Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

116 ADVANCED TOPICS IN CONSUMER DEMAND THEORY [CHAP. 5
5.11 Starting from panel B of Fig. 5-4, draw a figure showing a hypothetical consumer’s equilibrium with a
40% reduction in the price of honey.
Fig. 5-13
When the price of honey falls by 40% ray OB extends to OB 00 as in Fig. 5-12. As a result, the new production
frontier becomes AB 00 H in Fig. 5-13. A hypothetical equilibrium position is given by point T on indifference curve
IV. Point T is reached with OW characteristics from saccharin and WT (equals OB) from honey, with no sugar
purchased. Area OAB 00 H is referred to as the feasible region and AB 00 H as the efficiency frontier.
5.12 With regard to the new approach to consumer theory, (a) what can you conclude as to the number of
goods purchased from the number of characteristics considered? (b) How could producers of sugar in
Fig. 5-13 regain this market? (c) If saccharin is very profitable, what quality changes are producers
of honey stimulated to introduce? How would these quality changes be reflected in Fig. 5-13?
(a)
(b)
(c)
In Figs. 5-4, 5-11, 5-12, and 5-13, we have seen that the goods have two characteristics and the consumer
purchases two goods when in equilibrium. In general, the number of goods consumed will never exceed
the number of characteristics desired.
Producers of sugar could regain the market they lost to honey if they succeed in reducing the price of sugar so
as to extend ray OA sufficiently in length so that a line from its new end point to point H leaves point B 00 inside
such a line or budget frontier (see Fig. 5-13).
If saccharin is very profitable, producers of honey are likely to attempt to reduce the caloric content of honey,
thereby rotating ray OB 00 clockwise toward ray OH in Fig. 5-13.
EMPIRICAL DEMAND CURVES
5.13 In a 1960 study, Chow found the following estimated demand function for automobiles in the U.S.:
X t ¼ 0:725 0:049P t þ 0:025M t
R 2 ¼ 0:90
e ¼ 0:6
e m ¼ 1:5
where X t ¼ per capita stock of automobiles at the end of period t
P t ¼ an automobile price index
M t ¼ expected per capita income
R 2 ¼ coefficient of determination
e and e m ¼ price and income elasticity of demand, respectively
With respect to the above results, what is the meaning of (a) the sign of the estimated coefficients, and
(b) the size of the estimated coefficients? (c) How did Chow estimate e and e m ?(d) What does R 2 ¼ 0.90
indicate?
(a)
The negative sign of the estimated coefficient of P t and the positive sign of the estimated coefficient of M t
indicate that X t is inversely related to P t and directly related to M t . Note that tastes are implicitly assumed
to be constant and no price of related goods (such as public transportation or gasoline) is included.