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Understanding Economic Growth: Supply of Goods and Production Function Dynamics

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This chapter explores the relationship between economic growth and the supply of goods, framed through the production function Y = F(K, L). It delves into the effects of constant returns to scale and the transformation to labor units, emphasizing the significance of output per worker (Y/L) and its determinants. The concepts of investment, saving, and depreciation are analyzed to define steady-state equilibrium conditions and their stability. The chapter also addresses capital accumulation, the impact of labor force growth, and factors influencing economic efficiency and growth, including investment in human capital and technological advancements.

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Understanding Economic Growth: Supply of Goods and Production Function Dynamics

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  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

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