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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)

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