Econ 100A-Spring 2008
Page 1
PS2 Answer Sheet
Department of Economics
Spring 2008
University of California
Prof. Woroch
Economics 100A
PROBLEM SET 2 ANSWER SHEET
I. TRUE or FALSE and EXPLAIN
1.
If the price elasticity of demand for ballet tickets is around –1.2 in the local market, then the Zellerbach
theater will increase its ticket revenues if it increases ticket prices a small percentage amount, e.g., 5%.
FALSE.
When elasticity equals to -1.2, a 1% increase in price will lead to a 1.2% decrease in sales. The
amount of money from each ticket will be higher, but the number of tickets sold will be lower.
For
example,
if the ticket price goes up by 5%,then
Q will decrease by 5*1.2 = 6%. So since TR = P*Q, and
since
P
2
= 1.05*P
1
and Q
2
=
(1 - 0.06)*Q
1
= 0.94*Q
1
then TR
2
=
0.94Q
1
* (1.05)P
1
= (0.99) Q
1
P
1
=
0.99TR
1
.
So, TR declines.
2.
Japanese consumers save significant amounts of their income even when their interest rates are nearly
zero, while facing much higher interest rates, American consumers save almost nothing.
One of these
two groups must violate one of the rationality assumptions of consumer preferences over consumption
streams.
FALSE.
T
he
relative preferences of consumers (indifference curves) for consumption in one period
relative to another along with interest rates and income, will determine their optimal bundles of saving
versus borrowing. Consumers on average, in Japan may have different preferences (utility functions),
than those in the U.S., i.e.
they may prefer to consume tomorrow (save) relative to today, while those in
the U.S., prefer consumption today over tomorrow,
on average. So the shapes of their indifference curves
will differ, resulting in different optimal bundles of consumption today (borrowing) and consumption in
the future (saving).
3.
If a Herschel has a
quasi-linear utility function
for potatoes and a composite good, then, assuming he is a
rational consumer, potatoes cannot be a Giffen good for him.
TRUE.
For Giffen goods, beyond a certain level of income, the good becomes so strongly inferior that the
income effect swamps the substitution effect making the change in goods demanded negative for a price
decrease. However, for a Quasi-linear utility function if potatoes form the non-linear portion of the utility
function, the demand for potatoes will not depend upon income.
So, Herschel will purchase the same
ratio of potatoes no matter how much his income increases.
In this case, there is no income effect, and so
there can be no period over which it is a Giffen good.
4.
If the production of tortillas exhibits diminishing marginal returns, then tortilla production must also
exhibit decreasing returns to scale.
FALSE. The concept of diminishing marginal returns requires the amount of one production factor to be
held constant whereas return to scale allows all production factors to change.
When all production
factors double, output can be more than double even if one production factor manifests diminishing
marginal returns.
Therefore, it is possible to have diminishing return at the same time with increasing
return to scale.
Tortilla production might exhibit decreasing returns to scale but not necessarily MUST
be so.