Intermediate Microeconomics--utility Alice’s utility function is such that she i

Question

Intermediate Microeconomics--utility

Alice’s utility function is such that she is always indifferent between 1 unit of x and 3 units of y. Suppose initially px = 2, py = 1, and I = 10. Alice chooses x and y to maximize her utility. Then the government imposes a 100% sale tax on x (the price of x doubles). How much MORE does the person have to earn in order to achieve the same level of utility as before? (Find the increase in income required to achieve the same utility level)

(a) 0

(b) 5 *

c) 10

(d) 18

The solution is apparently five, but I can't seem to come-up with that answer. How do I approach this problem?

Explanation / Answer

Alice’s utility function is such that she is always indifferent between 1 unit of x and 3 units of y.This means that 1x=3y. Now px = 2, py = 1, and I = 10. So px(x)+py(y)=I. Putting x=3y and solving for x and y , we get x=30/7 and y=10/7. Now given that the price of x doubles which is px=4. So now the new income required is 4(30/7)+1(10/7)=130/7 or the income needed is 18.57.

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