A bstractUsing the trucking industry as an example, this paper extends the empirical research on multiproduct firms to analyze the efficient numbers of firms in the industry. The paper first considers the issue of size related economies and argues that although there are limited economies of scale, economies of scope appear to be sufficiently strong to explain the observed large number of mergers and acquisitions that have occurred in the industry. The paper then considers the efficient number of firms in the industry. Using the concept of ray-average cost, it shows that for the output combinations observed in the industry, the efficient number of firms required to serve industry output is quite large.

A multiproduct cost function for the regulated trucking industry is developed and estimated that utilizes network variables as arguments in the cost function. Using a cross-section of large regulated common carriers in 1976, it is shown that (1) substantial economies of network configuration and network operation exist, with well-connected networks and concentrated traffic flows yielding significant cost savings; and (2) the use of aggregate output measures and the omission of network variables may lead to substantial bias, indicating that researchers should use disaggregate output data in estimating trucking costs.

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

D ESPITE the rapid development of techniques of regional economic analysis during the past fifteen years, most regional models have continued to focus upon selected aspects of the regional economy rather than upon its totality. Economic base models and regional input-output models have concentrated upon the relationships between the output and employment in the export sectors and the local sectors;' comparative cost models have concentrated upon the response of the export sectors to changes in relative regional production costs;2 and regional econometric models have concentrated upon the determinants of employment in the export sectors and the relationships between regional economic activity and that of the nation.3 This disparate collection of partial-equilibrium models generally does not make it possible to determine the full general-equilibrium effects of a given economic change on the total regional economy. For example, although economic base/input-output models permit the estimation of the indirect and induced employment and output effects arising from a change in final demand or the level of activity in the export sector, they treat the level of activity in the export sector as exogenous and do not permit factor substitution. Similarly, although comparative cost models explicitly recognize that the location of export industries is largely determined by relative production costs, they do not consider the interrelationships among the industries within the export and local sectors or the role that factor substitution can play in regional employment levels. Finally, although regional econometric models generally use a neoclassical labor demand function, and hence explicitly consider factor substitution, they do not fully differentiate between the factor-substitution and production cost effects of a change in regional input prices. Furthermore, they do not account for the full set of linkages among the industries in the export and local sectors. The growing need for comprehensive regional models for planning and policy analysis suggests that there would be substantial value in having models that synthesize the relevant aspects of existing regional economic theory into a single integrated construct. Such an integrated model would be useful for both forecasting and policy evaluation and should include the following fea-. tures: First, it should recognize that factor substitution is possible and that an increase in the regional price of any given factor will tend to cause substitution in favor of other factors (the factorsubstitution effect); Second, it should recognize that an increase in any input price in a region relative to that in other regions will tend to increase production costs in the region in question. The result will be a reduction in the comparative locational advantage for the affected region and a tendency toward a relative shift in employment in national-market industries away from that region to lower-cost regions (the location effect); Third, it should be able to quantify the relative magnitudes of the factor-substitution effect and the location effect arising from any given change in regional input prices; Fourth, it should recognize that a complex set of interrelationships exists not only between the export sector and the local sector, but also among the various industries within each sector. Received for publication May 17, 1978. Revision accepted for publication December 7, 1978. * University of Massachusetts at Amherst, Massachusetts Institute of Technology, and Regional Science Research Institute, respectively. Work on this model has been supported by the Commonwealth of Massachusetts. The authors are grateful to Edward M. McNertney for contributions to the development and estimation of many of the equations and to Roy E. Williams for a mathematical and statistical review of the model and for programming the model. ' See, for example, Isard (1960), Tiebout (1962), Bourque et al. (1967), Miernyk (1970), and Polenske (1974). 2 See, for example, Weber (1928), Hoover (1937), Isard (1956) and Borts and Stein (1964). 3See, for example, Friedlaender et al. (1975), Adams et al. (1976), and Glickman (1977).