Dynamic Price Competition: Theory and Evidence from Airline Markets

Abstract

Mike Whinston, and several conference and seminar participants.NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

Organizational Structure and Pricing: Evidence from a Large U.S. Airline

“…In order to rationalize observed prices as "optimal," this requires making demand more elastic, decreasing markups (over opportunity costs), and understating consumer surplus (by a factor of four). 33 While relaxing capacity constraints is always beneficial in the dynamic programs we simulate-because the associated value functions are monotonic in capacity (Gallego and Van Ryzin, 1994;Betancourt et al, 2023)-this is not true given the pricing heuristic used by the firm. In particular, if the lowest fares on the menu are in fact on the inelastic side of demand (as we document in Section 4), then an increase in capacity could cause the heuristic to more often default to prices that are not revenue maximizing, reducing revenues.…”

“…Third, the dynamic program naturally "solves the coordination" problem that we identified where department inputs (and the use of the heuristic) can lead to pricing on the inelastic side of demand. By solving a dynamic program, prices are always on the elastic side of demand (Gallego and Van Ryzin, 1994;Betancourt et al, 2023).…”

“…Instead, we estimate a flexible demand model for air travel using a recently proposed methodology (Hortaçsu et al, 2023). We use these estimates to simulate demand and measure welfare in counterfactuals.…”

“…For routes with exactly two daily frequencies, we find that both flights have identical prices 60% of the time. In the case of substitute flights at other airlines, the pricing department may choose a similar fare menu to its competitors Betancourt et al (2023). document similar price matching in markets with competition.…”

“…In a dynamic pricing model with a single firm, opportunity costs are positive values as they are defined by the difference in continuation values if the firm had one fewer seat to offer, i.e., OC t = V t (C) − V t (C − 1). As shown inBetancourt et al (2023), the optimal price comes from maximizing Q t (p t )(p t − OC t ), which is solved via backward induction. Given a demand function that is continuously differentiable such that Q t (p t )(p t − OC t ) attains a max where p * ̸ = 0 or ∞ , then it follows from the resulting markup formula that e D (p * ) ≤ −1.…”