A Stochastic Model of Consumer Behavior and Optimal Advertising

Charles S. Tapiero

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Consumer Market Behavior and Pricing Marketing and Advertising Strategies Innovation Diffusion and Forecasting

Abstract

A stochastic consumer behavior model is constructed transforming Nicosia's (Nicosia, F. M., 1966. Consumer Decision Processes. Prentice-Hall, Englewood Cliffs, New Jersey.) postulates into probability hypotheses. Nicosia's deterministic model is obtained in the mean evolutions and variance-covariances, defined by a system of linear differential equations obtained. This system, forming together with mean evolutions a closed system of five simultaneous differential equations is studied for stability, to devise optimal communication strategies and for suggesting an estimation technique.

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1964CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK*1975THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS**This paper is another in a series of interrelated theoretical and statistical studies of corporate financial and investment policies being made under grants from the Rockefeller Foundation, and more recently the Ford Foundation, to the Harvard Business School. The generous support for this work is most gratefully acknowledged. The author is also much indebted to his colleagues Professors Bishop, Christenson, Kahr, Raiffa, and (especially) Schlaifer, for extensive discussion and commentary on an earlier draft of this paper; but responsibility for any errors or imperfections remains strictly his own.[Professor Sharpe's paper, “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk” (Journal of Finance, September 1964) appeared after this paper was in final form and on its way to the printers. My first section, which parallels the first half of his paper (with corresponding conclusions), sets the algebraic framework for sections II, III and VI, (which have no counterpart in his paper) and for section IV on the equilibrium prices of risk assets, concerning which our results differ significantly for reasons which will be explored elsewhere. Sharpe does not take up the capital budgeting problem developed in section V below.]1970Information and Consumer Behavior 1959Models of Man.1976The Economics of Information 1976Optimal Advertising Policy Under Dynamic Conditions 1972The economics of advertising 1971Stochastic Models of Buying Behavior.

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