{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Macro1_PS4sol

# Macro1_PS4sol - Macroeconomics 1 Master APE 2010-2011 PS4...

This preview shows pages 1–2. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Macroeconomics 1. Master APE. 2010-2011. PS4 Prof. Xavier Ragot / T.A : Eric Monnet Solutions 1 Bellman equations 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 > . Assume the utility function is of CRRA form, u ( c t ) = c 1- σ t- 1 1- σ , with σ > . For more details on the answers of this exercise, interpretations of Euler equation, and Envelope theorem, have a look at the notes/slides of your third class on con- sumption and at the attached handout on dynamic programming 1- Formulate this problem using Bellman equation and derive the rst-order nec- essary conditions. Provide details of your use of the Envelope Theorem. Interpretessary conditions....
View Full Document

{[ snackBarMessage ]}