Question

Antonio has a $650 per semester from his father to buy textbooks for classes. New text books average $150 per book while used books cost only $75 each.   The bookstore announces that there will be a 10 percent increase in the price of new books and a 20 percent increase in the price of used books. Antonio’s father offers him an extra $50 per semester.

a. Show what happens to Antonio’s budget line without the extra $50 What happens to Antonio’s budget line. Illustrate the change with new books on the vertical axis.

b. Show what happens to Antonio’s budget line with the extra $50 What happens to Antonio’s budget line. Illustrate the change with new books on the vertical axis.

c. Show whether Antonio is better off or not with the extra $50 per semester.

Answer 1

Initially, Budget line: $650 = $150 x N + $75 x U [Where N: Number of new books and U: Number of used books]

When N = 0, U = 650/75 = 8.7 [Horizontal intercept] & When U = 0, N = 650/150 = 4.3 [Vertical intercept]

In the graph, AB is the initial budget line with these intercepts.

(a) New price of N = $150 x 1.1 = $165 & New price of U = $75 x 1.2 = $90

New budget line: $650 = $165 x N + $90 x U

130 = 33N + 18U

When N = 0, U = 130/18 = 7.2 [Horizontal intercept] & When U = 0, N = 130/33 = 3.9 [Vertical intercept]

In following graph, CD is the new budget line with above intercepts.

(b) New income ($) = 650 + 50 = 700, New price of N = $150 x 1.1 = $165 & New price of U = $75 x 1.2 = $90

New budget line: $700 = $165 x N + $90 x U

140 = 33N + 18U

When N = 0, U = 140/18 = 7.8 [Horizontal intercept] & When U = 0, N = 140/33 = 4.2 [Vertical intercept]

In above graph, EF is the new budget line with above intercepts.

(c) After increase in price of the goods, the budget line without extra $50 income lies to the right of the budget line with extra $50 income. Therefore Antonio is better off with the extra $50.