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 ° ° t 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.
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