Advertising Decision Rules in a Multibrand Environment: Optimal Control Theory and Evidence

The authors postulate that the firm pursues a present value profit maximization goal in determining its advertising strategy. Advertising is included in the profit function nonlinearly as a factor cost and as a demand stimulant. On the basis of optimal control theory, an optimal advertising-sales ratio decision rule is formulated with respect to the brand's demand parameters. Reliably collected data on sales and advertising expenditures on a bimonthly basis were used to obtain empirical estimates of the brand parameters. A simultaneous estimation of the demand parameters of all the competing brands was performed to harness efficiently the information inherent in the system of brand demand equations. Comparing the firm's behavior on brand advertising with the derived decision rule ratio suggests the potential usefulness of such analytical models for improving the productivity of advertising expenditures and for determining the change in advertising policy which would be appropriate in the event of changes in a brand's demand sensitivity.