Antonio's Budget Line Analysis After Price Change

A. What happened to Antonio's budget line? Illustrate the change with new books on the vertical axis.

A. After the price change, Antonio's budget line would rotate inward.

When the price of books increases, his total budget for buying books decreases. Hence, the line representing his budget would shift leftward or inward. In the given scenario, Antonio purchases new college textbooks during his first year at school at the cost of $80 each. Used books cost only $50 each. As a result, we can set up an equation for Antonio's initial budget line as follows: 50x + 80y = B where x and y represent the number of used books and new books, respectively. B is the budget that Antonio has allocated for the purchase of books. He bought five books during his first year; thus, his initial budget line would have a slope of -5/4 and intercepts of B/50 and B/80 along the horizontal and vertical axes.

B. Is Antonio worse or better after the price change? Explain.

B. Antonio is worse after the price change. He now requires additional funds to purchase the same number of books as before, which he cannot afford with his current budget. The new price for new books is $88 per book, while the new price for used books is $52.50 per book. Thus, his new budget line can be expressed as follows: 50x + 88y = B+40. We can show that Antonio's new budget line is parallel to the initial budget line by comparing their slopes (-5/4). Nonetheless, the new budget line has a higher intercept on the vertical axis than the initial budget line (B+40/88 instead of B/80).

As a result, Antonio cannot afford to buy the same number of books as he did before the price change since his budget for purchasing the same number of books has decreased. In conclusion, Antonio is worse off after the price change.