Question

Sarah prefers buying new books to used books. During her first year at school, she spends all her money ($500) on buying new textbooks. The price of new textbooks was $100 while the used books sold for $50 each. When the bookstore announces that there will be a 10% increase in the price of new books with no change in the price of old textbooks, Sarah's father offers her $50 extra to buy books. a) (5 points) What happens to Sarah's budget line? Illustrate the change with new books on the vertical axis. (write the budget equation and draw the budget line to back up your explanation) b) ( 5 points) Is Sarah worse or better off after the price change? Explain.

Answer 1

a. Sarah's budget line on X-axis shifts by 1 quantity as with the increase in price of new books by 10% she still buys 5 new books for $550 after her dad gives her extra $50. But, if she chooses to spend the money on old books she could have bought 11 old books for $550 (11*50 = 550).

b.

New Books = Y , Price of New Books = P_y

Old Books = X , Price of Old Books = P_x

Budget line equation : X .P_{x +} Y.P_{y =} I

                 

C. Sarah is worse off after the change because she can purchase the same quantity of new books i.e. 5 books after her budget increase by $50. This is due to 10% increase in price of new books and hence price of one book now costs her $110. She still prefers new books to old ones and therefore with the total spending of $550 she gets the same quantity of new books. She would have been better off if she shofted her preference to old books. Price of old books remain same and so she could buy 11 old books for $550. Another option she has is to allocate her resources between the both types of books. But in that case also she would be worse of as price of new books has increased.