Measuring and Testing Advertising-Induced Rotation in the Demand Curve

Second, advertising can rotate the demand curve even when the price-
advertising interaction terms are not included. For a double-log model featuring
constant elasticity (model C), the demand curve must rotate to offset the advertising-
induced shift effect to keep the own-price elasticity unchanged in most cases. As an
illustration let two demand curves be Q₁ = P^-η and Q₂ = P^-ηA^α with the own-price
elasticity (absolute value), advertising expenditure, and advertising elasticity taking
the hypothetical values of 2, 500, and 0.05, respectively. A horizontal comparison
(Q is the horizontal axis) of slopes between Q1 and Q2 clearly shows that a positive
and advertising-induced shift in demand makes the demand curve flatter. The shift
effect and shift-related rotation effect, in this case, are both 0.05. Relaxing the
assumption of fixed prices will alter the magnitude of the shift and shift-related
rotation effects, but will not change the fact that advertising rotates the demand
curve unless supply elasticity is unitary. Advertising can also rotate the demand
curve through its influence on budget shares (in models D and E). We, therefore,
consider the rotation effects as shift-related if they are induced by a shift in demand
caused by advertising. All the rotation effects in models A - E are shift related.
Note the shift-related rotation effects are function specific, as they arise in models C
- E due to constraints on functional forms (e.g., constant elasticity in model C) and
could disappear otherwise (as in models A and B).

The last implication builds upon the second one. Combining the rotation
effects with and without the price-advertising interaction effects yields the
interaction-related rotation effects. In the presence of a price-advertising interaction
term, the rotation effects in models F - J combine an interaction-related rotation

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