probset8

# probset8 - \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 8 } \\ \multicolumn{2}{c} {Due Thursday, November 5} \end{tabular*} \end{center} {\bfseries 1. Life Cycle Saving} Consider a consumer who is employed for $T+1$ periods: $t=0,1,. ..,T$. During each period of employment, the consumer receives labor income $w_{t}$, which as the notation indicates can vary over time. Let $k_{t}$ denote the consumer's stock of assets at the beginning of period $t$, and assume that $k_{0}=0$, so that the consumer begins his or her career with no assets. For all $t=1,2,. ..,T$, $k_{t}$ can be negative; that is, the consumer is allowed to borrow. However, the consumer must eventually save for retirement, a requirement that is captured by imposing the constraint $$k_{T+1} \geq k^{*} > 0$$ on the terminal value of the stock of wealth. Let $r_{t}$ be the interest rate earned on savings, or paid on debt, during each

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## probset8 - \documentclass[12pt]cfw_article...

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