If your income is $9.00 and the prices of X and Y are $2.00 and $1.00, respectively, what quantities of each will you purchase to maximize utility?

Complete question:

You are choosing between two goods, X and Y, and your marginal utility from each is as shown in the table above. If your income is $9 and the prices of X and Y are $2/unit and $1/unit, respectively, what quantities of each will you purchase to maximize utility?

A. X - 3; Y - 3

B. X - 4; Y - 1

C. X - 2; Y - 5

D. X - 1; Y - 6

Answer:

X - 2; Y - 5

Solution:

Total utility is maximized when

MUx / Px = MUy / Py

This is satisfied when x = 2 [MUx / Px = 16 / 2 = 8] and

y = 5 [MUy / Py = 8 / 1 = 8]. Total cost = 2 x $2 + 5 x $1 = $9 [Budget is exhausted]

Note: Another option would be x = 4 & y = 6, but that would exceed the budget.