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The Multi-Product Firm

Published online by Cambridge University Press:  07 November 2014

J. C. Weldon
J. C. Weldon*
Affiliation:
McGill University
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Extract

It appears that very little has been written about the multi-product firm. What has been done is largely an extension of single-product theory to those multi-product firms which have their origin in related demands and related supplies. For example, the utilities of two or more products may be so interrelated as to produce a joint demand. In such event, if the products are linked in a technical sense, as, say, the pieces and pawns of a chess-set, then they will be marketed by a single firm, usually under a name inclusive of the component products. If there is no such technical link, still the products (e.g., knives and forks) are more likely to be produced by a single firm than are unrelated products. Again, regardless of demand, the production of one product by a firm may necessarily result in the production of other products. To take the classic example of joint supply, the production of wool entails the production of mutton.

Each of these cases presents special analytic difficulties, notably problems of cost imputation. Various writers have essayed solutions, some of which have found their way into text-books, and some of which (by no means a separate class) are still matters of controversy.

The present paper, however, is not concerned with the extension of single-product theory to multi-product situations. Rather, it is an effort to analyse those features of the multi-product firm which belong to it as such. In effect, this means that it concerns costs and receipts peculiar to the multi-product firm, other costs and receipts being considered as given. This approach serves to emphasize those factors which give rise to the multi-product firm and which limit its size. It must be remembered that all firms are potentially producers of all products. Single-product theory demonstrates why no single-product firm expands its production without limit, and shows on what grounds a choice of output is made. Multi-product theory is required to show why expansion by variation is also limited, and on what grounds a choice of output is made when there is no restriction of the number of products.

Type
Articles
Information
Canadian Journal of Economics and Political Science/Revue canadienne de economiques et science politique , Volume 14 , Issue 2 , May 1948 , pp. 176 - 190
Copyright
Copyright © Canadian Political Science Association 1948

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References

1 We can cite the following as being representative of the literature on the multi-product firm. Alfred Marshall (Principles of Economics, bk. v, chap. VI, 5th edition or later) discusses related demands and supplies. Professor G. J. Stigler (Theory of Price) devotes a section to multi-product costs and receipts, though as an extension of single-product theory. Dr. S. Carlson (A Study on the Pure Theory of Production) examines a highly artificial multi-product firm as a guide to the analysis of poly-periodic production. Dr. C. F. Roos (Dynamic Economics) makes a symbolic analysis of joint demand and loss-leaders. Professor R. D. G. Allen (Mathematical Analysis for Economists) refers briefly to the same problem. There is also interesting material to be found in the writings on railway rates and public utilities, e.g., Professor R. T. Bye's “Demand and Joint Supply in Relation to Public Utility Rates” (Quarterly Journal of Economics, Nov., 1929).

2 The definitions are paraphrases of those given by Professor R. Triffin. See Monopolistic Competition and General Equilibrium Theory, pp. 93-5.

3 It may be objected that we should write in our definition “discounted net revenue” or something of the kind instead of “net revenue,” in the manner of several recent articles. But since this refinement is ignored in the rest of the paper, we ignore it here. No doubt whatever corrections are required in this respect to single-product theory can be applied with little difficulty to what follows.

4 If entrepreneurial return is taken as a function of net revenue, there is ample evidence that the first derivative is not always positive (as it should be under our assumption). This is especially true when net revenue must be derived from frequency distributions, as when risk is considered.

5 Much of this is more appropriate to single-product theory. It is only mentioned here to avoid ambiguities.

6 In the event that the manager has no specialty, then this expression must include a term k A.

7 A word may be said to justify the use of such algebraic expressions as those given above. What the writer attempts to do is to use the simplest expressions that contain the facts at hand. Specialization loss, for example, must be a function of the rates of output of products in which the manager is not a specialist; further, it is almost certain to be a nearly linear function, at any rate for relevant ranges of output. The expression given, then, shows this information. It is true that any such expression says more than is wanted. But the alternative of using geometric figures is not wholly commendable. Thus, we frequently draw parabolas to express marginal costs, and say that it is legitimate because there is general understanding that we wish to convey only part of the idea of parabola. With a like understanding it is equally legitimate, and rather more succinct, to use similar algebraic expressions.

8 These values (A 0, B 0, C 0,.…) are frequently used as common denominators of the products in the text below. They are considered to be equivalent rates in relation to whatever cost is being analysed. It is not necessary to the argument that the definition in terms of managerial efficiency be retained.

9 The expression does not hold if any of the m values A, B, C, … is m times or more the corresponding value of A 0, B 0, C 0, … It can be assumed, however, that no manager handles such a multiple of his optimum output.

10 Common production co-ordination costs are evidently equal to the sum of all co-ordination costs less all “separate production” co-ordination costs.

11 If necessary, this can be done by definition.

12 Separate production of n products entails hiring n sets of workers. Under common production, any one set can replace the n sets if the output of each product is sufficiently low.

That is, as x approaches zero, divisibility savings approach a fraction of the worker costs implied by separate production.

13 If we consider common transportation costs as a multi-valued function of the aggregate of separate transportation costs, this is equivalent to saying that the elasticity of this function is everywhere greater than unity. This is certainly true when output is generally high, and is likely to be true at all outputs.

14 These conclusions may be contrasted with those of single-product theory. There it is found that the task of selecting an absolute maximum is easier for the competitive firm than for the monopoly. Since the multi-product firm is the typical firm, our argument suggests that this conclusion is reversed in the real world.

15 Professor Keirstead points out that a certain razor-blade company operated in just this way a few years ago: it gave away razors in order to create a demand for blades. One may also mention the newspaper publisher, who sells papers below cost in order to increase advertising revenue. His position is peculiar in that he is required to charge something for his first product in order to sell his second.

16 We shall assume that the products are independent.