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.

[1]  Dan Horsky,et al.  Market Share Response to Advertising: An Example of Theory Testing , 1977 .

[2]  Arnold Zellner,et al.  Estimating the parameters of the Markov probability model from aggregate time series data , 1971 .

[3]  J. P. Gould,et al.  Diffusion Processes and Optimal Advertising Policy , 1976 .

[4]  R. Dorfman,et al.  Optimal Advertising and Optimal Quality , 1976 .

[5]  Alfred A. Kuehn,et al.  A Model for Budgeting Advertising , 1976 .

[6]  D. Horsky.  A theoretical and empirical analysis of the optimal advertising strategy , 1974 .

[7]  Suresh P. Sethi,et al.  Optimal Control of the Vidale-Wolfe Advertising Model , 1973, Operational Research.

[8]  Thomas John Aird.  Computational solution of global nonlinear least-squares problems. , 1973 .

[9]  Richard E. Quandt,et al.  Nonlinear methods in econometrics , 1973 .

[10]  Neil E. Beckwith.  Multivariate Analysis of Sales Responses of Competing Brands to Advertising , 1972 .

[11]  Maurice W. Sasieni,et al.  Optimal Advertising Expenditure , 1971 .

[12]  F. Bass.  A Simultaneous Equation Regression Study of Advertising and Sales of Cigarettes , 1969 .

[13]  A. Dobell,et al.  Optimal investment policy: An example of a control problem in economic theory , 1967, IEEE Transactions on Automatic Control.

[14]  W. Massy.  Order and Homogeneity of Family Specific Brand-switching Processes , 1966 .

[15]  O. Mangasarian.  Sufficient Conditions for the Optimal Control of Nonlinear Systems , 1966 .

[16]  Kristian S. Palda.  The Measurement of Cumulative Advertising Effects , 1965 .

[17]  Melvin F. Shakun.  Advertising Expenditures in Coupled Markets---A Game-Theory Approach , 1965 .

[18]  George P. H. Styan,et al.  Markov Chains Applied to Marketing * , 1964 .

[19]  L. Telser.  Advertising and Cigarettes , 1962, Journal of Political Economy.

[20]  K. Arrow,et al.  OPTIMAL ADVERTISING POLICY UNDER DYNAMIC CONDITIONS , 1962 .

[21]  L. Friedman.  Game-Theory Models in the Allocation of Advertising Expenditures , 1958 .

[22]  M. L. Vidale,et al.  An Operations-Research Study of Sales Response to Advertising , 1957 .

[23]  M. Kendall,et al.  The Logic of Scientific Discovery. , 1959 .