Steiner (1987) developed this analysis utilizing the notion of advertising response
function, the relationships between sales and advertising input and assuming the
presence of a threshold level.8. The existence of a threshold level in the sales-
advertising relationship is generally supported by empirical evidence. It means that
beneath a certain level there is essentially no sales response. In other words, some
positive amount of advertising is necessary before any sales impact can be detected.
More precisely, the advertising response function is S-shaped, convex in advertising
up to an inflection point after which it is concave. 9
Formally, the advertising response function may be expressed in terms of the
advertising elasticity, defined as the proportionate rate of change in sales with respect
to advertising and it is therefore immediate derive the implications for the optimal
advertising expenditure. Dorfman and Steiner defined the standard approach
according to which the joint optimum of price (P) and advertising expenditure (A) in
the case of a monopolist is given by equality of the ratio of advertising- to- sales A/S
(advertising intensity) with the ratio of the advertising elasticity of demand, eA, to the
absolute price elasticity of demand, eP: A/S = eA/e P, where S = PQ, and Q denotes the
output level.
On the basis of the condition of Dorfman and Steiner, the optimal advertising intensity
depends on how increases in advertising affect the firm's cost and demand.The
condition simply states that more advertising will be undertaken the more profitable it
is.
If the advertising response function is S-shaped, the marginal returns to advertising
are increasing for some initial region and the advertising elasticity is greater the longer
the region of increasing returns to advertsing. Since advertising expenditures are key
determinants of the strength of a brand and affect the brand's retail penetration and
support, as well as the retailer’ s margin, these three "dual stage effects " increase the
advertising effectiveness. Therefore, in a dual- stage model there is a mechanism at
work leading to extend the region of incresing returns to advertising (and R&D).
Therefore, advertising elasticities and advertising intensities are
(eA)d > (eA)s ⇒ (A*/S)d > (A*/S)s (1)
where d refer to dual- stage and s the single- stage model. In other words in a dual-
stage model, the shape and position of the manufacturer’ s response function to non-
price strategies is different from that in the single- stage one. The eA/eP ratio
characterizing optimal advertising intensity in the DS condition is increased by a
factor determined by the margin- depressing impact of advertising. As a result, on the
basis of the Dorfman- Steiner condition, a dual- stage model implies higher optimal
advertising and R&D expenditures (Steiner, 1973; Albion, 1983; Steiner, 1993). The
8 Following Steiner, here we only focus on advertising but clearly the same analysis can
be extended to the determinants of all the expenditures contributing to the strengh of
a brand, for example R&D and other marketing expenditures.
9 The S-shaped advertising response function is a common assumptiom in the
advertising literature. Several economist (see Comanor and Wilson, 1974; Porter, 1976;
Arndt and Simon,1983) claim that there are initial increasing returns to scale for
advertising.
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