probset6

Probset6 - Problem Set 6 EC720.01 Math for Economists Peter Ireland Boston College Department of Economics Fall 2009 Due Thursday October 22 1 The

Info iconThis preview shows pages 1–2. 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: Problem Set 6 EC720.01 - Math for Economists Peter Ireland Boston College, Department of Economics Fall 2009 Due Thursday, October 22 1. The Permanent Income Hypothesis The permanent income hypothesis describes how a forward-looking consumer optimally saves or borrows to smooth out his or her consumption in the face of a fluctuating income stream. This problem formalizes the permanent income hypothesis using a two-period model. So consider a consumer who lives for two periods, earning income w during period t = 0 and w 1 during period t = 1. Let c and c 1 denote his or her consumption during periods t = 0 and t = 1 and let s denote his or her amount saved (or borrowed, if negative) during period t = 0. Suppose that savings earn interest between t = 0 and t = 1 at the constant rate r . Then the consumer faces the budget constraints w ≥ c + s (1) at t = 0 and w 1 + (1 + r ) s ≥ c 1 (2) at t = 1. Finally, suppose that the consumer’s preferences are described by the utility function ln( c ) + β ln( c 1 ) , (3) where the discount factor lies between zero and one: 0 < β < 1. a. Find the values for c * , c * 1 , and s * that solve the consumer’s problem – choose c , c 1 , and s to maximize the utility function in (3) subject to the constraints in (1) and (2) – in...
View Full Document

This note was uploaded on 02/19/2010 for the course ECON 720 taught by Professor Ireland during the Fall '09 term at BC.

Page1 / 3

Probset6 - Problem Set 6 EC720.01 Math for Economists Peter Ireland Boston College Department of Economics Fall 2009 Due Thursday October 22 1 The

This preview shows document pages 1 - 2. Sign up to view the full document.

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