Constant Returns to Scale (Linear) Model — Sales Response Function


Constant Returns to Scale (Linear) Model - Sales Response Function — Marketing mix Modelling

Exhibit 35.2-1   Constant Returns to Scale (Linear) Model.

The simplest functional form is the linear model which represents constant returns to scale:

$$ S=α+βX $$

Where:

  • S is sales, the dependent variable, and
  • X is the independent variable representing the marketing effort for the marketing mix element.
  • α and β are model parameters. α is the intercept — the sales when there is no marketing effort. β is coefficient for X. A unit change in X results in a change of β units in sales.

The linear model is theoretically unsound because it suggests that sales increase indefinitely. However, from a practical viewpoint, within a relatively small operating range, a linear model can provide a satisfactory approximation of the true relationship.


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