We study multiproduct firms in the contexts of unregulated monopoly, regulated monopoly and Cournot oligopoly. Using the concept of consumer surplus as a function of quantities (rather than prices), we present simple formulas for optimal prices and show that Cournot equilibrium exists and corresponds to a Ramsey optimum. We then discuss a tractable class of preferences that involve a generalized form of homotheticity. Profit-maximizing quantities are proportional to efficient quantities. We discuss optimal monopoly regulation when the firm has private information about its cost vector, and find situations where optimal regulation leaves relative price decisions to the firm.

We study a multiproduct pricing problem in which the prices of the products are restricted to discrete and finite sets. The demand for a product is a function of the prices of all the products. The prices of the products can be changed through time, subject to the aggregate consumption of each resource not exceeding its availability over the planning horizon. The focus of our work is the deterministic variant of this problem (wherein customer-arrival rates are deterministic), which is a key subproblem whose solution can be used to build effective policies for the stochastic variant (as in Gallego and Van Ryzin 1997). When the demand rate of each product is a concave function of the prices, we obtain an efficient and effective solution to the deterministic problem; the worst-case optimality gap of our solution depends on the curvature of the objective function. We obtain a similar performance guarantee for our solution under the linear attraction demand model and a special case of the MNL demand model. For a general demand function, the worst-case optimality gap of our solution depends on the curvature of both the objective function and the demand function. For the special case where the demand rate of a product depends only on its own price and not on the prices of the other products, we show that the deterministic problem can be efficiently solved via a linear program.

Edgeworth's paradox of taxation occurs when an increase in the unit cost of a product causes a multiproduct monopolist to reduce prices. We give simple illustrations of the paradox, including how it can arise with uniform pricing. We then give a general analysis of the case of linear marginal cost and demand conditions, showing how the matrix of cost passthrough terms is similar to a positive definite matrix, and so has positive eigenvalues. When the firm supplies two substitute products we show how Edgeworth's paradox always occurs with a suitable choice of cost function. We then establish a connection between Ramsey pricing and the paradox in a form relating to consumer surplus, and use it to find further examples where consumer surplus increases with cost.

Excerpt from Price and Non-Price Determination in the Multiproduct Firm, 227-66 See T. E. Pfouts, The Theory of Cost and Production in the Multiproduct Firm, Econometrica XXIX (october pp. 650-658 for a non-linear formulation. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

This book provides the tools needed to analyse the present and the future of economic regulation.

In principle, a multiproduct firm can set separate prices for all possible bundled combinations of its products (i.e., "mixed bundling"). However, this is impractical for firms with more than a few products, because the number of prices increases exponentially with the number of products. In this study we show that simple pricing strategies are often nearly optimal -- i.e., with surprisingly few prices a firm can obtain 99% of the profit that would be earned by mixed bundling. Specifically, we show that bundle-size pricing -- setting prices that depend only on the size of bundle purchased -- tends to be more profitable than offering the individual products priced separately, and tends to closely approximate the profits from mixed bundling. These findings are based on an array of numerical experiments covering a broad range of demand and cost scenarios, as well as an empirical analysis of the pricing problem for an 8-product firm (a theater company).