DSE 2009

[riddhima]

A consumer spends an income of Rs. 100 on two goods, dosas and pizzas.
Let x denote the number of dosas and y the number of pizzas consumed
(fractions allowed). The consumer’s utility function is U =exp (x^2 + y^2) . If the
price of a dosa is Rs. 5, and the price of a pizza is Rs. 10, then the number of
pizzas this consumer will buy is
a) 0
b) 10
c) 5
d) 8

The answer key says the answer is a) 0, my answer comes out to be d) 8

I have solved it simply by equating MRS to price ratio and then solving for the budget equation,
MRS= x/y= 1/2
2x=y

Budget equation

5x + 20x = 100 (substituted the value of y =2x)

x= 4
y=8

Help me, where I am going wrong!

Thanks much! :)

[Prerna Rakheja]

Hi Riddhima,

A quick way to check your answer is by calculating utility at (4,8) and comparing it with (20,0). You will get exp^ 80 v/s exp^400.

Hence, its not safe to use MRS equal to the price ratio condition everywhere. Its advisable to look into the conditions under which this is applicable.

[madhur1987]

hi riddhima the utility fn here is concave so solution must be somewhere at corner since price of dosa is less so he will consume all dosa and choose corner of dosa

[duck]

Hey Madhur.. :)

Here the the utility function is convex and Indifference curves are concave.

[madhur1987]

thanx duck:) yes IC is concave thats why corner solutn