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Unformatted text preview: Problem Set 11 EC720.01 - Math for Economists Peter Ireland Boston College, Department of Economics Fall 2009 Due Tuesday, December 8 Human Capital Accumulation and Economic Growth This problem set asks you to use dynamic programming to characterize the solution to a variant of the model of human capital accumulation and economic growth studied by Robert Lucas, “On the Mechanics of Economic Development,” Journal of Monetary Economics , July 1988, pp.3-42 and, long before that, by Hirofumi Uzawa, “Optimum Technical Change in an Aggregative Model of Economic Growth,” International Economic Review , January 1965, pp.18-31. The specific version of that model considered here comes from Dirk Bethmann, “A Closed-Form Solution of the Uzawa-Lucas Model of Endogenous Growth,” Journal of Economics , January 2007, pp.87-107. In this model, a representative consumer divides up his or her time into an amount u t devoted to education, technical training, and other activities that add to the stock of human capital and an amount 1- u t devoted to producing goods and services for consumption and investment in physical capital. Let h t and k t denote the stocks of human capital and physical capital at the beginning of each period t = 0 , 1 , 2 ,... , let c t denote the amount of output consumed during each period t = 0 , 1 , 2 ,... , and assume that the two stocks evolve according to γu t h t ≥ h t +1 (1) and k α t [(1- u t ) h t ] 1- α ≥ c t + k t +1 (2) for all t = 0 , 1 , 2 ,... . Equation (1), with γ > 1, describes how human capital gets built up through time u t allocated to schooling and training. Equation (2), with 0allocated to schooling and training....
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- Fall '09
- Economics, Capital accumulation, ht