f09_ramseyhw

# f09_ramseyhw - φ units of new capital in the future. A)...

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Homework Problems - Due in section 10/16 1. Consider a Ramsey model with depreciation of δ , population growth of n , a time discount rate of β and production function of y = k 1 / 2 . Solve for the steady state level of consumption per capita in terms of the three parameters. 2. Consider two Ramsey economies which are the same in every respect except for their time discount rates, β . People in country A discount the future more than those in country B (i.e. β A < β B ). Assume both countries start oF at the same initial capital stock, k 0 , which is below both of their steady states. Which country will have higher initial consumption? Is it possible for the two countries stable arms to cross? 3. A Ramsey model with population growth of n is in steady state. There is an unanticipated increase in n . Draw graphs of how ln c t , ln k t , and r t +1 change over time in response to the change in population growth. 4. Let the dynamic budget constraint facing the Ramsey economy be k t +1 = φ [ f ( k t ) + (1 - δ ) k t - c t ], where φ < 1, meaning that each dollar of your savings only generates
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Unformatted text preview: φ units of new capital in the future. A) Set up and show the ±OC for the Lagrangian, B) Does φ < 1 make the steady state level of k ss higher or lower than when φ = 1?, C) Graph the time paths of ln k t and ln c t following a surprise decrease in φ . 5. Take a Ramsey model in which the budget constraint is k t +1 = f ( k t ) + (1-δ ) k t-(1 + τ ) c t , where τ functions like a consumption tax. The economy starts in steady state in period zero. Draw a graph of ln c t for each of the following four cases: • In period 5, there is a surprise increase in τ , and this increase is permanent • In period 5, there is a surprise increase in τ , and this increase will only last until period 10 • In period 0, it is announced that in period 5 there will be a permanent increase in τ • In period 0, it is announced that in period 5 there will be a 50% chance that τ will increase 1...
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## This note was uploaded on 11/10/2011 for the course ECON 601 at Cornell.

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