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Equilibrium Price Dispersion under Demand Uncertainty: The Roles of Costly Capacity and Market Structure

James D. Dana

1999
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The Rand Journal of Economics
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When capacity is costly and prices are set in advance, firms facing uncertain demand will sell output at multiple prices and limit the quantity available at each price. I show that the optimal price strategy of a monopolist and the unique pure-strategy Nash equilibria of oligopolists both exhibit intrafirm price dispersion. Moreover, as the market becomes more competitive, prices become more dispersed, a pattern documented in the airline industry. While generating similar predictions, the model
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... differs from the revenue management literature because it disregards market segmentation and fare restrictions that screen customers. of prices and quantity limits at each price, I show that there exists a unique purestrategy equilibrium in price distributions even when no pure-strategy equilibrium exists in prices (see Bryant, 1980) . In other words, the model predicts an equilibrium with intrafirm price dispersion in which each firm offers its output at multiple prices (as opposed to random prices). The oligopoly equilibrium is symmetric and the market price distribution converges to Prescott's competitive equilibrium as the number of firms approaches infinity. As competition increases, the average price level falls and the degree of price dispersion increases. This result arises for the same reasons that a monopolist typically does not raise its price by the entire amount of an increase in costs, while competitive firms pass through all of their cost increases. This inverse correlation between price dispersion and market concentration has been observed in the airline industry. In particular, Borenstein and Rose (1994) showed empirically that price dispersion is greater on city-pair routes that are served by a larger number of carriers. Borenstein and Rose attribute this result to price discrimination and argue that point using a monopolistic-competition model with certain demand. 2 However, their empirical results are also consistent with this article's theory that price dispersion is due to capacity costs (i.e., perishable assets) and demand uncertainty. 3 Furthermore, this model is consistent with other characteristics of the airline industry, characteristics that the price discrimination theory does not address. In particular, capacity utilization rates (load factors) are higher for airlines that charge lower fares. For example, in 1993 the major airlines whose yields (prices) were below average had an average load factor (capacity utilization) of 64.25% and a yield of 13.80 cents, while the major airlines whose yields were above average had an average load factor of 59.92% and a yield of 16.40 cents. 4 This is the natural prediction of a model with costly and perishable capacity, price rigidities, and demand uncertainty and is difficult to explain in models that do not have each of these assumptions. 5 Yield management, now commonly called revenue management, is the use of market segmentation and seat-inventory control (i.e., assigning limits on the availability of seats at each fare) to maximize firm revenues (or profits). Sophisticated revenue management systems are now used by airlines, hotels, car rental companies, commercial shippers, and increasingly in other industries to manage demand uncertainty and to ensure that their products and services are available even when demand is high. Because of customer segmenting restrictions (or "fencing") such as advanced-purchase discounts, Saturday-night stayover requirements, nonrefundable purchases, and volume discounts, revenue management is usually considered to be a form of third-degree price discrimination. However, in a model in which market segmentation and price discrimination are not feasible, I show that demand uncertainty and the perishable nature of the assets are alone sufficient to explain intrafirm price dispersion and may help explain 2 They consider a variant of Borenstein's (1985) model where consumers have heterogeneous "travel" (waiting) costs in a circle location model and product variety (departure times) is fixed while they vary the market structure. However, most models of oligopoly price discrimination, including Borenstein (1985) , Holmes (1989) , and Gale (1993), do not predict a positive correlation between price dispersion and market structure. 3 These two theoretical explanations are not inconsistent with one another. In fact, if the existence of price dispersion for other reasons facilitates airlines' use of discriminatory restrictions, then they may be complementary. 4 These calculations are based on data from Department of Transportation Form 441. Yield is defined as total operating revenue divided by the number of passenger miles flown by paying customers. Load factor is defined as the number of passenger miles flown by paying customers divided by the number of available seat miles. 5 An alternative explanation of this result is that airlines with greater market power (and hence higher prices) have excess capacity in order to deter entry.

doi:10.2307/2556068
fatcat:tq6ekt5yljfsvlf25rkuqfscyy