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# 2009-HW4 - constraint b Assume that the agent needs to...

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ECO 320L-HW4 Due November 18, 2009 Classtime 1. Questions for review 4, 8, and 12 from chapter 9. 2. Problems 2, 3, and 9 from chapter 9.. 3. Questions for review 5, and 7 from chapter 10. 4. Consider a monetary intertemporal model where individuals live for 2 periods: young ( t ) and old ( t + 1). In addition to money there is a riskless bond which pays a nominal interest rate R . The consumer works ( N t hours) in the first period of life and consumes ( C t +1 ) consumption good in the second period. The real wage in the first period is w t . The nominal prices of consumption good are P t and P t +1 . Let M t and B t are nominal money and bond holdings a young agent carries from time t to t + 1. Profits are zero. a Write down the first period and second period budget constraint of the agent and derive his lifetime budget
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Unformatted text preview: constraint. b Assume that the agent needs to carry money from ﬁrst period to the second period to ﬁnance his consumption in the second period, i.e. cash-in-advance constraint has to hold: P t +1 C t +1 = M t . Using the cash-in-advance constraint and lifetime budget constraint, derive the expression for the nominal money demand of the young agent at time t and his consumption at time t + 1 . c Assuming that the consumers utility function is given by U ( c t +1 ,N t ) = c t-N 2 t . Solve for the consumer’s optimal labor supply at time t and consumption at time t +1. How does the consumer’s optimal labor and consumption choice depend on the level of price level and the inﬂation rate? 1...
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