Monopoly Price-Advertising Decision-Making Under Uncertainty

Abstract

THIS paper uses the Capital Asset Pricing Model (CAPM) to examine the joint price (quantity)-advertising decision for the monopolist under uncertainty. A generalized form of uncertainty is treated where the variability of sales volume (price) depends on the price (quantity)-advertising decision in a flexible manner. In contrast, previous models (Horowitz [6] and Dehez and Jacquemin [3]) assume that uncertainty is exogenous. The Dorfman-Steiner Theorem is generalized to the uncertainty case and the comparative statics properties of the model explored. Specifically, the results are shown to depend on: (a) the precise form in which uncertainty enters the random demand function; (b) the relationship between the risk-adjusted price (quantity) elasticity of demand and advertising, and (c) the covariance of the random cash flow with the random rate of return of the market portfolio. Unambiguous results are obtained in all cases for the additive and multiplicative uncertainty models. For the generalized uncertainty case, unambiguous results are obtained for exogenous shifts in demand. Determinate results are obtained for general changes in risk if the variance of sales volume (price) increases with price (sales volume).