Shall we play a game? Solow growth model Steady state Break-even investment Rule of 70 Depreciation Dilution

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1 National Income & Business Cycles Why growth matters? Learn the closed economy Solow model See how a country s standard of living depends on its saving and population growth rates Importance of productivity growth Policies to promote growth 0 1 Solow growth model Steady state Break-even investment Rule of 70 Depreciation Dilution Productivity Sustainable growth rate Capital flows Foreign Direct Investment (FDI) Shall we play a game? Life expectancy is less than 50 years 1 out every 10 infants dies before the age of one More than 90% of households have no electricity, refrigerator, telephone, or car Fewer than 10% of adults have completed high school. What country is it? 2 3

2 for poor countries Data on infant mortality rates: 20% in the poorest 1/5 of all countries 0.4% in the richest 1/5 In Bangladesh, about 80% of people live on less than $2/day. One-fourth of the poorest countries have had famines during the past 3 decades. Poverty is associated with oppression of women and minorities. Economic growth raises living standards and reduces poverty. 4 5 Anything that effects the long-run rate of economic growth even by a tiny amount will have huge effects on living standards in the long run. annual growth rate of income per capita 2.0% 2.5% 25 years 64.0% 85.4% for rich countries percentage increase in standard of living after 50 years 169.2% 243.7% 100 years 624.5% 1,081.4% 6 can make a positive difference in the lives of hundreds of millions of people. These lessons help us understand why poor countries are poor design policies that can help them grow learn how our own growth rate is affected by shocks and our government s policies 7

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4 Given what you have learned so far, what causes differences in incomes? Y = A K α L 1- α due to Robert Solow, won Nobel Prize for contributions to the study of economic growth a major paradigm: widely used in policy making benchmark against which most recent growth theories are compared looks at the determinants of economic growth and the standard of living in the long run K is no longer fixed: investment causes it to grow, depreciation causes it to shrink. 2. L is no longer fixed: population growth causes it to grow. 3. The consumption function is simpler. In aggregate terms: Y = F (K, L ) Define: = = Assume constant returns to scale Divide through by L: 4. No G or T (only to simplify presentation; we can still do fiscal policy experiments) 5. Cosmetic differences

5 Output per worker, y 1 MPK f(k) Note: this production function exhibits MPK. Capital per worker, k 16 Y = In per worker terms: y =, where c = and i = s = the saving rate (an exogenous parameter) Note: s is the only lowercase variable that is not equal to its uppercase version divided by L Consumption function: (per worker) (remember, no G ) 17 saving (per worker) = = Output per worker, y f(k) = National income identity is Rearrange to get: (investment = saving, like in chap. 3!) sf(k) Using the results above, i = 18 k 1 Capital per worker, k 19

6 Assume that the population--and labor force-- grow at rate n. (n is exogenous) EX: Suppose L = 1000 in year 1 and the population is growing at 2%/year ( ). Then L = n L so L = in year The basic idea: increases the capital stock, and reduces it. Change in capital stock = investment depreciation dilution k Since, this becomes: δ The equation of motion for k 21 (δ + n)k =, the amount of investment necessary to keep constant. Break-even investment, (δ+n)k = the rate of depreciation n = population growth rate Break-even investment includes: to replace capital as it wears out to equip new workers with capital (otherwise, k would fall as the existing capital stock would be spread more thinly over a larger population of workers) Capital per worker, k 22 23

7 δ If investment is just enough to cover depreciation ( δ ) then capital per worker will remain : k =. This constant value, denoted k *, is called the. Investment and depreciation δ 24 Capital per worker, k 25 Investment and depreciation δ δ An increase in the saving rate investment causing k to : Investment and depreciation (δ+n)k s 1 f(k) Capital per worker, k 26 k 27

8 Higher s k*. And since y =, k* y*. Thus, the Solow model predicts that countries with higher rates of saving and investment will have levels of capital and income per worker in the long run An increase in n causes an in breakeven investment, leading to a steady-state level of k. Investment, break-even investment δ Higher n k*. And since y = f(k), k* y*. Thus, the Solow model predicts that countries with higher population growth rates will have levels of capital and income per worker in the long run. Capital per worker, 30 31

9 Income per person in 2000 (log scale) Determine what happens to each variable when population growth is 0 and when it is n? Fill in whether at the steadystate the variable is constant or whether it grows or declines and at which rate: Population growth = 0 L: K: Y: k: Population growth = n L: K: Y: k: y: y: Output and Investment Productivity growth investment which leads to a steadystate level of income per capita f 1 (k) (δ+n)k s 1 f(k) k Countries below the steady-state level of capital per worker will and countries above the steady-state level of capital per worker will The further below its steady-state level of capital per worker a country is, the it will grow After a war or a natural disaster, a country will grow Capital should flow from rich to poor countries Why? Is that happening? 34 35

10 36 37 What can cause growth in the Solow model? However, in a new steady-state: Can the above sources of growth continuously rise? In the long run, the rate of is the dominant factor determining how quickly living standards rise 38 From 1950 to 2000, U.S. farm sector productivity nearly tripled. The real price of computer power has fallen an average of 30% per year over the past three decades. Percentage of U.S. households with 1 computers: 8% in 1984, 62% in : 361m Internet users, 740m cell phone users 2011: 2.4b Internet users, 5.9b cell phone users 2001: ipod capacity = 5gb, 1000 songs. Not capable of playing episodes of Entourage. 2009: ipod capacity = 120gb, 30,000 songs. Can play episodes of Entourage. 39

11 Differences in income per capita: y = Ak α Both capital per worker (k) and total factor productivity (A) explain differences in incomes per capita around the world Richer countries have both more capital per worker and higher total factor productivity capital per worker explains about of the difference in incomes per capita TFP explain about of the difference in incomes per capita Is GDP per capita a good measure of the living standards? What are some other measures? 42 43

12 1. The Solow growth model shows that, in the long run, a country s standard of living depends positively on its saving rate. negatively on its population growth rate. positively on total factor productivity 2. An increase in the saving rate leads to higher output in the long run faster growth temporarily but not faster steady state growth In the long run, only a continuous increase in productivity growth can lead to sustained increase in the standard of living 4. Both capital per worker and total factor productivity explain income differences around the world 46