Technical Note—Optimizing Risk-Balancing Return Under Discrete Choice Models

We examine a firm’s pricing decision when managing a broad product line with the goal of optimally balancing the expected return on product investment with the revenue or profit risk associated with uncertain customer choices. We consider the multinomial logit (MNL) model and the mean-variance objective function and illustrate how the level of risk tolerance influences the firm’s optimal markups. We show that the solution approach and results generalize to the nested logit (NL) choice model and alternative risk-adjusted objectives. This paper is the first in the literature addressing risk-sensitive pricing under discrete choice models. Our analysis presents how the firm’s optimal pricing decision evolves with increasing risk sensitivity. The optimal risk-balancing solution stands in contrast to the profit-maximizing solution: for example, (i) the firm’s distaste for risk not only causes the firm to discount its products in exchange for lower profit volatility but also reduces the firm’s incentive to price differentiate among the products; (ii) although risk drives the firm to attain a higher total market share through lower prices at the cost of lower profit, certain products may gain, whereas others may lose in market share; and (iii) the optimal risk-balancing markups follow the sequence of product quality, whereas the optimal adjusted markups (i.e., markups adjusted for product-specific price sensitivity) follow the reverse sequence of quality.