U.S. GDP 6,400. GDP in billions of 1992 dollars 3,200 1,600

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1 Figure 10-1 U.S. GDP Since 1890 Aggregate U.S. output has increased by a factor of 43 since Source: : Historical Statistics of the United States; : National Income and Product Accounts. 6,400 U.S. GDP GDP in billions of 1992 dollars 3,200 1,

2 Table 10-1 The Evolution of Output per Capita in Five Rich Countries Since 1950 Annual Growth Rate Output per Capita (%) Real Output per Capita (1996 dollars) /1950 France ,489 21, Germany ,642 21, Japan ,940 22, United Kingdom ,321 21, United States ,903 30, Average ,259 23, Source: : Penn World Tables, constructed by Robert Summers and Alan Heston (pwt.econ.upenn.edu). Extended from 1992 to 2000 by using rates of real GDP growth from the OECD Economic Outlook, and population growth rates from the IMF International Financial Statistics (IFS). The average in the last line is a simple (unweighted) average.

3 Figure 10-2 Growth Rate of GDP per Capita Since 1950 Versus GDP per Capita in 1950; OECD Countries Countries that had a lower level of output per capita in 1950 have typically grown faster. Source: See Table South Korea, the Czech Republic, Hungary, and Poland are not included because of missing data. Annual growth rate of GDP per capita (percent) 6 Japan 5 Portugal 4 Greece Germany 3 Turkey 2 United Kingdom United States New Zealand GDP per capita in 1950 (1992 dollars)

4 Figure 10-4 Growth Rate of GDP per Capita, ,Versus GDP per Capita in 1960; OECD, Africa, and Asia. Asian countries are converging to OECD levels. There is no evidence of convergence for African countries. Source: See Figure Annual growth rate of GDP per capita (percent) OECD Africa Asia GDP per capita in 1960 (1992 dollars)

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7 Figure 10-5 Output and Capital per Worker Increases in capital per worker lead to smaller and smaller increases in output per worker. Output per worker, Y/N D9 C9 B9 A9 Y/N F(K/N, 1) A B C D Capital per worker, K/N

8 Figure 10-6 The Effects of an Improvement in the State of Technology An improvement in technology shifts the production function up, leading to an increase in output per worker for a given level of capital per worker. F(K/N, 1) Output per worker, Y/ N B9 A9 F(K/N, 1) A Capital per worker, K/N

9 Figure 11-1 Capital, Output, and Saving/Investment Capital stock Output/income Change in the capital stock Saving/investment

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11 The Solow Model III: The Steady State We are in the steady state when K t+1 = K t. Recall: k t+1 k t = sy t δk t sy t = δk t saf(k t ) = δk t saf(k ) = δk Example: Assume Af(k) = k s k = δk s δ = k k = ( ) s 2 δ 4

12 Figure 11-2 Capital and Output Dynamics When capital and output are low, investment exceeds depreciation, and capital increases. When capital and output are high, investment is less than depreciation and capital decreases. Depreciation per worker K t /N Output per worker, Y/N Y*/N B C Output per worker f(k t /N) Investment per worker sf(k t /N) D A (K 0 /N) K*/N Capital per worker, K/N

13 Figure 11-3 The Effects of Different Saving Rates A country with a higher saving rate achieves a higher level of output per worker in steady state. Output per worker, Y/N Y 1 /N Y 0 /N Depreciation per worker K t /N Output per worker f(k t /N) Investment per worker s 1 f(k t /N) Investment per worker s 0 f(k t /N) K 0 /N K 1 /N Capital per worker, K/N

14 Figure 11-4 The Effects of an Increase in the Saving Rate on Output per Worker An increase in the saving rate leads to a period of growth until output reaches its new higher steady-state level. (Without technological progress) Output per worker, Y/N Y 1 /N Y 0 /N Associated with saving rate s 1 >s 0 Associated with saving rate s 0 t Time

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16 Figure 11-6 The Effects of the Saving Rate on Consumption per Worker in Steady State An increase in the saving rate leads to an increase, then to a decrease in consumption per worker in steady state. Consumption per worker, C/N Maximum steady state consumption per worker s G 0 1 Saving rate, s

17 The Solow Model V: Human Capital and Technological Progress Sources of growth 1. Physical Capital Accumulation F (K, N) 2. Human Capital Accumulation F (K, H) 3. Technological Progress F (K, N, A) (3): The GDP per effective worker ŷ = Y/NA = f(k/an) = f(ˆk) where ˆk is now capital per effective worker. NB: We can use the same graph as before in ˆk but now if ŷ = Y/AN is constant then y = Y/N grows as long as A grows. 6

18 Figure 12-1 Output per Effective Worker Versus Capital per Effective Worker Because of decreasing returns to capital, increases in capital per effective worker lead to smaller and smaller increases in output per effective worker. Output per effective worker, Y/AN f(k/an) Capital per effective worker, K/AN

19 Figure 12-2 Dynamics of Capital per Effective Worker and Output per Effective Worker Capital per effective worker and output per effective worker converge to constant values in the long run. Output per effective worker, Y/AN Y ( AN ) * B C D Required investment ( g A g N )K/AN Production f(k/an) Investment sf(k/an) A (K/AN) 0 (K/AN)* Capital per effective worker, K/AN

20 Table 12-1 The Characteristics of Balanced Growth Rate of growth of: 1 Capital per effective worker 0 2 Output per effective worker 0 3 Capital per worker g A 4 Output per worker g A 5 Labor g N 6 Capital g A + g N 7 Output g A + g N

21 Figure 12-3 The Effects of an Increase in the Saving Rate: I An increase in the saving rate leads to an increase in the steady-state levels of output per effective worker and capital per effective worker. Output per effective worker, Y/AN Y ( AN ) 1 Y ( AN ) 0 f(k/an ) ( g A g N )K/AN s 1 f(k/an ) s 0 f(k/an ) (K/AN) 0 (K/AN) 1 Capital per effective worker, K/AN

22 Figure 12-4 The Effects of an Increase in the Saving Rate: II The increase in the saving rate leads to higher growth until the economy reaches its new, higher, balanced growth path. B Associated with s 1 > s 0 Capital, K (log scale) B slope (g A g N ) A A Associated with s 0 t Time B Associated with s 1 > s 0 Output, Y (log scale) B slope (g A g N ) A A Associated with s 0 t Time