Econ 100ASpring 2010
Page 1
Problem Set 2 Answers
Department of Economics
Spring 2010
University of California
Prof. Woroch
Economics 100A
PROBLEM SET 2 ANSWER SHEET
I.
SHORT ANSWER QUESTIONS
1.
For each of the following goods, explain whether you believe a price increase will lead to a large or
small substitution effect and a large or small, positive or negative income effect: (i) common table
salt, (ii) rent for a one bedroom apartment in Berkeley, (iii) a day ski pass to Northstar ski resort.
Be
sure to support your reasoning with real world examples.
Answer: (i) Since most people do not spend a large portion of their income on table salt, we can
imagine that the income effect could be negative; indeed, a little salt adds flavor but too much salt
ruins it, so consumption will peak at a certain amount; there are no great substitutes for salt so the
substitution effect will also be small.
(ii) Most people spend a large fraction of their income on rent,
therefore it is likely that there will be a large negative income effect involved with a price increase in
rent (i.e., an individual's disposable income will be reduced substantially) and the substitution effect
will depend on availability of substitutes (sharing an apart with a friend, moving back with your
parents, living in your car).
(iii) In this case, it is easy to imagine other forms of entertainment that
compare to skiing, therefore we expect a large substitution effect but small (negative) income effect
from an increase in the price of a day ski pass.
2.
A consumer must choose whether to buy a computer for $1,000 and $120 per year for internet access
for three years or she can receive a $400 rebate on the computer but agree to pay $300 per year for
three years for internet access. At what yearly interest rate will the consumer be indifferent between
the two options?
Assume that the consumer is only concerned with the present value of the cost of a purchase plan.
In
that case, the consumer will be indifferent between the two plans when the interest is such that they
have the same present value:
1,000 + 120 + 120(1+r)
1
+ 120(1+r)
2
= 600 + 300 + 300(1+r)
1
+ 300(1+r)
2
220 = 180(1+r)
1
+ 180(1+r)
2
220(1+r)
2
180(1+r)=180
220r
2
+260r140=0
Notice that the first year’s payment for internet service is not discounted – as if it is paid upfront at
the same time as the purchase price of the computer.
In addition second and third year internet
service payments must be made at the beginning of each of those two years.
Using the quadratic formula (
i.e.
, the solution to the quadratic equation ar
2
+ br + c = 0 is given by
the two values: r = [b ± (b
2
– 4ac)
½
]/2a ), we can solve for the value of r (the interest rate) which will
make the consumer indifferent between the two alternatives. If we do this, we get that r = 40.2%. For
any interest rate lower than this, the consumer will choose the first (nonrebate) option.
(Note that
while both plans extend over three years, we do not allow for any uncertainty regarding future
payments.)
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 Spring '08
 Woroch

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