Problem code: 020609MICRO

[Amit Goyal]

A consumer spends Rs 80 on x1 and x2 and his utility function is u(x1 , x2) = (x1 . x2) ^ 1/2 { square root of the product of x2 and x2} . If he is known to have rejected two bundles (2,3) and (6,1) which cost the same amount. Find the optimum bundle
 
Now suppose the price of x2 is fixed but the govt. can change the price of x1 as well as his money income. What would be the price of x1 and income of the consumer such that he finds (6,1) to be optimal bundle?

----------------------------------------------------------------posted by Vishruti

[Kamal1]

As for the 1st part we can solve the 2 simultaneous equations to get p1= 10 and p2=20
x1=4 x2= 2

for the 2nd part set the condition for oprimization to get p2=60

budget equation will be 10 x1 + 60x2= m

again x1= m/2p1=6

m=120

the price should be increased by 40 and m by 40

the consumer will be worse off

[vishruti]

@kamal@

your answer to the first part of the question is correct

but for the second part p2 is not equal to 60 but
following is the solution to the second half

i suggest you to re read the question carefully and find out what is asked...

If (6,1) is optimum bundle at (P1, 20, M)
x1 = M/2P1 = 6

And

x2 = M/2P2 = 1
     = M / 2.20 = 1

This implies M= 40
And P1 = 10 / 6

[namrata]

my answer is m=40 and x1= 10/3...

[vishruti]

the answer is correct but you have replied after the solution has been posted...so no points will be credited

and its px1=10/3 and not x1 = 10/3

[namrata]

Sorry that was a typeo