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# 2009-HW2 - solve the consumer’s optimal consumption C...

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ECO 320L-HW2 Due September 23, 2009 Before the Class Note: I will solve the questions below in the class. As a result, no HW’s will be accepted after the class starts. 1. Problems: Chapter 4, # 3 and 5. 2. Suppose that the representative consumer’s utility function is given by U ( C,l ) = ln( C ) + ln( l ) . Assume that the consumer’s yearly time endow- ment is h . The consumer’s real wage rate is w and he also earns non-wage income π. The government collects a proportional labor income tax at the rate t from the consumer. (a) Write down the budget constraint of the consumer. (b) Write down the consumer’s optimality condition. (c) Using the consumer’s optimality condition and the budget constraint,
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Unformatted text preview: solve the consumer’s optimal consumption C , leisure l, and labor supply N S as functions of h, w, t, and π. (d) Assume that h = 5000 hours, π = \$30000, w = \$10 /hour , and and t = 0 . 25 . Calculate the optimal consumption, leisure, and labor supply for the consumer. (e) Now assume that the tax rate is increased to t = 0 . 50 . Calculate the new values consumption, leisure, and labor supply. What happened to these variables as a result of the tax increase. 3. Repeat question (2) above assuming that the representative consumer’s utility function is given by U ( C,l ) = C . 3 l . 7 . 1...
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