macro prelim 2010 - Macro Prelim 2010 Each question should...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Macro Prelim 2010 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. 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 where -- = 1 1 1 ) ( C C u , and the constants > 0 and > 1. 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 households problem. Define . ' ) ' ( exp ) ( = t dt t r t R b) Interpret the condition (*) . ) ( ) ( lim t R t K t The households problem is to maximize U for a given K (0) subject to the instantaneous budget constraint and the condition (*). c) Write down the Hamiltonian for the households problem. d) Write down Hamiltons equations for the households problem. e) Solve for the optimal path of consumption. Now we assume the economy has a production sector with a constant returns to scale technology )), ( ( ) ( ) ( )) ( ) ( ), ( ( ) ( t k f t L t A t L t A t K F t Y = = where A ( t ) = exp( gt ) for some constant g and ....
View Full Document

Page1 / 5

macro prelim 2010 - Macro Prelim 2010 Each question should...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online