Question

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

a. An offer of $40 extra will rotate Antonio’s budget line clockwise. Thus, his budget line changes from L₁ to L₂.

b. Due to the price change, Antonio will be better off since he moves to a higher indifference curve with a new consumption level.

Step-by-step solution

Determining the relative prices

Due to the change in prices, the relative price of old textbooks to new textbooks decreased from 0.625 to 0.596, as computed below:

$$\begin{gathered} \mathrm{Relative}\mathrm{price}\mathrm{at}\mathrm{old}\mathrm{prices} \\ \frac{50}{80}=0.625 \\ \mathrm{Relative}\mathrm{price}\mathrm{at}\mathrm{new}\mathrm{prices} \\ \frac{52.5}{88}=0.596 \\ \mathrm{Since},\mathrm{for}10\%\mathrm{rise},\mathrm{the}\mathrm{price}\mathrm{of}\mathrm{new}\mathrm{textbook}\mathrm{will}\mathrm{be} \\ 80+\frac{10}{100}\times 80=\$88 \\ \mathrm{for}5\%\mathrm{rise},\mathrm{the}\mathrm{price}\mathrm{of}\mathrm{old}\mathrm{textbook}\mathrm{will}\mathrm{be} \\ 50+\frac{5}{100}\times 50=\$52.5 \end{gathered}$$

Determining the budget lines

Antonio will react to the relative price decrease in the following two ways.

1. If new and old texts are not substitutes, Antonio will be just as well off when the price of new texts rises, and his father gives him $40.

U₁ is the indifference curve when goods are not substitutes.

L₁and L₂ are the initial and final price line/budget lines.

Suppose Antonio chooses to buy more old textbooks due to a relative price decrease. His indifference curve shifts upward, showing his increased consumption of old textbooks (if the old textbooks are substitutes for the new ones) when his income increases.

Antonio moves from indifference curve U₁ to U₂, shown in the figure above.

Antonio’s welfare after the price change

If Antonio chooses to buy a greater number of old textbooks in response to the relative price decrease (given the extra $40) and moves to a higher indifference curve.

A shift from a lower indifference curve to a higher indifference curve means that Antonio’s welfare has improved, and he is better off due to the price change.