Sample Exam Solutions - University of Maryland College Park...

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University of Maryland College Park, Maryland Economics 600°August 2007 Dynamic Part: Exam You have 90 minutes to solve this exam. Any written or printed material is allowed. No electronic media are permitted. The total number of points on the exam is 50. PLEASE WRITE YOUR NAME AND STUDENT ID ON EACH BOOKLET YOU USE. 1 A Consumer Durables Problem Consider a consumer with in°nite horizon (consumer cares about futrue generations as much as she cares about herself). In each period, the consumer can consume two types of goods: perishable goods (such as food) denoted c t , and durable goods (such as automobiles or electron- ics, which provide utility for more than one period), denoted d t . The consumer±s in°nite horizon preferences over the consumption of the two goods is given by: 1 X t =0 ° t [ ± log c t + (1 ° ± ) log d t ] where 0 < ° < 1 is the consumer±s discount factor and ± is a constant. Durables provide consumption utility for many periods, but the stock of durables depreciates at a rate ² in each period. The consumer can also
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