Congestion and the sale of pizzas : a theorem on home delivery

Abstract

Recently the pricing problem of a monopolist producing several different qualities of a product has received some attention in the literature. Mussa and Rosen (1978) studied the optimal product mix of a monopolist producing different qualities and facing consumers differentiated by their preference for quality, and Itoh (1983) analysed the welfare aspects of the problem. Gabszewicz and Thisse (1980), Shaked and Sutton (1982) and Gabszewicz et al (1986) have examined the relation of the degree of heterogeneity among consumers, and the number of firms characterising the market in equilibrium. In this literature, product quality is exogenous. By contrast, situations where product quality is endogenously determined by the number of consumers in the market has received less attention after the early work of Levy-Lambert (1968) and Marchand (1968) in the theory of general equilibrium and clubs. Congestion externality however is an important feature in a wide variety of industries. Since the quality of a service fast deteriorates with increase in number of customers relative to servicing capacity, almost all service industries, and product industries with a significant service component (e.g. retailing, restaurants, bars) are prone to congestion externality. Recently two papers by Chander and Leruth (1989) and Leruth (1993) have developed a model of product differentiation by congestion level in a market with heterogeneous consumers, and shown that with heterogeneous consumers, a monopolist finds it optimal to product differentiate through congestion levels. The present paper relates to the general issue of monopolist decision making under congestion and heterogeneous consumers, but examines a different problem. In some industries it is possible for the seller to offer a product with zero congestion by means of home delivery. Home delivery is then used as a way of reducing congestion in the selling place thus improving the quality of the product sold there and increasing its demand. At the same time it creates a second product with zero congestion and can mop up consumer surplus from the other, more congestion-conscious end of the market. Home delivery of pizzas, for example, is not only a product that saves consumers’ transport cost but also serves to deliver the product without the congestion at the eating place or the queue for takeaway.