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) f(k) Capital per worker, k Output per worker, y 1 MPK

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) sf(k) k* Capital per worker Investment, Depreciation f(k) Consumption per worker Investment per worker Output per worker

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

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

Stability of Steady State Equilibrium Once k*, steady state level of capital per worker, is achieved, it will remain stable. At k 1 < k*, investment exceeds depreciation. So, investment increases to raise k 1 to k* At k 2 > k*, depreciation exceeds investment. So, investment decreases to lower k 2 to k*

Increase is Saving An increase in saving results in a higher level of capital per worker. s 1 f(k) δk k1*k1*k2*k2* Capital per worker Investment, Depreciation s 2 f(k)

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 sf(k) δk k* k1k2 Capital per worker Investment, Depreciation

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. sf(k) (δ+n 1 )k k1*k1* k2*k2* Capital per worker Investment, Depreciation (δ+n 2 )k

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 sf(k) (δ + n + g)k k* Capital per worker Investment, Depreciation

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