Question

Claire, a university student, has a budget of 150 dollars to spend on books at the beginning of academic year. There are two types of books she is interested in: economics textbooks (xtb) and sci-fi novels (xsc). Suppose the price of each textbook is 20 dollars, while the price for each sci-fi novel is 10 dollars.

(a) Write down Claire’s budget line and draw it in a (xtb,xsc)-plane.

(b) Suppose Claire receives a 50-dollar gift card from a friend. The gift card can be used to buy either type of book. What is her new budget line?

(c) What would change if Claire finds out that the gift card can only be used to buy economics textbooks?

(d) The bookstore owner agrees that Claire can use the gift card to purchase novels. However, he tells her that each 1 dollar on the gift card is worth 1−ρ dollars when Claire spends it on sci-fi novels; assume 0 < ρ < 1. In this case, what is her budget line?

Answer 1

a)   Claire’s budget line :

20 xtb + 10 xsc = 150

b) Since gift card of 50 $ will be treated as additional income only.

20 xtb + 10 xsc = 150 + 50

New budget line: 20 xtb + 10 xsc = 200

c) New budget line: 20 xtb + 10 xsc = 150 as he can only spend the amount on the economics textbook. So, there will a kink in the budget line.

d) Assuming that he can use the gift on only sci-fi novels and rho = 0.50

New budget line: 20 xtb + 10 xsc = 150 as he can only spend the amount on the economics textbook. So, there will a kink in the budget line.