1. Technological Progress and the Production Function AN = Effective Labor = Labor in Efficiency Units Assuming: Constant returns to scale Given state of technology 2Y = F(2K,2AN) xY = F(xK,xAN) Y/AN = f(K/AN)

2. Technological Progress and the Production Function f(K/AN) Output per effective worker, Y/AN Capital per effective worker, K/AN Decreasing returns to Kapital per Effective Worker

3. Investment sf(K/AN) Investment, Capital, & Output per Effective Worker Production f(K/AN) Output per effective worker, Y/AN Capital per effective worker, K/AN

4. Determining the needed to maintain a given Assume: Then: A population growth rate/yr (g N ) N grows at same rate as g N Rate of technological progress g A Growth rate of effective labor (AN) = g A + g N If: g A = 2% & g N = 1%, then AN growth = 3% Investment per effective worker to keep capital per effective worker steady

5. Determining the needed to maintain a given The level of investment needed to maintain : Must offset depreciation, δK Must outfit new workers with capital, g N K Must give all workers additional capital to keep up, g A K Amount of Investment Needed/Effective Worker to maintain a constant K/AN =

6. Dynamics of Capital & Output Investment sf(K/AN) Production f(K/AN) Required investment ( + g A + g N )K/AN Output per effective worker, Y/AN Capital per effective worker, K/AN A B (K/AN) o C D Observe (K/AN) 0 : AC > AD (K/AN)* *

7. Dynamics of Capital & Output Observations about the Steady State: Growth rate of Y = growth rate of AN = g Y g Y = (g A + g N ) Output growth rate [= g A + g N ] independent of s Capital growth rate g K = (g A + g N ) Capital keeps up with labor force and technology Per worker output growth rate = g Y – g N = g A

8. Dynamics of Capital & Output The Characteristics of Balanced Growth Growth: rate of 1. 2. 3. 4. 5. 6. 7. Capital per effective worker0 Output per effective worker0 Capital per workerg A Output per workerg A Laborg N Capitalg A +g N Output g A +g N

9. The Effects of the Savings Rate f(K/AN) Output per effective worker, Y/AN Capital per effective worker, K/AN A (K/AN) 0 0 ( + g A + g N )K/AN s 0 f(K/AN) Savings = s 0 Steady-state = & 0 0 s 1 f(K/AN) (K/AN) 1 B Savings increase to s 1 S 1 f(K/AN) Steady-state = & 1 1 1

10. The Effects of an Increase in the Savings Rate Output, Y (log scale) Time t Associated with s 0 Associated with s 1 > s 0 B slope (g A + g N ) B A A Capital, K (log scale) Time t Associated with s 0 Associated with s 1 > s 0 B slope (g N + g A ) B A A

11. Slide #11 Technological Progress and Growth The Facts of Growth Revisited A Review Observations on growth in developed countries since 1950: Sustained growth 1950-mid 1970s Slowdown in growth since the mid 1970s Convergence: countries that were further behind have been growing faster

12. Slide #12 The Facts of Growth Revisited Understanding These Trends Determinants of Fast Growth: Higher rate of technological progress (g A ) Higher level of capital/effective worker (K/AN) Capital Accumulation vs. Technological Progress

13. Growth of Output per Capita, g Y/N Rate of Technological Progress, g A 1950-731973-87Change1950-731973-87Change (1)(2)(3)(4)(5)(6) France4.01.8-2.24.92.3-2.6 Germany4.92.1-2.85.61.9-3.7 Japan8.03.1-4.96.41.7-4.7 United Kingdom2.51.8-0.72.31.7-0.6 United States2.21.6-0.62.60.6-2.0 Average4.32.1-2.24.41.6-2.8 Inferring rate of technological progress, g A For Y = F(K,AN) g Y = αg K + (1- α)(g N + g A ) where α = capital share of national income (1 - α) = labor share of national income Can measure Solow residual (total factor productivity) as g Y not explained by capital growth and labor force growth Residual = g Y – {α g K + (1 – α) g N } Then (1-α) g A = Residual … or g A = Residual/ (1-α)

14. Technological Progress and Growth The Findings 1950-1973 high growth of output per capita due to technological progress Since 1973 slowdown in growth of output per capita due to a decrease in the rate of technological progress Convergence is the result of technological progress Capital Accumulation vs. Technological Progress