Re: DSE 2006

Posted by Amit Goyal on Jun 24, 2011; 3:47pm
URL: http://discussion-forum.276.s1.nabble.com/Re-DSE-2006-tp6511699p6512510.html

Consider a competitive exchange economy with 2 agents (1 and 2) and 2 goods (X and Y). Agent 1's endowment is (0,5) and Agent 2's endowment is (10,0). Agent i's objective is to chose (xi, yi)  to maximize his utility min{xi, yi}.

Using the demand functions, we get the following:
Lets compute demands at prices (1,0) first
Individual 1 demands 0 units of good x and at least 0 units of good y.
Individual 2 demands 10 units of good x and at least 10 units of good y.

Market clearing condition fails because at least 10 units of good y are demanded and we only have 5.

Lets compute demands at prices (0,1) now
Individual 1 demands at least 5 units of good x and 5 units of good y.
Individual 2 demands at least 0 units of good x and 0 units of good y.

So market can clear when 1 demands (x, 5) and 2 demands (10-x, 0) for any 5<=x<=10.