Daniel l. Rubinfeld
Daniel l. Rubinfeld
Daniel l. Rubinfeld
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132 Part 2 Producers, Consumers, and Competitive Markets<br />
They might be asked hm\' they vvould expect others to behave. Although indirect<br />
approaches to demand estimation can be fruitfuL the difficulties of the inter<br />
\'ie,v approach ha\'e forced economists and marketing specialists to look to<br />
alternative methods,<br />
In direct marketing experiments, actual sales offers are posed to potential customers.<br />
An airline, for example, might offer a reduced price on certain flights for<br />
six months, partly to learn how the price change affects demand for flights and<br />
partly to learn how competitors will respond.<br />
Direct experiments are reaL not hypothetical, but even so, problems remain. TI1e<br />
wrong experiment can be costly, and even if profits and sales rise, the firm CalU10t be<br />
entil"ely sure tl1at tl1ese increases resulted from the experimental change; oilier factors<br />
probably chal1ged at the same time. Moreover, the response to experiments-which<br />
consmners often recognize as short-lived-may differ from the response to pennanent<br />
chal1ges. Finally, a fil"m can afford to hT only a limited number of experiments.<br />
25<br />
20<br />
15<br />
10<br />
Chapter 4<br />
Individual and Market Demand<br />
33<br />
The Statistical Approach to Demand Estimation<br />
Finns often rely on market data based on actual studies of demand. Properly<br />
applied, the statistical approach to demand estimation can help researchers sort<br />
out the effects of variables, such as income and the prices of other products, on<br />
the quantity of a product demanded. Here we outline some of the conceptual<br />
issues involved in the statistical approach.<br />
Table 4.5 shows the quantity of raspberries sold in a market each year.<br />
Infonnation about the market demand for raspberries would be valuable to an<br />
organization representing growers because it would allow them to predict sales on<br />
the basis of their own estimates of price and other demand-determining variables.<br />
Let's suppose that, focusing on demand, researchers find that the quantity of raspberries<br />
produced is sensitive to weather conditions but not to the current market<br />
price (because farmers make their planting decisions based on last year's price).<br />
The price and quantity data from Table 4.5 are graphed in Figure 4.1S. If we<br />
believe that price alone determines demand, it would be plausible to describe the<br />
demand for the product by drawing a straight line (or other appropriate curve),<br />
Q = a - bP, which "fit" the points as shown by demand curve D. (The "leastsquares"<br />
method of curve-fitting is described in the appendix to this book.)<br />
o<br />
25 Quantity<br />
Price and quantity data can be used to determine tl1e form of a demand relationship.<br />
But the same data could describe a single demand curve 0 or furee demand curves<br />
dl< dc, and d 3 that shift over time.<br />
Does c,urve 0 (given by the equation Q = 2S.2 - 1.00P) really represent the<br />
demand tor the product The answer is yes-but only if no important factors<br />
other than product price affect demand. In Table 4.5, howevel~ we have included<br />
data tor one other \'ariable: the average income of purchasers of the product.<br />
Note that income (1) has increased twice durinG the studv sUGGestinG that the<br />
d:l<br />
.' 0"' 00 0 c<br />
ema~1l curve h~s shltted twice. Thus demand curves d , 1<br />
d , 2<br />
and d 3<br />
in Figure<br />
4.1S gl\'~ a more hkely description of demand. This demand relationship would<br />
be descnbed algebraically as<br />
YEAR aUANTlTY (a) PRICE (P) INCOME (I)<br />
1988 4 24 10<br />
1989 7 20 10<br />
1990 8 17 10<br />
1991 13 17 17<br />
1992 16 10 17<br />
1993 15 15 17<br />
1994 19 12 20<br />
1995 20 9 20<br />
1996 22 5 20<br />
Q = a - bP + cI (4.4)<br />
The inco~e term in the demand equation allo\'\'s the demand curve to shift in a<br />
parallel tashion as income changes. (The demand relationship, calculated usinG<br />
the least-squares method, is gi\'en by Q = S.OS A9P + .SU.) 0<br />
The Form of the Demand Relationship<br />
Because the demand relationships discussed above are straiGht lines the effect<br />
of a I G'.' . . 0'<br />
.. c 1anoe m pnce on quantIty demanded IS constant. However~ the price elasbc~y<br />
of de~1and varies with the price leveL For the demand equation<br />
Q - 17 - bP, tor example, the price elastiCity Ep is<br />
Ep (.1Q/.1P)(PIQ) = -b(PIQ) (4.5)