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Macro1_PS4

# Macro1_PS4 - Macroeconomics 1 Master APE 2010-2011 PS4 Prof...

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Unformatted text preview: Macroeconomics 1. Master APE. 2010-2011. PS4 Prof. Xavier Ragot / T.A : Eric Monnet Discrete time intertemporal optimization and the theory of consump- tion In order to use Bellman equations to solve the optimization problem, use the handout available on the webpage. Chapter 7 from D.Romer's Advanced Macroeco- nomics as well as your course notes will provide some help to understand the dy- namic theory of consumption. The mathematical appendix in M.Wickens's Macroe- conomic Theory (chp.15) as well as the second chapter (section 2.4) of the book can also be useful. These textbooks are available at the library. 1 Bellman equations in a problem with certainty Let's revisit an in nite consumption-savings problem in which household are facing an exogenous income stream y t (instead of a xed initial endowment), that is known to the household with certainty. The income stream can vary overtime. Households solves the following problem : Max c t ,s t +1 = ∞ X t =0 β t u ( c t ) subject to : c t + s t +1 = (1 + r t ) s t + y t , ∀ t with consumption ( c t ≥ ), saving ( s given), and the interest rate at time t r t > ....
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Macro1_PS4 - Macroeconomics 1 Master APE 2010-2011 PS4 Prof...

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