Macroeconomics Chapter 314 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 315 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 316 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 317 Growth Questions  What can policymakers do to increase growth rates of real GDP per person?

Macroeconomics Chapter 318 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 319

Macroeconomics Chapter 320

Macroeconomics Chapter 321 Production Functions  MPL – Marginal Product of Labor Diminishing Marginal Product of labor  MPK – Marginal Product of Capital Diminishing Marginal Product of Capital

Macroeconomics Chapter 322 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 323 Per Worker Production Function  y=f(k) y  output per worker k  capital per worker

Macroeconomics Chapter 324

Macroeconomics Chapter 325 An example: Cobb-Douglas Production Function

Macroeconomics Chapter 326 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 327 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 328 Solow Growth Model  Model ignores: Government  No taxes, public expenditures, debt, or money International Trade  No trade in goods or financial assets

Macroeconomics Chapter 329 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 330 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 331 Solow Growth Model

Macroeconomics Chapter 332 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 333 Solow Growth Model  From the per worker production function ∆y/y = ∆Y/Y − ∆L/L ∆k/k = ∆K/K − ∆L/L

Macroeconomics Chapter 334 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 335 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 336 Solow Growth Model  Real saving = s · (Y −δK)  Real saving = (saving rate) · (real income)

Macroeconomics Chapter 337 Solow Growth Model  Y−δK=C+s · (Y−δ K) Real income = consumption + real saving

Macroeconomics Chapter 338 Solow Growth Model  Y = C + I  Real GDP = consumption + gross investment  Y−δK = C + (I−δK)  Real NDP = consumption + net investment

Macroeconomics Chapter 339 Solow Growth Model  C+s · (Y−δK) = C+I−δK or  s · (Y−δK) = I−δK  Real saving = net investment

Macroeconomics Chapter 340 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 341 Solow Growth Model  Divide both sides by K  ∆K/K = s · Y/K − sδ

Macroeconomics Chapter 342 Solow Growth Model  ∆k/k = ∆K/K − ∆L/L  ∆k/k = s · (Y/K) − sδ − n

Macroeconomics Chapter 343 Solow Growth Model  Y/K =(Y/L) / (K/L)  Y/K = y/k

Macroeconomics Chapter 344 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 345 Solow Growth Model

Macroeconomics Chapter 346 Solow Growth Model

Macroeconomics Chapter 347 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 348 Solow Growth Model

Macroeconomics Chapter 349 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