The marketing mix operates as
a co-ordinated programme designed to achieve business imperatives. It is
therefore not surprising that often the elements of the mix interact
synergistically, to produce an effect greater than the sum of their individual
effects.
For example, the elements of consumer promotions,
like discounts, displays and co-op advertising, often have a synergistic impact
lifting sales more than the sum of their individual impact on sales. Or for example,
investments in marketing instruments such as theme advertising strengthen a
brand’s equity, resulting in the lowering of consumers’ sensitivity to changes
in price.
These interaction effects influence the sensitivity
of one or more elements of the marketing mix, to changes in another element of
the mix. They are captured in response functions by including an additional
term (X1×X2) which represents the product of the two
interacting variables.
The multiplicative model implies
that the dependent variable is affected by an interaction of the variables of
the marketing mix. Its functional form is written as:
$$ S= e^α \prod_j^{variables} X_j^{β_j} = e^α X_1^{β_1}X_2^{β_2}X_3^{β_3} ... X_J^{β_J}, X_j >0$$
In its logarithmic form however the interaction effects are
no longer explicit:
$$ ln(S)=α+β_1lnX_1+β_2lnX_2+β_3lnX_3 ... +β_JlnX_J $$
If there is the need to include interaction effects after
taking logs, the transcendental logarithmic (translog) model is
one approach for doing so:
$$ ln(S)=α+β_1lnX_1+β_2lnX_2+β_3lnX_3 ... $$
$$ +β_{12}lnX_1lnX_2+β_{13}lnX_1lnX_3+β_{22}lnX_2lnX_2 ... $$
$$ +β_{11}(lnX_1)^2+β_{22}(lnX_2)^2+β_{33}(lnX_3)^2 ... $$
A related notion, interdependency, exists when a company’s decisions on one element of the marketing mix impact its
decisions on some of the other elements of the mix. This may result from the
outcome of concerted strategies, or the trade-offs that companies need to make
with limited budgets. For example, pricing decisions impact margins, which in
turn may have a bearing on the brand’s budget on other instrument such as
advertising. Interdependence may also exist within different forms of an
instrument — conventional and online advertising for instance.
