(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 165
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140 PART 2 • Producers, Consumers, and Competitive Markets
TABLE 4.6
DEMAND DATA
YEAR
QUANTITY (Q)
PRICE (P)
INCOME (I )
2004
4
24
10
2005
7
20
10
2006
8
17
10
2007
13
17
17
2008
16
10
27
2009
15
15
27
2010
19
12
20
2011
20
9
20
2012
22
5
20
The price and quantity data from Table 4.6 are graphed in Figure 4.19. If we
believe that price alone determines demand, it would be plausible to describe the
demand for the product by drawing a straight line (or other appropriate curve),
Q ϭ a Ϫ bP, which “fit” the points as shown by demand curve D. (The “leastsquares” method of curve-fitting is described in the appendix to the book.)
Does curve D (given by the equation Q = 28.2 - 1.00P) really represent the
demand for the product? The answer is yes—but only if no important factors other
than price affect demand. In Table 4.6, however, we have included data for one
other variable: the average income of purchasers of the product. Note that income
(I) has increased twice during the study, suggesting that the demand curve has
shifted twice. Thus demand curves d1, d2, and d3 in Figure 4.19 give a more likely
description of demand. This linear demand curve would be described algebraically as
Q = a - bP + cI
(4.2)
The income term in the demand equation allows the demand curve to shift in a
parallel fashion as income changes. The demand relationship, calculated using
the least-squares method, is given by Q = 8.08 - .49P + .81I.
The Form of the Demand Relationship
Because the demand relationships discussed above are straight lines, the effect of
a change in price on quantity demanded is constant. However, the price elasticity
of demand varies with the price level. For the demand equation Q = a - bP, for
example, the price elasticity EP is
E P = (⌬Q/⌬P)(P/Q) = -b(P/Q)
(4.3)
Thus elasticity increases in magnitude as the price increases (and the quantity
demanded falls).
Consider, for example, the linear demand for raspberries, which was estimated to be Q = 8.08 - .49P + .81I. The elasticity of demand in 1999 (when Q = 16
and P = 10) is equal to -.49 (10/16) = -.31, whereas the elasticity in 2003 (when
Q = 22 and P = 5) is substantially lower: -.11.
