An Empirical Analysis of the Optimal Advertising Policy

This paper determines an optimal policy for investment in advertising for a firm that wishes to maximize its discounted profits. To that end, an integrated approach consisting of model formulation, empirical investigation, and optimization is carried out. A model of market share response to advertising is formulated as a first-order Markov process, with nonstationary transition probabilities. These probabilities are assumed to be a function of the advertising goodwill accumulated by the firm and its competitors. The model as specified is nonlinear in its parameters, and nonlinear regression techniques are applied to estimate them. It is shown that this nonlinear form offers, via likelihood ratio tests, a unique opportunity for testing the model, and in a resulting empirical test, the model is found to be consistent with the data. Given these empirical findings, an optimal advertising policy is derived by the use of optimal control theory. The managerial implications of the recommended multi-period policy are examined, and the policy's sensitivity to managerial inputs and economic conditions is analyzed and illustrated.