IH2_PSA - Problem Set 5 Growth Model in Continuous Time...

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Problem Set 5: Growth Model in Continuous Time Econ720. Fall 2009. Lutz Hendricks 1 Capital income tax [Romer 2.9] Consider a Ramsey economy on its balanced growth path. At time 0 the government starts to tax capital income, so that the interest rate facing the household is r ( t ) = (1 ) f 0 ( k t ) where I have assumed that ± = 0 . Tax revenues are rebated to the household in a lump-sum fashion. The change in the policy is unanticipated. 1. How does the tax a/ect the _ k = 0 and the _ c = 0 loci? 2. How do the balanced growth values of c and k change? 3. Describe the changes at time 0 and the transition path thereafter. 4. Show that the saving rate on the balanced growth path ([ y c ] =y ) is decreasing in . 5. Imagine there are two countries that di/er only in . Do the residents of the high countries have an incentive to invest in the low country or vice versa? 6. How do your answers change if the tax revenues are used to pay for government purchases instead of being rebated? 2 Continuous Time CIA Model. Cash and Credit Goods. Crusoe solves the following problem: max Z 1 0 e u ( c t ; g t ) dt subject to the budget constraint _ k t + c t + g t + _ M t =p t = f ( k t ) + x t and the CIA constraint c t ± M t =p t The notation is standard. There are two consumption goods, which are perfect substitutes
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This note was uploaded on 10/29/2009 for the course ECON 720 at UNC.

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IH2_PSA - Problem Set 5 Growth Model in Continuous Time...

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