Chapter 7: Economic Growth

1. Chapter 7:Economic Growth

2. Supply of Goods Production Function: Y = F(K, L) Assume constant returns to scale: zY = F(zK, zL) Express in labor units: z = 1/L: Y/L = F(K/L, 1) or y = f(k)

3. Supply of Goods Production Function: y = f(k) Output per worker, y f(k) MPK 1 Capital per worker, k

4. Demand for Goods Express Y = C + I in per unit of labor: Y/L = C/L + I/L y = c + I = (1-s)y Where (1-s) = MPC and s = MPS y = (1-s)y + i i = y- (1-s)y = sy = sf(k) This is Investment = Saving

5. Demand Components f(k) = (1-s)f(k) + sf(k) Investment, Depreciation f(k) Output per worker Consumption per worker sf(k) Investment per worker k* Capital per worker

6. Capital Depreciation Capital depreciation = δk where δ>0 is depreciation rate Depreciation Depreciation, δk Capital per worker, k

7. Steady State Equilibrium Steady state of capital accumulation is achieved when sf(k) = δk Investment, Depreciation δk Depreciation<Investment sf(k) Depreciation>Investment Capital per worker k2 k1 k*

8. Stability of Steady State Equilibrium • Once k*, steady state level of capital per worker, is achieved, it will remain stable. • At k1 < k*, investment exceeds depreciation. So, investment increases to raise k1 to k* • At k2 > k*, depreciation exceeds investment. So, investment decreases to lower k2 to k*

9. Increase is Saving An increase in saving results in a higher level of capital per worker. Investment, Depreciation δk s2f(k) s1f(k) Capital per worker k1* k2*

10. Income per capita vs. Investment

11. The Golden Rule Level of Capital • A steady state level of capital per worker at which consumption per worker is maximized. • Above the Golden Rule steady state level, increases in steady state capital per worker reduce consumption per worker

12. The Golden Rule Level of Capital A steady state equilibrium at which consumption per worker is maximized Investment, Depreciation δk sf(k) k1 k2 k* Capital per worker

13. Labor Force Growth • Define n as the rate of labor force growth • The amount of capital per worker required to offset depreciation and population growth is (δ + n)k • Steady state equilibrium condition is f(k*) = (δ + n)k* • Population growth shifts (δ + n)k up reducing the level of capital per worker

14. Impact of Labor Force Growth Labor force growth results in a lower level of capital per worker. Investment, Depreciation (δ+n2)k (δ+n1)k sf(k) k2* k1* Capital per worker

15. Income Per Capita vs. Population Growth

16. Economic Efficiency • Rewrite production function as Y = F(K, LE), where E is an indicator of the efficiency of labor • Divide by (LE) to gety = f(k) where y = Y / (L  E) and k = K / (L  E) • Define n = rate of labor force growth and g = rate of efficiency improvement

17. Steady State Equilibrium Steady state of capital accumulation is achieved when sf(k) = (δ+n+g)k Investment, Depreciation (δ + n + g)k sf(k) k* Capital per worker

18. Determinants of Economic Growth • Investment in physical capital • Proper maintenance of physical capital • Investment in human capital • Decrease labor force growth • Increases worker efficiency • Investment in technological advancement • Investment in infrastructure

19. Reasons for Recent Slow Growth • Measurement problem of inflation as quality improvement is not taken into account • Fluctuating oil prices • Reduced worker quality • Depletion of Ideas