Bayesian updating on price elasticity of uncertain demand

One of the most important aspects in the job of a design engineer is to choose the design alternative with the highest expected utility for the firm. In a profit-maximizing setup, the expected utility at a given price is determined by the demand for the product at that price as well as the utility function over profit. This paper provides a mechanism for characterizing the uncertainty about demand as a function of its price. We characterize the demand distribution using a scaled Poisson process. We then show how to estimate demand by fitting its expectation and variance at a given price to the Poisson process. 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.