example PO Walras sol - Class Advanced Microeconomics II...

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: Class Advanced Microeconomics II Solution Problem Set 12, Exercise 2 Spring 2008 1 Solution Problem Set 12, Exercise 2 2. Consider an Exchange Economy with three consumers whose consumptions are all ∈ R 2 + . The consumers have the following utility functions: U 1 ( x 1 ) = ln x 1 1 + ln x 1 2 , U 2 ( x 2 ) = q x 2 1 · q x 2 2 , U 3 ( x 3 ) = 7 · x 3 1 · x 3 2 . The consumers endowments are: e 1 = (1 , 6) , e 2 = (3 , 2) , e 3 = (5 , 1). Focus on the following allocations: x 1 = ((2 , 3) , (2 , 4) , (5 , 2)) , x 2 = 31 10 , 31 10 , (3 , 3) , 29 10 , 29 10 , x 3 = 7 2 , 7 2 , 5 2 , 5 2 , (3 , 3) . (a) Check, whether these allocations are Pareto-efficient or not. (b) Compute the WEA. Solution (a) We know, that any (interior) Pareto-efficient allocation/Pareto-optimum (PO) requires: MRS 2 / 1 1 ! = MRS 2 / 1 2 ! = MRS 2 / 1 3 . We compute the three MRS 2 / 1 : 1 MRS 2 / 1 1 = 1 x 1 2 1 x 1 1 = x 1 1 x 1 2 , MRS 2 / 1 2 = (1 / 2)( x 2 1 ) 1 / 2 ( x 2 2 )- 1 / 2 (1 / 2)( x 2 1 )- 1 / 2...
View Full Document

This note was uploaded on 01/29/2012 for the course ECONOMICS 101 taught by Professor Tikk during the Spring '11 term at University of Toronto- Toronto.

Page1 / 4

example PO Walras sol - Class Advanced Microeconomics II...

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