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midterm 2009

# midterm 2009 - ECON 7240 Spring 2009 Midterm Each question...

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Unformatted text preview: ECON 7240 Spring 2009 Midterm 3/2/09 Each question should be answered with a clear and concise explanation. Yes-no questions should be answered with a supportive argument or counterexample. Please write legibly. 2 hours 1) Consider the following continuous-time dynastic model. Each household has a population L ( t ) = exp( nt ) for a constant n and chooses consumption per household member C ( t ) to maximize , )) ( ( ) ( ) exp( ∫ ∞- = dt t C u t L t U ρ where ) exp( 1 ) ( C C u α α-- = , and the constants α , ρ > 0. The household earns labor income W ( t ) L ( t ) and is initially endowed with capital K (0). Capital K ( t ) earns the instantaneous return r ( t ). Income can either be consumed or saved as capital. a) Write down the instantaneous budget constraint for the household’s problem. (4 points) Define . ' ) ' ( exp ) ( = ∫ t dt t r t R b) Interpret the condition (*) . ) ( ) ( lim ≥ ∞ → t R t K t (4 points) The household’s problem is to maximize U for a given K (0) subject to the instantaneous budget constraint and the condition (*). ECON 7240...
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midterm 2009 - ECON 7240 Spring 2009 Midterm Each question...

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