probset6 -...

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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 6 } \\ \multicolumn{2}{c} {Due Thursday, October 22} \end{tabular*} \end{center} {\bfseries 1. The Permanent Income Hypothesis} The permanent income hypothesis describes how a forward-looking consumer optimally saves or borrows to smooth out his or her consumption in the face of a fluctuating income stream. This problem formalizes the permanent income hypothesis using a two- period model. So consider a consumer who lives for two periods, earning income $w_{0}$ during period $t=0$ and $w_{1}$ during period $t=1$. Let $c_{0}$ and $c_{1}$ denote his or her consumption during periods $t=0$ and $t=1$ and let $s$ denote his or her amount saved (or borrowed, if negative) during period $t=0$. Suppose that savings earn interest between $t=0$ and $t=1$ at the constant rate $r$. Then the consumer faces the budget constraints \begin{equation} w_{0} \geq c_{0} + s \tag{1} \end{equation} at $t=0$ and \begin{equation} w_{1} + (1+r)s \geq c_{1} \tag{2} \end{equation} at $t=1$. Finally, suppose that the consumer's preferences are described by the utility function \begin{equation} \ln(c_{0}) + \beta \ln(c_{1}), \tag{3} \end{equation} where the discount factor lies between zero and one: $0<\beta<1$. \begin{description}
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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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probset6 -...

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