Intermediate macroeconomics chapt07

Chapter 7: Economic Growth 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) Supply of Goods Production Function: y = f(k) Output per worker, y f(k) MPK Capital per worker, k 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 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 Capital Depreciation Capital depreciation = δk where δ>0 is depreciation rate Depreciation Depreciation, δk Capital per worker, k Steady State Equilibrium Steady state of capital accumulation is achieved when sf(k) = δk Investment, Depreciation δk DepreciationInvestment Capital per worker k1 k* k2 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* 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* Income per capita vs Investment 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 The Golden Rule Level of Capital A steady state equilibrium at which consumption per worker is maximized Investment, Depreciation δk sf(k) k1 k* k2 Capital per worker 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 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 Income Per Capita vs Population Growth 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 get y = 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 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 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 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