This paper reports a new theorem and proof for optimizing the advertising budget. The theorem is that the optimal rate of advertising is equal to gross profit multiplied by advertising elasticity. This does not involve a ratio of elasticities, and so is an advance on the Dorfman-Steiner theorem...

This paper reports a new theorem and proof for optimizing the advertising budget. The theorem is that the optimal rate of advertising is equal to gross profit multiplied by advertising elasticity. This does not involve a ratio of elasticities, and so is an advance on the Dorfman-Steiner theorem...

Decision on the use of different advertising media is a critical issue in marketing. Drawing on some literature related to the dynamic Nerlove-Arrow model, we propose a nonlinear programming framework for discussing how different advertising media may jointly affect the demand for a good....

The optimal control problem of determining advertising efforts for a seasonal good in a heterogeneous market is considered. We characterize optimal advertising exposures under different conditions: the general situation in which several wide-spectrum media are available, under the assumption of...

Cooperative advertising is an important incentive offered by a manufacturer to influence retailers' promotional decisions. We analyze a retail market duopoly where one or both of competing retailers are supported by the manufacturer in their advertising costs. We model the problem as a...

This paper considers the problem of optimizing the institutional advertising expenditure for a firm which produces two products. The problem is formulated as a minimum-time control problem for the dynamics of an extended Vidale-Wolfe advertising model, the optimal control being the rate of...

This paper considers an optimal control problem for the dynamics of a contagion model, the optimal control being the rate of advertising expenditure that maximizes the present value of net profit streams over an infinite horizon. By using a Green's theorem approach, it is shown that there are...

We examine an oligopoly model of advertising competition where each firm's market share depends on its own and its competitors' advertising decisions. A differential game model is developed and used to derive the closed-loop Nash equilibrium under symmetric as well as asymmetric competition. We...

A model of new-product adoption is proposed that incorporates price and advertising effects. An optimal control problem that uses the model as its dynamics is solved explicitly to obtain the optimal price and advertising effort over time. The model has a great potential to be used in obtaining...

Firms that want to increase the sales of their brands through advertising have the choice of capturing market share from their competitors through brand advertising, or increasing primary demand for the category through generic advertising. In this paper, differential game theory is used to...