EXPRESS: Single vs. Variable Pricing under Uncertainty with Limited Capacity

Abstract

This paper studies a firm's pricing strategies under joint uncertainty in costs and demand (market size), with potential capacity constraints. We organize four pricing strategies along a single dimension: the amount and type of realized information a firm commits its pricing rule to use, ranging from none, under single pricing , to both cost and demand , under the most flexible strategy; between these extremes, demand-based pricing conditions price on realized demand alone, and cost-based pricing conditions price on realized cost alone. We examine the implications of this informational flexibility for three stakeholders: the firm, consumers, and society. We note that, across all capacity levels, the firm’s profit is maximized by the most flexible pricing strategy, namely, pricing based on both cost and demand realizations. In contrast, the pricing strategy that maximizes consumer surplus and social welfare depends on the severity of the capacity constraint. Under tight capacity, demand-based pricing and pricing based on both cost and demand realizations dominate. However, when capacity is sufficiently large (i.e., an uncapacitated setting), cost-based pricing maximizes consumer surplus and social welfare. Interestingly, for intermediate capacity levels, single pricing might be the best option for both consumers and society, even though it commits the firm to using the least information. The above results are robust to both discrete and continuous demand distributions. We further show that when costs and demand are positively correlated, single pricing still might be socially optimal. Overall, the paper shows how the information a pricing rule commits to use interacts with capacity constraints to shape the profit and welfare effects of pricing flexibility, offering guidance on when each strategy is likely to be favorable for the stakeholders.