problem code : 030609MICRO

[vishruti]

A consumer purchases only two goods and divides his expenditure equally between them. Is he worse off when his income goes up by 5% and the price of one of the goods goes up by 10%? Assume Cobb Douglas preferences      u(x1,x2) = (x1 . x2) ^ 1/2

[Kamal1]

No.

She will be atleast as well off as she was before because she can afford her old consumption bundle.

x1= m/2p1
x2= m/2p2

under the new scenario the budget line is 1.1px11 +p2x22 = 1.05m
The old consumption bundle satisfies it.

In general we cannot comment whether he will be better off or not coz the new bundle wasnt available in the base period if he decides to consume above the intersection point.

Only a doubt: when it is given that preferences are cobb douglas do we need the requirement of equal ependiture?

[vishruti]

ok

to check if the consumer is better off or not

we check the utility in 2 situations

you can see the solution following

X1 = M / 2P1
X2 = M / 2P2
AND P1X1 = P2X2
Now substituting in utility function we get

INDIRECT UTILITY
= {M^2 / 4 P1 . P2 }^1/2
 =  M / 2 {P1 . P2}^1/2

LET M=100  P1 =1 P2 =1

U (A) = 50

NOW INCREASE M BY 5% & P1 BY 10%

U(B)= 105 / 2 {1.1}^1/2

THEN COMPARE TWO UTILITITES BY U (A)< U (B)

BY TAKING U (A)<U (B) WE GET 11000 < 11025
 
THUS THE CONSUMER IS NOT NECCESARILY WORSE OFF

this problem has nothing to do with revealed prefrences