probset11

# probset11 - \documentclass[12pt]cfw_article...

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\documentclass[12pt]{article} \usepackage{amsmath} \usepackage{geometry} \geometry{top=1in,bottom=1in,left=1in,right=1in} \setlength{\parindent}{0in} \setlength{\parskip}{2ex} \begin{document} \begin{center} \begin{tabular*}{6.5in}{l@{\extracolsep{\fill}}r} \multicolumn{2}{c} {\bfseries Problem Set 11} \\ \multicolumn{2}{c} {Due Tuesday, December 8} \end{tabular*} \end{center} {\bfseries 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,'' \emph{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,'' \emph{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,'' \emph{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 \gamma u_{t} h_{t} \geq h_{t+1} \tag{1} and k_{t}^{\alpha} [(1-u_{t})h_{t}]^{1-\alpha} \geq c_{t} + k_{t+1} \tag{2}

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## This note was uploaded on 02/19/2010 for the course ECON 720 taught by Professor Ireland during the Fall '09 term at BC.

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probset11 - \documentclass[12pt]cfw_article...

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