Dynamic optimal pricing and (possibly) advertising in the face of various kinds of potential entrants

Abstract Several nonlinear stochastic models are developed for a dynamic profit-maximizing firm with respect to its price and (possibly) advertising decisions under threat of entry. The optimal price-advertising policies for these models are characterized by the use of the Maximum Principle. While the optimal policy will depend on the assumed functional forms, it is shown that, under certain plausible assumptions, the optimal policy is to increase profit by charging a higher price and decrease the resulting threat of entry by a higher level of advertising.

[1]  Richard Schmalensee,et al.  Brand Loyalty and Barriers to Entry , 1974 .

[2]  Martin Shubik,et al.  Strategy and market structure , 1959 .

[3]  B. P. Pashigian.  Limit Price and the Market Share of the Leading Firm , 1968 .

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

[5]  S. Sethi.  Dynamic Optimal Control Models in Advertising: A Survey , 1977 .

[6]  F. Pyatt.  Profit Maximisation and the Threat of New Entry , 1971 .

[7]  J. Bain.  Barriers to new competition , 1957 .

[8]  Edwin Mansfield,et al.  ENTRY, GIBRAT'S LAW, INNOVATION, AND THE GROWTH OF FIRMS , 1962 .

[9]  Gerald R. Faulhaber,et al.  Cross-Subsidization: Pricing in Public Enterprises , 1975 .

[10]  Morton I. Kamien,et al.  LIMIT PRICING AND UNCERTAIN ENTRY , 1971 .

[11]  O. Williamson.  Selling Expensse as a Barrier to Entry , 1963 .

[12]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[13]  D. Gaskins,et al.  Dynamic limit pricing: Optimal pricing under threat of entry , 1971 .

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

[15]  William S. Comanor,et al.  Advertising and Market Power , 1974 .

[16]  F. Modigliani,et al.  New Developments on the Oligopoly Front , 1958, Journal of Political Economy.

[17]  William S. Comanor,et al.  The Effect of Advertising on Competition: A Survey , 1979 .

[18]  L. Telser,et al.  Competition, collusion, and game theory , 1972 .

[19]  G. Stigler.  The Theory of Price , 1948 .

[20]  Carl M. Harris,et al.  The Pareto Distribution as a Queue Service Discipline , 1968, Oper. Res..

[21]  George J. Stigler,et al.  The Organization of Industry , 1969 .

[22]  R. Litzenberger,et al.  A State-Preference Model of Optimal Financial Leverage , 1973 .

[23]  Marvin Zelen,et al.  Mathematical Theory of Reliability , 1965 .

[24]  William J. Baumol,et al.  Weak Invisible Hand Theorems on the Sustainability of Multiproduct Natural Monopoly , 1977 .

[25]  Angelo Miele,et al.  Extremization of Linear Integrals by Green's Theorem , 1962 .

[26]  J. Friedman.  On Entry Preventing Behavior and Limit Price Models of Entry , 1979 .

[27]  Yehuda Kotowitz,et al.  Advertising, Consumer Information, and Product Quality , 1979 .

[28]  Suresh P. Sethi,et al.  Nearest feasible paths in optimal control problems: Theory, examples, and counterexamples , 1977 .