Unformatted text preview: increases in the efficiency of labour E are analogous to increases in the labour force L. Technological progress causes the efficiency of labour E to grow at some constant rate g. If g = 0.02, then each unit of labour becomes 2 percent more efficient each year, and output increases as if the Page 24 of 52 Jessica Gahtan Prof: Mokhles Hossain Macroeconomics ECON2000 Fall 2013 labour force had increased by 2%. This form of technological progress is called labour augmenting, and g is called the rate of labour augmenting technological progress. The effective number of workers L x E is growing at rate n + g. We now let k = K/(L x E) and y = Y/(L x E). We can again write y = f(k). Now the equation showing the evolution of k over time is: Δk = sf(k) – (δ + n + g)k As before, the change in capital stock equals investment minus break even investment. Now, however, δk is needed to replace depreciating capital, nk is needed to provide capital for new workers, and gk is needed to provide for the new “effective workers” created by technology. In the steady state, capital per effective worker and output per effective worker are constant. Output per worker is growing at rate g, and total output is growing at rate n + g. According to the Solow model, only technological progress can explain sustained growth and persistently rising living standards. The Golden Rule level of capital is now defined as the steady state that maximizes consumption per effective worker. Consumption per effective worker is: c* = f(k*)  (δ + n + g)k* Steady state consumption is maximized if MPK = δ + n + g, or MPK  δ = n + g That is, the net marginal product of capital equals the rate of growth of total output. Comparing the Solow model to empirics Balanced growth: the Solow model predicts that technological progress causes the values of many variables to rise together in the steady state, called balanced growth. This holds true in the long run data for the US economy. The capital output ratio has remained approximately constant over time, as has the real rental price of capital. Convergence: convergence is the question of whether economies that start off poor grow faster than economies that start off rich. If there is no convergence, they remain poor. The Solow...
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 Fall '10
 Henriques
 Economics, Macroeconomics

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