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PSet8_F2011 - UNIVERSITY OF CALIFORNIA DEPARTMENT OF...

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UNIVERSITY OF CALIFORNIA Economics 202A DEPARTMENT OF ECONOMICS Fall 2011 M. Obstfeld/D. Romer Problem Set 8 Due in lecture, Thursday, December 1 1. Consider a consumer who lives for two periods. The consumer’s lifetime utility is U = u(c 1 ) + u(c 2 ), u’(·) > 0, u”(·) < 0. The consumer’s period-1 labor income, Y 1 , is certain, and is equal to The consumer’s period-2 labor income, Y 2 , is uncertain, with mean and variance . The consumer’s initial wealth is zero. a. Assume the consumer can borrow and lend at an interest rate of r = 0, and that there are no other financial assets. What is the first-order condition for c 1 ? For parts (b)-(d), assume that in addition to the safe asset with a real return of zero, there is a second, risky asset whose return has a mean and variance . The payoff to the risky asset is uncorrelated with Y 2 . b. Without using any math, explain in a sentence or two whether the consumer will purchase a strictly positive amount, a strictly negative amount, or none of this asset.
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