Uncertainty, Capacity, and Market Share in Oligopoly: A Stochastic Theory of Product Quality

Abstract

The markets represented by the textbook definitions of monopoly, oligopoly, and monopolistic competition tend to merge into one another in real life. Customers (the demand side of the market) are constrained by technological requirements, or by the conviction that one supplier's product is superior to that of another, but only up to a certain point. They may, for several reasons, take their business elsewhere or even change their purchasing requirements permanently, even though the market structure for the product or component is not characterized as being competitive. Hotelling (1929), Stigler (1968), and others have discussed the role of nonprice factors in the decisions of firms and customers. More recently, De Vany (1976) has treated the role of service quality in a monopoly by defining the service offered by the firm to include the customer's cost of waiting for the product. Monopoly in this model is not absolute: a customer may cancel an order if, on arrival, he finds the expected delay too long. In the short run it makes no difference to the monopolist whether the cancelling customer has a substitute service or whether he leaves the market altogether. De Vany models the monopoly market as a The behavior of a duopoly is examined in terms of a stochastic model in which firms have three control parameters: price, capacity, and an estimate of quality. Customers choose a source firm and, if their estimate of delay at source is too large, they switch (jockey) to the alternate source. Arrivals and production are random. For a given set of control variables the model computes market shares. Given the form of the cost functions of the firms, one can compute the optimal values of the parameters in the short run and in the long run.