Bayesian Updating of the Price Elasticity of Uncertain Demand

Abstract

In the context of value creation in systems engineering, it is important to consider the contribution of each component of the system to the overall value. This consideration is particularly important for profit-maximizing firms, whose objective is to maximize the expected utility of profit. To determine the profit of each alternative, it is necessary to obtain an estimate of the demand for each design at a given price. Because uncertainty about the demand is always present, it is essential to incorporate this uncertainty into the profit and the design analysis. This paper provides a method for characterizing the uncertainty about demand as a function of its price. We characterize the demand distribution using a scaled Poisson process and show how to estimate demand. We illustrate the results using a numeric example applied to a regional engineering firm that designs small hybrid vehicles. Finally, we provide an approximate analytic solution for the optimal price of a product that offers the highest expected utility for the design firm. Our results indicate that the more risk-averse firm has a lower optimal price than the less risk-averse firm. We also calculate the expected value of perfect information on the demand at any price via Bayesian updating.