47507-midterm

# 47507-midterm - ECO 475 Fall 2007 Midterm Exam Jay H Hong...

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Unformatted text preview: ECO 475, Fall 2007, Midterm Exam Jay H. Hong Oct 24, 2007 This exam has 3 questions, for a total of 100 points. You have 2 hours. Manage your time wisely. Feel free to make an appropriate assumption if needed. Good luck!! 1. Two Production Possibilities (35 points) There is an economy with many identical consumers who have preferences ∞ ∑ t =0 β t u ( c t ) where c t is own consumption at time t period. There are two possible ways to produce output. Output can be produced either by using the first production technology, which can be written as y t = F ( k t ) where k t is capital or by using the second technology, which y t = G ( k t ) = B · k t where B > 1. Notice that the second technology is linear. Capital depreciates at rate δ . Assume that the usual assumptions on instantaneous utility function, u ( · ) are satisfied. Also assume that F > 0, F 00 < 0, F (0) = 0, F (0) = ∞ , F ( ∞ ) = 0. Output can be used either for consumption or investment. k > 0 is given. (a) (3 points) [ Economy I ] Imagine an economy where the second technology is not available and you are only allowed to use the first technology. Write down the Bellman’s equation. What are the state and control variables? (b) (3 points) [ Economy II ] Imagine now you are only allowed to use the second technology. Write down the Bellman’s equation. What are the state and control variables? Derive the Euler equation....
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## This note was uploaded on 09/06/2011 for the course ECO 475 taught by Professor Hong during the Fall '07 term at Rochester.

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47507-midterm - ECO 475 Fall 2007 Midterm Exam Jay H Hong...

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