Suppose music CDs and movie DVDs give the same utility to Jane, and she has $200 to spend on music CDs and movie DVDs. The price of a movie DVD is $15, and the price of a music CD is $10. Which of the following is the most affordable bundle for maximizing her utility?
A)10 music CDs and 5 movie DVDs
B)10 music CDs and 10 movie DVDs
C)5 music CDs and 5 movie DVDs
D)15 music CDs and 5 movie DVDs
E)5 music CDs and 10 movie DVDs

Question

Quizplus · Accepted Answer

To maximize utility, Jane should allocate her budget in such a way that the marginal utility per dollar spent on both goods is equal. Let's calculate the marginal utility per dollar for each good:

Marginal utility of a music CD = 1
Marginal utility of a movie DVD = 2/3

Since the marginal utility per dollar of a movie DVD is higher than that of a music CD, Jane should spend more on movie DVDs and less on music CDs. At the same time, Jane should keep spending on movie DVDs until their marginal utility per dollar is equal to that of a music CD. We can do this by setting up the following equation:

MU(movie DVD)/Price(movie DVD) = MU(music CD)/Price(music CD)

Solving for the number of movie DVDs:

2/3 / 15 = 1 / 10
20 = 3x
x = 6.67

So Jane should buy 6 movie DVDs and spend the rest of her budget on music CDs. The most affordable bundle that satisfies these conditions is 5 music CDs and 10 movie DVDs (since buying an additional music CD would cause its marginal utility to drop below that of a movie DVD).

Suppose Music CDs and Movie DVDs Give the Same Utility