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Unformatted text preview: Macroeconomic Policy Class Notes Long run growth 3: Sources of growth Revised: October 24, 2011 Latest version available at www.fperri.net/teaching/macropolicyf11.htm In the previous lecture we concluded that the returns to capital that is MPK + 1- were the key factor behind saving decisions. This class we will analyze what determines returns to capital. The marginal product of capital is how much additional output gets produced with an additional unit of capital. Technically it is the derivative of output relative to the capital stock, but with the production function we are using it turns out to be simply proportional to the average productivity of capital, where the factor proportionality is given by , that is MPK = Y K If we write the production function Y = AK ( L * H ) 1- where K is capital stock, L is labor input, H is the average level of education of the workforce and A is total factor productivity (the efficiency of production) (Relative to the case analyzed in the previous class we not considering raw labor input but we are weighting it by the education) we obtain that MPK = AK ( L * H ) 1- K = AH 1- ( L K ) 1- = A H 1- k 1- (1) that shows the key determinants of the marginal product of capital. The marginal product of capital depends positively on (the share of capital in production), on the average education of the workforce, on the total factor productivity A and depends negatively on the level of capital stock per worker (due to decreasing returns). The evidence suggests that does not vary greatly across countries, so if we want to understand why returns to capital differ across countries we should focus on A, H and k. In figure 1 we see how different levels of total factor productivity are key in determining the performance of an economy. Notice also that high returns to capital Sources of growth 2 are necessary and sufficient condition for factor accumulation, they are sufficient in the sense that if returns to capital are high (like in Germany in 1945) the factor accumulation will take place, either from domestic sources or from foreign sources. If returns are low, even if capital accumulation is forcefully imposed, as it has been done in some African countries or in some planned economies, it will not have persistent effects on capital and income per worker. 5 10 15 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Understanding Returns to Capital Capital per Worker Returns to Capital Germany, 1945 Africa, 1990 Returns with High A Returns with low A R Figure 1: Figure 1: Understanding Returns to capital Figure 2 shows the key determinants of return to capital in various countries (The value are all relative to the US so that a number of 0.90 means 90% of the US level). Observe that for example Uganda has low capital per worker and hence, onlevel)....
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