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midterm-14-451-spring2003

midterm-14-451-spring2003 - 14.451 Midterm George-Marios...

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14.451 Midterm George-Marios Angeletos Spring 2003 You have 1.5 hours . You must answer all questions. No books or notes are allowed. The fi rst question is stated in discrete time. But if you feel more comfortable in continuous time, feel free to give your answer in continuous time. Good luck! Question 1 Consider the neoclassical growth model, in discrete time. There is no exogenous technological change and no population growth; the size of population and labor is 1 . The technology is Cobb- Douglas: y t = f ( k t ) = k α t where k t denotes the capital stock, y t denotes output or income, and α (0 , 1) . Firms are compet- itive. Hence, r t = f 0 ( k t ) and w t = f ( k t ) f 0 ( k t ) , implying y t = r t k t + w t , where r t is the return on capital and w t is the wage rate. We introduce a government in the model. The government imposes a time-invariant fl at-rate tax on the consumption expenditures of households. It uses the revenues from the consumption tax to fi nance a public good that provides utility to households. The government budget in period
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