Economics 100A
University of California, Santa Cruz
Fall 2003
Professor Lori Kletzer
Problem Set # 1: Solutions
1. Goods that are perfect substitutes are generally priced equally, or nearly so. For
example, stores often price different brands of golf or tennis balls all at one level,
or at very similar prices because they must be produced to professional
association standards, and so by definition good substitutes. Different brands of
basic food commodities such as bread and milk are also usually priced in a very
narrow range at a given store.
2. MU = 10 + 6X – X2
a)
Unit of X:
MU:
0
10
1
15
2
18
3
19
4
18
b) No. Marginal utility of the 8th unit would be negative.
3.
a)
5
15
6
10
7
3
b)
c)
d) They are perfect substitutes.
e) X is a good and Y is a bad, providing exactly the opposite of X in utility per unit.
MU z MU B
, the ratio of marginal utility
=
Pz
PB
per dollar should be equal for the last unit of all commodities. For Moe, the
marginal utilities per dollar are equal, for Curly they are not. Curly needs to
increase his expenditures on bats, and decrease expenditures on hats, which will
cause the marginal utility of hats to rise and marginal utility of bats to fall.
4. Based on equation 4.6 in the book, i.e.
5. Because the price of books falls when Carmela purchases more than 5 books in
one week, the budget constant is non-linear. As the following figure shows, the
budget line is kinked at a. This non-linearity makes it possible that a single
indifference curve could be tangential to the constraint in two places. In this case,
the consumer is indifferent between purchasing 3 books per week at full price and
purchasing 10 books per week with the discount.
6. False. In order to make predictions using economic theory, it is best to change
only one parameter at a time. In this case income rises and price falls. If the good
is inferior, the effects will be in the opposite directions.
7. To separate the income and substitution effects, draw the imaginary budget line
L*. In this case because the income effect partly offsets the substitution effect,
coffee is an inferior good. See the following figure.