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Figure 10-1 U.S. GDP Since 1890 Aggregate U.S. output has increased by a factor of 43 since 1890. Source: 1890–1929: Historical Statistics of the United States; 1929–2000: National Income and Product Accounts. 6,400 GDP in billions of 1992 dollars U.S. GDP 3,200 1,600 800 400 200 1890 Oliver Blanchard Macroeconomics, 3E 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 © 2003 Prentice Hall, Inc Upper Saddle River, NJ 07458 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) 1950–1973 1974–2000 1950 2000 2000/1950 France 4.1 1.6 5,489 21,282 3.9 Germany 4.8 1.7 4,642 21,910 4.7 Japan 7.8 2.4 1,940 22,039 11.4 United Kingdom 2.5 1.9 7,321 21,647 3.0 United States 2.2 1.7 11,903 30,637 2.6 Average 4.3 1.8 6,259 23,503 3.7 Source: 1950–1992: 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. Oliver Blanchard Macroeconomics, 3E © 2003 Prentice Hall, Inc Upper Saddle River, NJ 07458 Figure 10-2 Growth Rate of GDP per Capita Since 1950 Versus GDP per Capita in 1950; OECD Countries Annual growth rate of GDP per capita 1950–1992 (percent) Countries that had a lower level of output per capita in 1950 have typically grown faster. Source: See Table 10-1. South Korea, the Czech Republic, Hungary, and Poland are not included because of missing data. Oliver Blanchard Macroeconomics, 3E 6 Japan 5 Portugal 4 Greece Germany Turkey 3 2 United States United Kingdom New Zealand 1 0 4000 8000 GDP per capita in 1950 (1992 dollars) 12000 © 2003 Prentice Hall, Inc Upper Saddle River, NJ 07458 Figure 10-4 Growth Rate of GDP per Capita, 1960–1992,Versus GDP per Capita in 1960; OECD, Africa, and Asia. Annual growth rate of GDP per capita 1960–1992 (percent) Asian countries are converging to OECD levels. There is no evidence of convergence for African countries. Source: See Figure 10-2. Oliver Blanchard Macroeconomics, 3E 7.5 OECD Africa Asia 5.0 2.5 0.0 2.5 0 5000 10000 GDP per capita in 1960 (1992 dollars) 15000 © 2003 Prentice Hall, Inc Upper Saddle River, NJ 07458 Figure 10-5 Output and Capital per Worker Output per worker, Y/N Increases in capital per worker lead to smaller and smaller increases in output per worker. D9 C9 Y/N F (K/N , 1) B9 A9 A Oliver Blanchard Macroeconomics, 3E B C Capital per worker, K/ N D © 2003 Prentice Hall, Inc Upper Saddle River, NJ 07458 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. Output per worker, Y/ N F (K/N , 1) B9 F (K/N , 1) A9 A Capital per worker, K/ N Oliver Blanchard Macroeconomics, 3E © 2003 Prentice Hall, Inc Upper Saddle River, NJ 07458 Figure 11-1 Capital, Output, and Saving/Investment Capital stock Output/income Change in the capital stock Saving/investment Oliver Blanchard Macroeconomics, 3E © 2003 Prentice Hall, Inc Upper Saddle River, NJ 07458 The Solow Model III: The Steady State • We are in the steady state when Kt+1 = Kt . • Recall: kt+1 − kt = syt − δkt syt = δkt sAf (kt) = δkt sAf (k∗) = δk∗ • Example: Assume Af (k) = √ k µ ¶2 √ √ s s s k = δk ⇒ = k ⇒ k∗ = δ δ 4 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. Output per worker, Y/N Depreciation per worker Kt /N Output per worker f (Kt /N ) Y */ N Investment per worker s f (Kt /N ) B C D A (K0/ N) Oliver Blanchard Macroeconomics, 3E K */ N Capital per worker, K/ N © 2003 Prentice Hall, Inc Upper Saddle River, NJ 07458 Figure 11-3 The Effects of Different Saving Rates Output per worker, Y/N A country with a higher saving rate achieves a higher level of output per worker in steady state. Depreciation per worker Kt /N Output per worker f (Kt /N ) Y1/ N Investment per worker s1f (Kt /N ) Y0/ N Investment per worker s0f (Kt /N ) K0/ N Oliver Blanchard Macroeconomics, 3E K1/ N Capital per worker, K/ N © 2003 Prentice Hall, Inc Upper Saddle River, NJ 07458 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. Output per worker, Y/N (Without technological progress) Associated with saving rate s1 >s0 Y1/ N Y0/ N Associated with saving rate s0 t Time Oliver Blanchard Macroeconomics, 3E © 2003 Prentice Hall, Inc Upper Saddle River, NJ 07458 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 0 sG 1 Saving rate, s Oliver Blanchard Macroeconomics, 3E © 2003 Prentice Hall, Inc Upper Saddle River, NJ 07458 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 /N A = f (K/AN ) = f (k̂) where k̂ is now capital per effective worker. • NB: We can use the same graph as before in k̂ but now if ŷ = Y /AN is constant then y = Y /N grows as long as A grows. 6 Figure 12-1 Output per Effective Worker Versus Capital per Effective Worker Output per effective worker, Y/AN Because of decreasing returns to capital, increases in capital per effective worker lead to smaller and smaller increases in output per effective worker. f (K/AN) Capital per effective worker, K/AN Oliver Blanchard Macroeconomics, 3E © 2003 Prentice Hall, Inc Upper Saddle River, NJ 07458 Figure 12-2 Dynamics of Capital per Effective Worker and Output per Effective Worker Output per effective worker, Y/AN Capital per effective worker and output per effective worker converge to constant values in the long run. Required investment ( gA gN )K/AN Production f (K/AN) (ANY )* Investment sf (K/AN) B C D A (K/AN)0 (K/AN)* Capital per effective worker, K/AN Oliver Blanchard Macroeconomics, 3E © 2003 Prentice Hall, Inc Upper Saddle River, NJ 07458 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 4 Output per worker 5 Labor 6 Capital gN gA + gN 7 Output gA + gN Oliver Blanchard Macroeconomics, 3E gA gA © 2003 Prentice Hall, Inc Upper Saddle River, NJ 07458 Figure 12-3 The Effects of an Increase in the Saving Rate: I Output per effective worker, Y/AN 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. f (K/AN ) (ANY ) (ANY ) 1 ( gA gN )K/AN s1f (K/AN ) 0 s0f (K/AN ) (K/AN)0 (K/AN)1 Capital per effective worker, K/AN Oliver Blanchard Macroeconomics, 3E © 2003 Prentice Hall, Inc Upper Saddle River, NJ 07458 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 Capital, K (log scale) Associated with s1 > s0 A B slope (gA gN ) A Associated with s0 t Time B Output, Y (log scale) Associated with s1 > s0 A B slope (gA gN ) A Associated with s0 t Time Oliver Blanchard Macroeconomics, 3E © 2003 Prentice Hall, Inc Upper Saddle River, NJ 07458