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

CHAP. 5] ADVANCED TOPICS IN CONSUMER DEMAND THEORY 117
(b)
(c)
The –0.049 coefficient of P t indicates that a 100% increase in P t reduces X t by 4.9%. The 0.025 coefficient of
M t indicates that a 100% increase in M t increases X t by 2.5%.
Since the coefficient of P t refers to DX/DP, multiplying DX/DP by P/X for 1960, we get
DX
DP P ¼ e(¼ 0:6 in 1960)
X
Similarly, since the coefficient of M t refers to DX/DM, multiplying DX/DM by M/X for 1960, we get
DX
DM M X ¼ e m(¼1:5 in 1960)
(d ) R 2 ¼ 0.90 indicates that 90% of the variation is explained or associated With the variation in P t and M t.
5.14 (a) Write the general form of the constant-elasticity demand function, (b) What is the meaning of the
various coefficients?
(a) Q x ¼ aP b x P c 0 M f u or In Q x ¼ In a þ b In P x þ c In P 0 þ f In M þ In u
(b)
where
Q x ¼ market quantity demanded of commodity X per unit of time
P x ¼ price of X
P 0 ¼ price of unrelated commodities
M ¼ money income
u ¼ error term
ln ¼ natural logarithm (to base e)
a ¼ constant or intercept
b ¼ price elasticity of demand
c ¼ cross elasticity of demand
f ¼ income elasticity of demand
The constant-elasticity demand function is the most commonly used demand function in applied
research because its coefficients give a direct estimate of the various elasticities.