Welfare Analysis of Dynamic Pricing
Management Science, 2018
35 Pages Posted: 30 Dec 2015 Last revised: 12 Jul 2018
Date Written: January 1, 2016
Dynamic pricing is designed to increase revenues or profits of the firm by adjusting prices in response to changes in the marginal value of capacity as described in Gallego and van Ryzin (1994). While thousands of papers have been written about dynamic pricing, this is to our knowledge the first paper to examine the impact of dynamic pricing in Gallego and van Ryzin (1994) on social welfare and consumers' surplus. We present a dynamic pricing formulation designed to maximize welfare and show that the optimal policy has the same structural property as the revenue-maximizing dynamic pricing policy. For sufficiently constrained systems, we show that the revenue maximizing dynamic pricing policy and the market clearing price are both asymptotically optimal for welfare. We also find that in most cases dynamic pricing improves consumers' surplus compared to the optimal static price for a revenue-maximizing firm. Our findings can potentially change the public image of dynamic pricing, and lead to rich managerial insights as well as policy implications: (1) for large-scale systems with scarce capacity, the central planner and a monopoly firm would essentially implement the same pricing policy; (2) a revenue-maximizing dynamic pricing policy can benefit customers when the demand elasticity is in a small bounded interval as is the case for several important demand functions.
Keywords: Dynamic Pricing, Revenue Management, Consumers' Surplus, Social Welfare, Pareto Efficiency
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