Re: DSE 2006

Posted by Chinni18 on Jun 07, 2012; 6:11am
URL: http://discussion-forum.276.s1.nabble.com/DSE-2006-tp7577468p7577535.html

For Q 21, 22, 23
We know that total endowment = (10,5)
U1 = min {x1, y1} and U2 = min {x2,y2} are the utility functions for agents 1 and 2 respectively
Setting p1 as the numeraire, we get optimal bundles as:
x1* = y1* = m1 / (1+p2) and x2* = y2* = m2 / (1+p2)

Budget constraints must satisfy
p1. 0 + p2. 5 = m1 and p1.10 + p2. 0 = m2 because (0,5) and (10,0) are initial endowments
=> 5 p2 = m1 and 10 = m2

Total demand for good 1 must add to 10
=> x1* + x2* = 10
=> {m1 / (1+p2)} + {m2 / (1+p2)} = 10
But we have obtained 5 p2 = m1 and 10 = m2
So {5 p2 / (1+p2)} + {10 / (1+p2)} = 10
=> p2 + 2 = 2 + 2 p2
=> p2 = 0
This doesn't make sense because x and y are complementary goods and not in excess supply

Do the process again by normalising p2=1
You get x1* = 5/(1+p1) and x2*=10p1 / (1+p1)
Again x1* + x2* = 10
=> 5 +10p1 + 10p1 = 10
No value of p1 can satisfy this
Look at the market for  y: y1*+y2* = 5
=> 5 +10p1 + 10p1 = 5
=> p1 = 0

With (p1,p2) = (0,1), you get x1*=5, x2*=0, y1*=5, y2*=0
So competitive eqbm allocation is (5,5) and (0,0)