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: Alejandro Badel Homework 1, Macro II Jonathan Heathcote : Answer 1) a) The set of Pareto E cient allocations coincides with the solutions to the planning problem. By the Inada conditions, solutions to this problem are always interior. Also, by strict concavity of the planners objective, the FOC are necessary and su cient. u & c 1 t u ( c 2 t ) = 1 & & & c 1 t + c 2 t = e 1 t + e 2 t := e t Using the functional form for u ( : ) , we get: c 1 t c 2 t & & = 1 & & & Imposing the resource constraint: Pareto = f c p 2 t ; c p 1 t 2 R 2 + such that c p 1 t = & 1 & & 1 & + (1 & & ) 1 & e t c p 2 t = (1 & & ) 1 & & 1 & + (1 & & ) 1 & e t & [0 ; 1] g Note that consumption varies across periods but the ratio of consumption remains constant. b) Denoting the Lagrange multiplier for the resource constraint of the Plan ner&s problem above by t = 2 , and recalling one of the FOC, t & c 1 t & & = t 2 & The FOC of the decentralized sequential markets problems are & c 1 t & & =...
View
Full
Document
 '05
 would

Click to edit the document details