1 Steves utility function is U BC where Bburgers per week a

1. Steve’s utility function is U = BC, where B=burgers per week and C=packs of cigarettes per
week. Steve’s income is $120, the price of a burger is $2, and that of a pack of cigarettes is $1.
(a) What is his marginal rate of substitution if burgers are on the vertical axis and cigarettes
are on the horizontal axis? (Hint: MUB = C and MUC = B.)
(b) How many burgers and how many packs does Steve consume to maximize his utility?

2. Vasco’s utility function is U = 10q1q2 2. The price of pizza, q1 is p1 = $5, the price of burritos,
q2 is p2 = $10, and his income Y = $150.
(a) What is his optimal consumption bundle?
(b) What share of his budget does he spend on pizza? And burritos?

3. Antonio buys new college textbooks during his rst year at a cost of $80 each. Used books
cost only $50 each. When the bookstore announces that there will be a 10% increase in the
price of new books and a 5% percent increase in the price of used books, Antonio’s father oers
him $40 extra.
(a) Draw two Antonio’s budget lines: one for before bookstore’s announcement and the other
for after announcement. (new books on the horizontal line and used books on the vertical
line)
(b) Can you tell whether Antonio gets better or worse o

Solution

A. What is his marginal rate of substitution if burgers on the vertical axis and cigarettes are on the horizontal axis? MRS = MUB/ MUC = (C/B )

b.   MRS = MUB/MUC = C/ B = PB/ PC

BPB + CPC = Y

B = Y /2PB = $120/ 2 × $2 = 30

C = Y /2PC = $120/ 2 × $1 = 60

2.This is the standard graph, where Ben’s budget line is linear and he consumes at the point where his indifference curve is tangent to his budget line. This places him on the highest possible indifference curve.

3.a. In the first year he spends $80 each on 5 new books for a total of $400. For the same amount of money he could have bought 8 used textbooks. His budget line is therefore 80*New+50*Used=400.   After the price change, new books cost $88, used books cost $52.5, and he has an income of $440. If he spends all of his income on new books, he can still afford to buy 5 new books, but can now afford to buy 8.4 used books if he buys only used books. The new budget line is 88*New+52.5*Used=440. The budget line has changed its slope and become flatter if we place used books on the horizontal axis. This will help you to draw the budge lines.

b. The first year he bought 5 books at a cost of $80 each for a total of $400. The new price of books is $88 and the cost of 5 new books is now $440. The $40 extra income will cover the price increase. Antonio is definitely not worse off since he can still afford the same number of new books. He may in fact be better off if he decides to switch to used books.