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

Antonio's budget line for used books shifts outward along the x-axis (horizontal), showing he can afford more used books. However, the budget line for new books remains constant, showing he cannot afford additional new books. Despite the increase in his budget, Antonio is worse off after the price change, as his purchasing power decreased, particularly for new books.

Step-by-step solution

Calculate New Prices

First, calculate the new prices of both new and used books after their respective price increases. A 10% increase on the price of new books which cost $80 gives \(80 * 0.10 = \$8\). The new price for new books is thus \(80 + 8 = \$88\). A 5% increase on the price of used books which cost $50 gives \(50 * 0.05 = \$2.5\). Thus, the new price for used books is \(50 + 2.5 = \$52.5\).

Calculate Antonio's New Budget

Next, calculate Antonio's new budget. Initially, Antonio could afford five new textbooks at $80 a piece, thus his initial budget was \(5 * 80 = \$400\). After his father gave him extra $40, Antonio's new budget is \(400 + 40 = \$440\).

Construct Initial and New Budget Lines

A budget line represents the number of goods a consumer can afford given the price of goods and their budget. The quantity of a good (in this case, new textbooks) the consumer can afford is found by dividing their budget by the price of the good. The initial quantity of new textbooks Antonio could afford was \(400 / 80 = 5\), and the new quantity is \(440 / 88 \approx 5\). This remains constant on the vertical axis (y-axis). The quantity of used books Antonio could initially afford was \(400 / 50 = 8\) and the new quantity is \(440 / 52.5 \approx 8.38\). This increases on the horizontal axis (x-axis). Thus Antonio's budget line shifts outward along the x-axis.

Determine Antonio's Position After the Price Change

Since the price of new books increased more than the price of used books, and Antonio could not get more of the former, but he can afford more of the latter, his purchasing power, especially towards new books has decreased. Therefore, Antonio is worse off after the price change, despite the increase in his budget.