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
Unformatted text preview: Solutions to Problem Set 8 EC720.01  Math for Economists Peter Ireland Boston College, Department of Economics Fall 2009 Due Thursday, November 5 1. Life Cycle Saving The consumer chooses sequences { c t } T t =0 and { k t } T +1 t =1 to maximize T X t =0 t c 1 t 1 1 subject to the constraints k = 0 given , w t + r t k t c t k t +1 k t for all t = 0 , 1 ,...,T , and k T +1 k * > . a. The Hamiltonian for the consumers problem can be defined as H ( k t , t +1 ; t ) = max c t t c 1 t 1 1 + t +1 ( w t + r t k t c t ) . b. According to the maximum principle, the solution to the consumers dynamic optimiza tion problem is characterized by the firstorder condition t c t t +1 = 0 , the pair of difference equations t +1 t = H k ( k t , t +1 ; t ) = t +1 r t and k t +1 k t = H ( k t , t +1 ; t ) = w t + r t k t c t , the initial condition k = 0 , and the terminal or transversality condition T +1 ( k T +1 k * ) = 0...
View Full
Document
 Fall '09
 IRELAND
 Economics

Click to edit the document details