Question

Amelia and Julian were traveling through time, and they decided to visit March 2020 in the hope of changing history. After arriving, they realized that their designated apartment was out of toilet paper. Given that they must go to the supermarket, they decided to buy both toilet paper (X) and paper towels (Y). Their preferences are given by U = 4X + Y, they have $150 to spend, and the prices are PX = 3 and PY = 2. How many units of paper towels do they buy?

Answer 1

This is the case of perfect substitutes. So, consumer will spend his entire income on the good for which marginal utility per dollar spent is higher.

A consumer maximizes utility where MUx/Px = MUy/Py

Here, MUx/Px = 4/3 = 1.33

MUy/Py = 1/2 = 0.5

So, MUx/Px >MUy/Py . Therefore they will spend their entire income on X i.e. toilet paper.

So, they will buy 150/3 = 50 units of toilet paper.

Since X and Y are substitutes so they won't buy any paper towel.

Hence , they will buy 0 units of paper towels.