10.7.3 Complex marketing mix interactions
The constant elasticity model is a very useful general model for representing the effects of the different elements of the marketing mix on sales and profit. However, managerial analysts may want to incorporate certain specific interactions into their demand models. A couple of examples will illustrate the situation.
1 It may be considered that the marginal effect of advertising is a function of distribution, because a greater number of retail outlets will increase the effects of a given advertising expenditure. A linear relationship may be involved as follows:
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2 It may be considered that a greater level of advertising reduces price elasticity, by increasing brand loyalty. This may be modelled as follows:
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These relationships then have to be incorporated into the demand equation, according to its mathematical form. For example, if (10.42) is substituted into a constant elasticity demand function, we obtain:
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The above examples just give an idea of the kind of interactions that can be incorporated into the marketing mix demand model. Obviously the equations become harder to work with mathematically, and may cause problems in regression analysis, but they may lead to more reliable and useful results, both in terms of testing economic theories, and in terms of making better managerial decisions.