Economics 140A
Answers to Exercise 5
2. (Fall 1990 Final Examination)
Q
t
and
PM
t
. We assume that
3
>
0
as movie theater tickets are likely substitutes
for video cassette rentals. As a result the slope
@Q
t
@PM
t
is constant and so the price
elasticity
@
ln
Q
t
@
ln
PM
t
varies with the magnitude of
Q
t
PM
t
. The second graph, which
corresponds to (2), reveals three possible relations between
Q
t
and
PM
t
. (Note,
the ±intercept²now corresponds to
PM
t
= 1
, because
ln 1 = 0
.) Under (2) the
price elasticity is constant and so the slope varies with the magnitude of
PM
t
Q
t
.
b) Economic theory, rather than a statistical measure such as
R
2
, should be
to model speci&cation. Suppose the average income of households in neighbor
hood
t
increased by $100 per month. Would this have the same a/ect for all
neighborhoods regardless of the
level
of average income in the neighborhood?
Undoubtedly not, as wealthy neighborhoods might regard such a change as negli
gible while poorer neighborhoods might increase consumption of services such as
cassettes is a/ected by the percentage change in average family income. To the
degree to which the price of video cassettes and movie tickets are constant across
the neighborhoods in the sample, the distinction between percentage change and
absolute change is moot. For these variables either functional form may be appro
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 Fall '08
 Staff
 Economics, Household income in the United States, ln Qt, ln yt, ln P Mt, P Mt, average admission price

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