Question

2. Van has $500 each semester to spend on books and sandwiches. Books are $100 each and sandwiches are $5 each. She has purchased 3 books this semester and 40 sandwiches. She tells you that her marginal utility from the next book is about 100 utils and the marginal utility from the next sandwich is about 15 utils. Has Van successfully maximized her utility this semester? How should she adjust her spending next semester?

Answer 1

Van has income, m = $500.

Price of Books, PB = $100.

Price of Sandwich, Ps = $5.

Her marginal utility from next Book, MUB = 100.

Her marginal utility from next Sandwich, MUs = 15.

We know that to maximize her utility, she must satisfy the condition,

Here,     and

Therefore,

Therefore Van is not maximizing her utility in this semester.

To maximize her utility in this semester, she would have to simultaneously increase MUB and decrease MUS. To increase MUB, she would have to purchase less books. And to decrease MUS, she would have to purchase more sandwiches.

Therefore, in the next semester she would have to simultaneously decrease the purchase of books and increase the purchase of sandwiches such that she spends her entire income on these two goods.