THE EXISTENCE of increasing returns to scale in production poses a number of difficult problems. In general equilibrium theory the problems are obvious. Standard results on the competitive equilibrium guarantee that when an equilibrium exists it is contained in the core of an economy. When the competitive equilibrium fails to exist, as is likely under increasing returns, the core may provide a useful equilibrium concept of its own. However, very little is known about the existence of a core except under conditions of constant returns to scale. One of the objectives of the present paper is to demonstrate the existence of the core in a general economy in which certain types of increasing returns are present. The second objective of this paper concerns partial equilibrium analysis. When it is asserted that a particular industry is an increasing returns industry it is not at all obvious what is being said, particularly when the industry produces more than one output. One aspect of increasing returns is the property of scale economies, which exist if by multiplying all inputs by a factor A > 1 it is possible to increase all outputs by at least a factor of A. A more primitive concept of increasing returns behavior is the concept of subadditivity of a cost function (or superadditivity of the production possibility set). Presumably the properties of subadditivity and economies of scale are both assumed of a given industry when it is said to have increasing returns. One particular problem involving increasing returns which has generated much recent research is the question of sustainability or supportability of natural monopoly.2 For this problem the existence of a core is of great interest, but at present, a set of necessary and sufficient conditions for a core to exist in a completely general model is not known. This paper is an attempt to advance the theory of natural monopoly, and of increasing returns industries in general, by considering a more general model of equilibrium than has previously been used. Thus, the paper is both a very general model of an essentially partial equilibrium problem and a rather specialized model of general economic equilibrium. In the next section, the basic model will be developed and its interpretation for both general and partial equilibrium will be discussed in greater detail.

It may not be possible to be wholly objective, as Messrs. Stimson and Thompson (among others) assert (see [Stimson, D. H., R. P. Thompson. 1975. The importance of ‘Weltanschauung’ in Operations Research: The case of the school busing problem. Management Sci. 21 (10, June) 1123–1132.]). Nevertheless, one should be as objective as possible in OR, or any other science, and this carries with it the concomitant duty of accurate and adequate descriptions—including descriptions of work by others to the extent that it may be pertinent.

The papers which follow have been assembled from two sources: the ones by Dr. Branch and by Professors Eastman and Kortanek were submissions to Management Science; the others formed one part of a program organized by Ezra Glaser for the American Association for the Advancement of Science's 1969 meetings in Boston. As vice president for AAAS' statistics section, Mr. Glaser had organized an all-day session on “Statistics, Governments and the Analysis of Social Problems.”

Presidential address about the background leading to TIMS formation. Delivered before the first national meeting of the Institute of Management Sciences, Oct. 21–22, 1954. Parts of the address are omitted.

I. Introduction, 87. — II. The business firm as organization, 89. — III. Control and costs, 91. — IV. Standard costs, 94. — V. Agent behavior, 98. — VI. Multiple commodity production and multiple agents — horizontal case, 103. — VII. Multiple agents — vertical case, 105. — VIII. Conclusion, 109.

Abstract The article presents views of the author on accounting participation. To date this work has progressed almost entirely without participation from accountants. This lack of participation has, I think, been unfortunate. Accounting participation might have served to accelerate certain developments. It should not have taken so long to realize, as scholar Andrew Hagen notes that national-income measurement is best thought of as double-entry bookkeeping, a perception that at once made clear that the exact relationship between income and output. Moreover, the process of analysis has not been carried through to its ultimate conclusion. It is particularly deficient on the balance-sheet and especially the equity, side. In hands of economists it was only natural that emphasis should rest on income measurement. Only recently and imperfectly, has attention begun to be devoted to the balance sheet. To date, however, resolution to the equity accounts hits not been successfully carried out. It is difficult to believe that this balance sheet backwardness would have occurred if accountants had participated more systematically in these developments.