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Unformatted text preview: ECON 476: Macroeconomics II: Business Cycles Homework 2 Due Date: Feb 3 (Recitation Hour). For all questions, if necessary, make appropriate assumptions. 1. Consider the following economy where households have identical prefer ences. Assume that the households own all factors of production (including the initial capital stock k ) all shares in firms and that these endowments are equally distributed across households. Households maximize T X t =0 β t u ( c t , 1 n t ) , < β < 1 given T X t =0 p t [ c t + i t ] ≤ T X t =0 p t [ r t k t + w t n t ] k t +1 = (1 δ ) k t + i t , for t = 0 , 1 ,...T . Here, p t is the price of a unit of output at time t , r t and w t is, respectively, the rental rate and wage rate in unit of output. Firms own nothing. They simply hire labor and capital and pay their services. The production technology is given by a constant returns to scale function y t = z t F ( k t ,n t ). The sequence of productivity { z t } T t =0 is known at time 0. Firms maximize the profittime 0....
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 Fall '07
 Chang
 Economics, Macroeconomics, rental rate, Kt Kt

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