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Chapter 3: Problem 10

Antonio buys five new college textbooks during his first year at school at a cost of \(\$ 80\) each. Used books cost only \(\$ 50\) each. When the bookstore announces that there will be a 10 percent increase in the price of new books and a 5 percent increase in the price of used books, Antonio's father offers him \(\$ 40\) extra. a. What happens to Antonio's budget line? Illustrate the change with new books on the vertical axis. b. Is Antonio worse or better off after the price change? Explain.

Short Answer

Expert verified
The budget line of Antonio has shifted due to changes in prices and increase in his budget. Generally, he can now buy fewer new books, but more used books. Whether he is better or worse off depends on his preference for new versus used books.

Step by step solution

01

Determine the initial budget line

Initially, Antonio can buy several combinations of new and used books. Suppose he spends all his money on new books, the number of new books he could buy would be his total money divided by the price of new books, which is \(\frac{M}{P_{N}}\). Similarly, if he only buys used books, the number of used books would be \(\frac{M}{P_{U}}\). Therefore, the equation of the initial budget line would be \(P_{N}N + P_{U}U = M\) where \(N\) is the quantity of new books, \(P_{N}\) is the price of new books, \(U\) is the quantity of used books and \(P_{U}\) is the price of used books.
02

Determine the new budget line

After the price changes of the books and the extra money from Antonio's father, the budget line changes. The prices of the new books and used books increase by 10% and 5% respectively, and Antonio receives an extra \(40\) dollars. If he spends all his new money on new books, the number of new books he could buy would be \((M + 40) / (P_{N} · 1.1)\). Similarly, if he spends all his money on used books, the number of used books he could buy would be \((M + 40) / (P_{U} · 1.05)\). Thus, the equation for the new budget line would be \((P_{N} · 1.1)N + (P_{U} · 1.05)U = M + 40\).
03

Compare the initial and new budget line

Looking at the new budget line compared to the initial one, a couple of things stand out. In terms of new books, Antonio can now buy fewer than before due to the price increase, despite the extra money. But for used books, because the price increase is half as much as the new books, and with the extra money, Antonio can actually buy more used books than before, if he decides to spend all his money on them, potentially improving his ability to buy books overall.
04

Evaluate Antonio's situation

Whether Antonio is better or worse off depends on his preferences. If he strongly prefers new books, he might be worse off as he can buy fewer new books than before despite the extra money. If he is indifferent between new and used books, or prefers used books, he could be better off as he can now buy more used books than before.

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Most popular questions from this chapter

Jane receives utility from days spent traveling on vacation domestically \((D)\) and days spent traveling on vacation in a foreign country ( \(F\) ), as given by the utility function \(U(D, F)=10 D F .\) In addition, the price of a day spent traveling domestically is \(\$ 100,\) the price of a day spent traveling in a foreign country is \(\$ 400,\) and Jane's annual travel budget is \(\$ 4000\). a. Illustrate the indifference curve associated with a utility of 800 and the indifference curve associated with a utility of 1200 b. Graph Jane's budget line on the same graph. c. Can Jane afford any of the bundles that give her a utility of \(800 ?\) What about a utility of \(1200 ?\) d. Find Jane's utility-maximizing choice of days spent traveling domestically and days spent in a foreign country.

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