Measuring and Testing Advertising-Induced Rotation in the Demand Curve



effect, as well as a shift-related rotation effect. Once segregated from the shift-
related rotation effects, the interaction-related rotation effects for models F - J
are
Yi /( c + YiAi ) , Yi /( cii + Yiln Ai), Yi /( cii + Yiln Ai ), Yi /( cii + Yidln A1 ), and

n

(Yi +Yi lnAiwjαij) /(cii +Yi lnAi - wi), respectively. Taking the Rotterdam model
j

(model I) as an example, the effect of advertising on the own-price elasticity can be
decomposed into three parts: an interaction-related rotation effect of

n

Yi /(cii + Yi lnAi) or- Yi /(ηiwi), a shift-related rotation effect ofwjαij , and the
j

negative of a shift effect of αii .6 Using the above interaction-related rotation effects
to measure the advertising-induced demand curve rotation is advantageous because
it reflects the “true” rotation effects indicated by the price-advertising interaction
terms γi ,s, and because of the ease of interpretation and comparison across demand
models since they are in the form of elasticities.

Additional insight can be obtained by noting that the second-order cross
partial derivatives of any particular function are unaffected by the order in which the
derivative is taken. Thus, in the simple case where quantity demanded
qD is defined
to be a function of price and advertising:

(7)    qD =D(p,A)

the following “duality relation” (Frisch 1959, p. 180) holds:

2 D = 2 D

p A A p ’

or, in elasticity notion,

11



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