Question

Antonio buys five new college textbooks during his first year at school at a cost of

​$8080

each. Used books cost only

​$5050

each. When the bookstore announces that there will be a

5050

percent increase in the price of new books and a

100100

percent increase in the price of used​ books, Antonio's father offers him​ $200 extra.

What happens to​ Antonio's budget​ line?

​1.) Using the line drawing​ tool, graph​ Antonio's original budget line. Label this line

Upper L 1L1.

​2.) Using the line drawing​ tool,

then

graph​ Antonio's new budget line. Label this line

Upper L 2L2.

Carefully follow the instructions​ above, and only draw the required objects.

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

Antonio will be

equally well off

if he continues to spend all of his income on new books. At the same​ time, he would be

worse off

if he were to spend a portion of his money on used books.01234567891011120123456789101112                                                  Used Books                                                           New Books

Upper L 2L2

Upper L 1L1

interactive graph

Question is complete. Tap on the red indicators to see incorrect answers.

Answer 1

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 there will be a 50% increase in the price of new books, and a 100% increase in the price of used books, Antonio’s father offers him $200 extra.

It shall be noted that initially, Antonio buys 5 new college textbooks at the cost of $80 each.

That means, Antonio was spending $400 on books before the changes in prices and before the extra money from his father.

Thus, the budget line is: 80*New + 50*Used = 400

Where,

New = New college textbooks

Used = Used Books

If Number of New college textbooks is measured along Y-axis and Used Books is measured along X-axis, the Y-intercept = $400/$80 = 5 and

the X-intercept = $400 / $50 =8

After the price change, Antonio gets $200 more

The new price of New textbooks = $80 + 50% of $80 = $120

The new price of Used books = $50 + 100% of $50 = $100

Thus, the new budget equation is 120*New + 100*Used = 600

Now, the Y-intercept of the new budget equation is = $600/$120 = 5

The X-intercept of the new Budget equation = $600/ $100 = 6

Thus, post the price change and increment of the budget by $200, while the Y-intercept measuring the maximum numbers of New textbooks remain unchanged at 5, the X-intercept measuring the maximum numbers of Used Books change from 8 to 6. The Budget line shift to the right to mark an increase in budget by $200.

1)

Antonio's Original Budget is:

2)

Antonio's New Budget equation is:

Since Antonio’s preferred bundle prior to the price and income changes (5 new books, 0 used books) is still affordable, he must be at least as well off as before.

Since there are additional bundles that are not affordable after the price and income changes that were affordable before, Antonio would be worse off if he were to spend a portion of his money on used books.