in the theory of value and prices.

15

We may call the perpendicular direction III d the “ maximumdirection.” It has the important property that its components III aand III /? are proportional to the marginal utilities of A and B.This follows from a theorem* of vector calculus or thus : III a andIII (3 are inversely proportional to OA, and OB,, that is directlyproportional to the prices of A and B and therefore proportional totheir marginal utilities.!

§ 15.

If (fig. 25) the separate curve systems of all individuals I, II, etc.are drawn, and the lines AB drawn in each case, they will be paral-lel. For the prices are Uniform among all individuals and OA andOB in each case are inversely as the prices.

Since the normals to these lines will also be parallel, this theoremmay be stated: The “ maximum■ directions ” of all are alike.

§ 16 <

These methods apply to the comparison of any two commoditiesand afford a means of graphically representing statistical relationsconnecting the demands for two articles so far as the variations inthe quantities of other articles can be eliminated.

The same principles apply to the production of two articles. Hidesand tallow are completing articles from a producer’s standpoint.Likewise coke and coal gas, mutton and wool, and in general anyarticle and its “ secondary product.”

On the other hand most articles are competing or substitutes froma producer’s point of view. The difficulty of producing cloth isgreatly increased if the same individual produces books. This isthe root of the principle of division of labor and leads to that im-portant contrast between production and consumption once beforealluded-to. This and other contrasts will be mentioned in Appen-dix II, § 8. Marshall and others are fond of using the expression“ fundamental symmetry of supply and demand.” This notion must•be supplemented by that of a “ fundamental asymmetry.” As socialorganization progresses each man (and each community or nation)tends to become producer of fewer things but consumer of moire.

* Gibbs, Vector Analysis, §§ 50-53.

f For by similar triangles: =

' ' 14 III 13 III /3 OA, pi