Mathematical Investigations in the Theory of Value and Prices

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1892 Excerpt: ...U and V as general functions of x and y see preface to this memoir has great attractions to the mathematician; but it seems less adapted to express the every day facts of economic life than of regarding, as Jevons did, the marginal utilities of apples as functions of x the quantity of apples simply. ' as follows. He is directed to alter this consumption combination by arranging bis quantities A and 13 of the two selected commodities (a) and (b) in all possible ways, but without changing the quantities C, D, etc. of other commodities. The marginal utility of each will vary not only in relation to its own quantity but also the quantity of the other commodity. Thus, g=F(A B, ) These may be regarded as derivatives with respect to A and B of where U, is the total utility to I of the consumption combination A, and Bt. In fig. 18 let the abscissa OX represent the quantities B, of (b) and the ordinates (OY) the quantities A, of (-). Any point P by its co-ordinates represents a possible combination of quantities A, and B, consumed by I. By varying point P all possible combinations of A, and B, are represented. At P erect a perpendicular to the plane of the page whose length shall represent the marginal utility of Aj for the combination, that is, the degree of utility of a small addition of A, (B, remaining the same). If P assumes all possible positions, the locus of the extremity of this perpendicular will be a surface. Again at P erect a different perpendicular for the marginal utility of B; its extremity will generate another surface. The first surface takes the place of a utility curve for (a), the second for (b). I These two surfaces may be regarded as the derivative surfaces! (with respect to the variation of A, and of BJ, from a primitive whose ord...