Knowledge that Transforms

1. Intrinsic tendencies towards contraction and expansion in an exchange system 261 2. The indebtedness factor in exchange contraction and expansion ....... 265 3. A simplified example of a planned exchange 272 4. The correction of the request-matrix by the principle of partaker's percentages 273 5. Generalized principles of correcting the request-matrix ..... ...... .. 282 6. The limitational condition for the total volume of operations ......... 286 7. A general differential method of adaptation for the minimum factors.. . 293 8. An analytic method of adaptation 302 9. A numerical example showing details of the computation .... ........ 306 10. Estimate of the amount of work involved when the number of variables is very great 320

THE relationship between a given pair of consumers' goods can assume various forms in an individual's scale of preferences. It is usual, however, to allot the pair of goods to one or other of two main classes, the classes of complementary and of competitive goods. A number of criteria or definitions of the distinction between complementary and competitive goods have been suggested, and of these the most precise, from the mathematical standpoint, are the simple criterion first put forward by Edgeworth and Pareto and the more complicated one given in a recent paper by the present author.' The object of these notes is to examine further both these definitions and, in particular, to discover what connection there is between them. The definition of complementary and competitive goods given by Edgeworth and Pareto assumes the existence of a total utility function which gives, for the individual under consideration, the utility of any combination (x, y, z, ) of the set of consumers' goods X, Y, Z, * , appearing in his scale of preferences. Denoting this function by u =4(x, y, z, ... ), the relation between any pair of goods X and Y de-