Optimum Advertising and Goodwill under Uncertainty

Abstract

This paper extends past studies of advertising based on goodwill to include the probabilistic effects of advertising and forgetting. A stochastic advertising model for a monopoly firm is constructed and resolved for specific forms of feedback advertising policy. Further, a diffusion-approximation model is also suggested. Using these models, we derive optimum advertising policies of the open-loop and feedback type. The essential implications of the paper are: (i) advertising is a “risky investment” in goodwill, substituting current certain expenditures for uncertain profits; (ii) risk-averse firms will advertise less and risk-taking firms more; (iii) large risk-aversion and forgetting rates both lead to the standard competitive result in advertising.