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: 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 Paretoefficient or not. (b) Compute the WEA. Solution (a) We know, that any (interior) Paretoefficient allocation/Paretooptimum (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.
 Spring '11
 Tikk
 Utility

Click to edit the document details