1. In this chapter, we learn: some facts related to economic growth that later chapters will seek to explain. how economic growth has dramatically improved welfare around the world. that this growth is actually a relatively recent phenomenon. some tools used to study economic growth, including how to calculate growth rates and why a “ratio scale” makes plots of per capita GDP easier to understand. The United States of a century ago could be mistaken for Kenya or Bangladesh today. Some countries have seen rapid economic growth and improvements to health quality, but many others have not. We will trace income and health trends as reported in the UNHDR Sustained increases in standards of living are a recent phenomenon. Modern economic growth only emerged in the most recent two or three centuries. Sustained economic growth emerges in different places at different times. Per capita GDP – living standards – differ remarkably around the world. The Great Divergence is the era of increased difference in standards of living across countries. Before 1700, nations differed only by a factor of two or three, while today it is over a factor of 50 for several countries.

3. From 1870 to 2000, United States per capita GDP rose by nearly 15- fold. A typical college student today will earn a lifetime income about twice his or her parents. If we observe a constant doubling time for a variable, e.g., population or real per capita income, the variable is growing at a constant annual rate. If income is growing at a constant rate it will be a straight line on a ratio scale; but if growth rates are rising, the slope will be increasing. When plotted on a ratio scale, it is easy to see that per capita GDP in the United States has grown at approximately 2 percent per year over the last 130 years.

4. The Rule of 70, Doubling Time, and the Ratio Scale Time to double (T) at constant growth rate (g): 2 = (1 + g) T or Ln 2 = 0.693 ≈ 0.70 = T Ln (1 + g) ≈ T g since for small g, Ln(1 + g) ≈ g so T = 70/g where g is expressed in percent The Rule of 70 says that if y t grows at a rate of g percent per year, then the number of years it takes y t to double is approximately equal to 70/g. Seemingly small differences in growth rates result in large differences over time. The time it takes to double only depends on the growth rate and not the initial value. If we know a variable’s doubling time, T, its average growth rate is g = 70/T

5. The Definition of Economic (or any) Growth A growth rate, g, is the percentage change in a variable. g x = dx/x From what we know about calculus, d(x * z) = dx + dz d(x n ) = d(x * x * x… * x) = n dx d[Ln(x)] = dx/x = g x = (x t+1 – x t )/x t The value of variable x next year is then x t+1 = x t * (1 + g x ) After t years of constant growth at rate g, a variable whose initial value is x 0 will equal x t = x 0 (1 + g) (1 + g) … (1 + g) = x 0 (1 + g) t If we know x t and x 0, the average compound rate of growth over t years is g = (x t / x 0 ) 1/t – 1

6. Division of two variables implies subtraction of the growth rates. z = x/y = x 1 y -1 dz = y -1 d(x 1 ) + x 1 d(y -1 ) = y -1 dx – 1y -2 x 1 d(y) dz/z = (y -1 dx)/(x 1 y -1 ) – (1y -2 x 1 d(y))/(x 1 y -1 ) = dx/x – y -1 dy = dx/x – dy/y = g x – g y Multiplication of two variables implies addition of the growth rates. z = xy = x 1 y 1 dz = y 1 d(x 1 ) + x 1 d(y 1 ) = y 1 dx + x 1 d(y) dz/z = (y 1 dx )/(x 1 y 1 ) + (x 1 dy)/(x 1 y 1 ) = dx/x + dy/y = g x + g y When a variable is raised to an exponent, the growth rate of the quantity is the exponent times the growth rate of the variable. z = x a = x x … x so dz = a x a-1 dx = and dz/z = (a x a-1 dx )/ x a = a dx/x = a g x

7. Y = Real GDP = Population * Per Capita Real GDP Y = N y g Y = g N + g y and g y = g Y - g N

8. Modern Growth around the World After World War II, growth in Germany and Japan accelerated. Convergence is the idea that poorer countries will grow faster to catch up to the level of income in richer countries. Brazil had accelerated growth until 1980 and then stagnated, while China and India have had the reverse pattern. When comparing levels of income on a ratio scale, recall that data points that are half below another country are actually much lower because the numbers on the vertical axis double. Convergence To US US Leapfrogged UK

9. Some countries have exhibited a negative growth rate over a forty year period. Other countries have sustained nearly 6 percent growth over the same period. Most countries have sustained about 2 percent growth. Small differences in growth rates result in large differences in standards of living.

10. The bulk of the world’s population is substantially richer today than it was in 1960. The fraction of people living in poverty has fallen since 1960. A major reason for these changes is the recent economic growth in China and India – which together account for 40 percent of the world population.

11. Growth Rules For Cobb-Douglas Production Function Y t = A t K t 1/3 L t 2/3 Applying rules of growth rates will show that g(Y t ) = g(A t ) + (1/3) * g(K t ) + (2/3) * g(L t ) We can estimate total factor productivity growth, g(A t ), as a residual g(A t ) = g(Y t ) - (1/3) * g(K t ) - (2/3) * g(L t )

12. The Costs of Economic Growth The benefits of economic growth include: improvements in health, higher incomes, and an increase in the range of goods and services, among other things. Costs of economic growth include environmental problems, global warming, income inequality across and within countries, and a loss of certain types of jobs. Economists generally have a consensus that the benefits of economic growth outweigh the costs.

13. 3.7 A Long-Run Roadmap Are there certain policies that will allow a country to grow faster? If not, what about a country’s “nature” makes it grow at a slower rate?

14. CHAPTER 3 An Overview of Long-Run Economic Growth Summary Viewed over the long course of history, sustained growth in standards of living is a very recent phenomenon. If the 130,000 years of human history were warped and collapsed into a single year, modern economic growth would have begun only at sunrise on the last day of the year. Modern economic growth has taken hold in different places at different times. Since several hundred years ago, when standards of living across countries varied by no more than a factor of 2 or 3, there has been a “Great Divergence.” Standards of living across countries today vary by more than a factor of 60.

15. Incomes in the poorest countries of the world are probably no more than twice as high as average incomes around the world a thousand years ago. Since 1870, growth in per capita GDP has averaged about 2 percent per year in the United States. Per capita GDP has risen from about $2,500 in 1870 to more than $37,000 today. Growth rates throughout the world since 1960 show substantial variation, ranging from negative growth in many poor countries to rates as high as 6 percent per year in several newly industrializing countries, most of which are in Asia.

16. Growth rates typically change over time. In Germany and Japan, growth picked up considerably after World War II as incomes in these countries converged to levels in the United Kingdom. Growth rates have slowed down as this convergence occurred. Brazil exhibited rapid growth in the 1950s and 1960s and slow growth in the 1980s and 1990s. China showed the opposite pattern.

17. Economic growth, especially in India and China, has dramatically reduced poverty in the world. In 1960, 2 out of 3 people in the world lived on less than $5 per day (in today’s prices). By 2000, this number had fallen to only 1 in 10.

19. Real Per Capita Incomes in Constant Dollars