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Unformatted text preview: Problem Set 8 EC720.01 - Math for Economists Peter Ireland Boston College, Department of Economics Fall 2009 Due Thursday, November 5 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 consumers stock of assets at the beginning of period t , and assume that k = 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 k * > 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 period t = 0 , 1 ...,T ; again as the notation suggests, this interest rate can vary over time. Then the consumers stock of assets evolves according to k t +1 = k t +...
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- Fall '09