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

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

Explanation / Answer

Px × x + Py × y = 10

As per the indifferent combination, 2 × 1 + 1 × 3 = 5

Therefore, the combination could be increased (10/5 =) 2 times.

2 × 2 + 1 × 6 = 10

Now the price of x becomes double, 4 × 2 + 1 × 6 = 14

Answer: Increase in income is (14 – 10 =) 4

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