Experimental Pricing As an Approach to Demand Analysis 15
The following restrictions were imposed:
SM. :-- 0
"Mi= Number of observations in age j
S6; =0
"I 2 + '2 "51 '7 = 0, + '2+ 2= 0' 143+ -9 = 0
E M ii = 'i = 0
Further it was assumed that Ik-j- was distributed normally with
zero mean and constant variance.
More briefly, the model can be expressed in terms of loga-
rithms by the polynomial form,
Yik-- = PO + + 6 k-i- + ;i+ PI IUk-ij- +2Xk-j-
+ P3Xk-j- + P4Xk-j- + P5k-i- + 6X6ik-i- + 'k-j-
or, in actual values by the monomial,
Yik,-= (lk-j-) (Aik-j-) (Xlik-i- lik-j- (X21k--V2k-j- (X3ii_)V3ik-j-
where
Aik-j- 0 ai 1 'k-i- '1
Vik-i-' PI + 4ogXlik-j-
V2ik-i- = 2+ 0lg X21k-i-
V31k-j-= P3 + P610 X31k-l-
In summary, the Pq's, i.e., regression coefficients of the model,
allow for possible differences in the slopes of the demand function
associated with price "age." The parameters, "i, 6S 'k-i-_nd A1,,
on the other hand, designate proportional shifts in the demand
function specified by the model.