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.