Experimental Pricing As an Approach to Demand Analysis 13
Price "age" was adopted as a source of variation because
customers could not reasonably be expected to make a once-and-
for-all, instantaneous adjustment to the new set of concentrate
prices imposed by the experiment. The result, reflected in cus-
tomer purchases, of this delayed reaction to a price change has
been termed "carry-over" effect. Given a basic (long-run) re-
lationship between price and quantity, price "age," conceivably,
could affect demand by shifting the demand curve, changing the
slope of the curve or both. It was anticipated that the "age"
parameters would provide satisfactory estimates of shifts in the
demand function associated with price "age." By permitting
the fitting of separate demand functions to the various price
"ages," the proposed model also provided for the detection of
possible changes in the slope of the function.
Because the effect of price "age" on purchases would possibly
vary from store to store, the decision was made to introduce store
x age interaction as a possible source of variation.
The reason for considering stores and weeks as sources of
variation is fairly obvious from the discussion of the economic
model. Although store-to-store variation in purchases per
customer unit could be isolated by ordinary analysis of variance
techniques, variation between weeks had to be partitioned into
"weeks within age" and "age." 8
Taking weekly purchases 9 in ounces of orange concentrate
per hundred customers as the predictive variable, the analytical
model assumed the following form: 10
Yi k-j- = + aA + pP + i -W tk+ p ijpr
+ PX';ik-i + P2X2ik-i-+ P3 ik-j-+ P4Xik-j-
+ PXik-i- + 6 ik-j- + ik-i-
8 See Table 2 of Appendix III for the key to the planned analysis of
covariance.
Although concentrate purchases in each store were recorded on a daily
basis, sales were aggregated into weekly purchases because this measure
would seemingly conform more closely to customer shopping habits. Fur-
thermore, from a computational standpoint, the model would have been
extremely unwieldy if daily purchases had been used.
An expression of the model in matrix notation appears in Table 1,
Appendix III.