SUMMARY
Unlike most approaches to demand analysis, the data for
this study were generated under semi-controlled conditions to
satisfy a previously specified economic model.
Generation of the underlying data involved measuring cus-
tomer responses to a set of deliberately introduced retail prices.
Five price levels were tested: the prevailing market price, prices
representing discounts below the market of 3, 6 and 8 cents
per 6-ounce can and one price representing a premium of 4
cents above the current market level. Test prices were intro-
duced in 10 retail stores in conformance with an experimental
design especially derived to permit statistical isolation of the
price effect, while at the same time coping with the problems of
carry-over effect and multiplicity of product brands.
Computational efficiency and prior economic theorization about
the problem led to the choice of a logarithmic "fixed unknown
constants" statistical model for analyzing the data. That is,
weekly purchases of orange concentrate per hundred customers
were assumed to be a function of the sum of a set of "class
constants" consisting of a price "age" effect, store effect, week
effect and effect of store x price "age" interaction, and of a re-
gression on price, with all components of the model expressed
in terms of logarithms.
Given the general model, the choice of a specific model neces-
sitated testing certain hypotheses about the model parameters.
In particular, the appropriate degree of the regression remained
to be determined and a choice made between fitting a single re-
gression or individual regressions for each price age. The sig-
nificance of the variation contributed by the specified "class
constants" also required examination.
Upon performing the necessary tests, the "best" estimating
model was found to be a quadratic single regression function
including all of the specified "class constants" with the excep-
tion of store x age interaction, which turned out to be non-
significant.
Application of the estimating model to the data yielded a
demand function for which price elasticity of demand varied
inversely with price. Derived estimates showed that demand
changed from an elastic to an inelastic relationship at the pivotal
price of about 12 cents per 6-ounce can of concentrate. The
revenue function generated by this demand relationship was
convex to the origin with minimum revenue occurring at the
point of unitary elasticity on the demand curve.