Experimental Pricing As an Approach to Demand Analysis 29
THE GENERAL DEMAND FUNCTION
Reference to the final form of the statistical model shows
that the estimated general demand function evolving from the
analysis was given by:
Y' = 5.71766 5.584685X', + 2.120746X'io.
Since price elasticity of demand for this function is expressed by
Np = -5.584685 + 4.241492X%9,28 estimated demand elasticity
was clearly a function of price.
It may further be observed that, beginning with the lowest
test price, demand elasticity decreased as price increased over
the entire range of prices tested. Moving from lower to higher
prices, demand changed from an elastic to an inelastic relation-
ship at the pivotal price of about 12.050 per 6-ounce can of con-
centrate. That is, the demand function was found to have uni-
tary elasticity at an estimated price of about 12.05.29 Estimated
demand elasticity at the various test prices obviously would be
either elastic or inelastic depending upon whether a particular
test price was higher or lower than the estimated price associated
with unitary elasticity.
A demand relationship of the foregoing nature is character-
ized by a revenue function convex to the origin with minimum
revenue occurring at the price corresponding to the point of
unitary elasticity on the demand curve.30
If Y = 5.71766 5.584685X + 2.120746X'0,
then dY Y -5.584685 + 4.241492X'
dY y[ -5.584685 + 4.241492X9
dX X
From the definition of price elasticity of demand, Np = X. ,the
SdX Y
equation for estimating demand elasticity becomes
N [-5.584685 + 4.241492X X, or Np = -5.584685 + 4.241492X9.
:X Y
"2The slight discrepancy between the estimated price associated with
unitary demand elasticity as given in Florida Experiment Station Bulletin
589 and the estimate appearing in this report arises because in the former the
iis were included in the model.
If the demand function in terms of logarithms is given by
Y' = 5.71766 5.584685X's + 2.120746X'1o, then the revenue function
expressed in logarithms would be equivalent to
R' = 5.71766 4.584685X', + 2.120746X'io.
Because R' is a monotonic function of R (total revenue), maximum or