A consumer has utility function Uq1 q2 q1q2 has income y 3 a

A consumer has utility function U(q1, q2) =q1+q2, has income y= 3, and faces prices p1= 1 and p2= 4. If the price of good 1 increases top1= 2, what are the substitution effect and the income effect of this price increase on the demand for good 1?

Solution

here we can see that the utility function is quasi concave in q1,

if we calculate the demand function for q1 then,

MRSq1,q2 = MUq1/MUq2 = 1/2sqroot q1

so put this equal to price ratio and we get

q1 = (p2/p1)^2

as q1 isnt the function of y, thus there wont be any income effect , but substitution effect is give by

4^2 - 2^2 =12