TRADITIONAL ECONOMIC ANALYSIS of the theory of the firm has concentrated on single-product firms. But, in reality, most businesses produce many products, and many regulatory and antitrust issues involve only these enterprises. In recent years, economists and policymakers dealing with antitrust and regulatory issues have increasingly recognized the need for a theory that can be used to evaluate the efficiency of market structures in industries dominated by a few firms operating in a diverse range of markets. For such firms, conventional concepts of structure and performance such as economies of scale, measures of concentration, and barriers to entry do not adequately capture the complexity of market relationships. A few examples illustrate the complexities introduced by the multi-product firm and highlight the need for a theory that can be used to evaluate performance and conduct in its markets. In many trucking and air city-pair markets, the efficient number of carriers appears to be relatively small (perhaps even one). Does this imply, however, that trucking firms and air carriers that compete in a wide range of city-pair markets should be regulated as natural monopolists or that mergers involving overlapping markets should be disallowed? In the petroleum industry, there is a current trend to diversify into other sources of fuel, and in cable TV markets there are numerous attempts to integrate vertically. What should economists look for in evaluating whether these changes in market structure are motivated by efficiency or by anticompetitive behavior? For a dominant firm, such as AT&T, there is a frequent complaint that the incumbent firm is preventing entry by cross-subsidizing one of its products, which faces competition by entrants, at the expense of other of its products. What kinds of regulatory intervention in pricing or in market structure must be considered

The economic gradient method is designed to provide guidance for the analysis and recommendation of change when information is available only over so narrow a range as to preclude a credible calculation of the global optimum. Using as data the gradients of the relevant functions evaluated at the current point of operation, the procedure calculates the direction of change from the status quo that yields the greatest feasible local rate of increase in the objective function of the decision maker. The calculation should be viewed as a benchmark because proposed movements of practical size must be assessed for feasibility. Under structural assumptions (standard for second-order conditions), the procedure can also be used to obtain an upper bound on the gain from effecting any particular (nonlocal) set of feasible changes in the decision variables. In Section I, we present the economic gradient method in a general form. We specialize the formulae in Section II to apply to pricing under a budget constraint with aggregate consumer welfare as the objective function.' Pilot empirical applications to U.S. Postal Service and long distance telephone rates are summarized in Sections III and IV.

This paper investigates the conditions under which a can find a set of prices and a set of products that are sustainable against competitive entry. By a natural monopoly we mean an industry whose cost function over some given set of products is such that no combination of several firms can produce an industry output vector as cheaply as it can be provided by a single supplier. A sustainable vector is a stationary equilibrium set of product quantities and prices which does not attract rivals into the industry. Even if a vector is not sustainable, a monopoly may still be able to protect itself from entry by changing its prices whenever and however necessary, in response to any entry that threatens at that moment. But, by definition, only a sustainable vector can prevent entry and yet remain stationary.

Investigates the conditions under which a 'natural monopoly' can find a set of prices and a set of products that are sustainable against competitive entry. Ramsey rule for Pareto optimal pricing under a budget constraint; Relation between subadditivity of costs and sustainability; Conditions sufficient for sustainable prices; Uncertainty of sustainability. (Из Ebsco)