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# exam-01 - Midterm Exam 1 Viktor Tsyrennikov Graduate...

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Midterm Exam1 Viktor Tsyrennikov Graduate Macroeconomics September 23, 2011 The exam is designed to be finished in 75 minutes. There are 2 problems, worth 40 and 60 points respectively. Read carefully the whole problem before answering. Show your work – guessed answers will not be accepted. Name: 1

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Question 1. Consumption tax Consider a saving model with endogenous labor supply and ˜ u ( c t , l t ) = log parenleftBigg c t - l 1+1 t 1 + 1 parenrightBigg , η > 1 . Government taxes consumption purchases in period t at rate τ t . Wage rate is constant and equals w = 1. Agent starts with a 0 = 0. a) Derive the consumption Euler equation. b) Compute per period tax revenue as a function of tax rate τ in the case with βR t +1 = 1 , t and τ t = τ, t . How does η affects the tax revenue schedule? Interpret your result. c) Suppose the interest rate increases temporarily and the government increases taxes to pay high interest on its debt: { R t +1 } 0 = { β - 1 , β - 1 + e, β - 1 , β - 1 , ... } , { τ t } 0 = { 0 , τ, 0 , 0 , ... } , τ < 1 . Characterize the path of c t , l t .
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