(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 165

140 PART • Producers, Consumers, and Competitive Markets TABLE 4.6 DEMAND DATA YEAR QUANTITY (Q) PRICE (P) INCOME (I ) 2004 24 10 2005 20 10 2006 17 10 2007 13 17 17 2008 16 10 27 2009 15 15 27 2010 19 12 20 2011 20 20 2012 22 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