supply of any factor increases by a moderate amount, and we assume that its conditions of demand are unchanged, the minimum elasticity of demand which will ensure an increase in its absolute share is not one, as in the case of a small increase, but one plus the proportionate increase in its amount.' Thus if the proportionate increase in the supply of the factor is twenty per cent., or one fifth, the minimum elasticity of demand that will ensure an increase in the absolute share of the factor will be one and a fifth. Similarly, the minimum elasticity of demand which will ensure an increase in its relative share is not the reciprocal of the relative share, before the increase, of all other factors taken together, but another quantity, for which no very simple verbal expression can be found.2

As regards changes in the demand for any factor, there is no need to distinguish between moderate and

As in the case of a small increase, the absolute share increases from xy to (x + dx) (y – dy). But, when the increase is of moderate size, the product of dx and dy cannot be neglected. The condition that a moderate increase in supply shall lead to an increased absolute share is, therefore, y d x xdy - dy dxo, or, since e, the elas

and Welfare, p. 92) argues as though the formula appropriate to a supply of a factor was equally appropriate to But this is not so. Compare the Note at the

small increase in the

a moderate increase. end of this chapter.

The condition that the relative share should increase is

small changes. Assuming that the elasticity of supply is not negative, the effect of an increase of demand, whether moderate or small, will be to increase both the absolute and relative shares of the factor, and, the amount of the increase in demand being given, to increase these shares the more, the greater the elasticity of supply.

§4. It remains to consider the nature of the movements liable to be set up in any of the other curves of demand and supply by an originating movement in any one of them.

A factor A may be said to be complementary to another factor B, if an increased supply of A causes an increased demand for B, or, more precisely, if a downward movement of the supply curve of A causes an upward movement of the demand curve of B. Similarly A may be said to be rival to B, if an increased supply of A causes a decreased demand for B, i.e., if a downward movement of the supply curve of A causes a downward movement of the demand curve of B.1

Since an increase in the supply of any factor, other things being equal, must increase the total product, and hence the total demand for all factors taken together, it follows that every factor must be complementary to all factors taken together, including itself, though it may be

1 If A is complementary (or rival) to B in this sense, it may generally be assumed that B is likewise complementary (or rival) to A. But, where the elasticity of supply of either A or B is zero, the relation obviously cannot be bilateral. Again, if A and B are complementary (or rival) in this sense, they will probably also be complementary (or rival) in the sense that an increased demand for A causes an increased (or decreased) demand for B. For the effects of a downward movement of the supply curve of A and of an upward movement of the demand curve of A are to this extent the same that, other things being equal, an increased quantity of A is employed. But, whereas an increased supply of A necessarily involves, other things being equal, an increased total product, an increased demand for A may involve only a change in taste or fashion, and no increase in total product. Generally speaking, every factor will be complementary to itself, an increased supply of it causing an increased demand for it.

rival to particular factors taken separately."

An elaborate mathematical treatment of changes in the demand and supply of a group of factors, some pairs of which were complementary and others rival, would, perhaps, yield new and interesting results. No such treatment, however, will be attempted here. It must suffice to point out that the situation of any factor is likely to be improved, both absolutely and relatively, by an increased supply of complementary, and a decreased supply of rival, factors.

§6. In order to apply to practice the abstract argument of this chapter, it is necessary to have some knowledge of the elasticities of demand and supply of different factors, and the extent to which the latter are complementary or rival to one another. But it should be noticed that the question of the magnitude of various elasticities and the question whether various factors are complementary or rival to one another, though it is possible to discuss them separately, are logically interdependent. For the elasticity of demand for one factor is affected by the elasticity of supply of another, and affected differently according as the two factors are complementary or rival.

If A is complementary to B, then, other things being equal, the greater the elasticity of supply of A, the greater is the elasticity of demand for B; but, if A is rival to B, the greater the elasticity of supply of A, the smaller the elasticity of demand for B.

* Compare Marshall (Principles, p. 665). " The various agents of production on the one hand are often rivals for employment; any one that is more efficient than another in proportion to its cost tending to be substituted for it, and thus limiting the demand price for the other. And on the other hand they all constitute the field of employment for each other; there is no field of employment for any one, except in so far as it is provided by the others; the national dividend which is the joint product of all, and which increases with the supply of each one of them, is also the sole source of demand for each of them."

NOTE ON THE CONCEPTION OF ELASTICITY OF DEMAND

AND SUPPLY.

§1. The statements of modern economists regarding elasticities of demand or supply sometimes contain an ambiguity, which it is the purpose of this Note to examine. This ambiguity is liable to arise, whenever it is attempted to apply the methods of the differential calculus to problems of demand or supply. In Marshall's Principles, elasticity of demand is defined as follows (p. 102): “We may say generally: the elasticity of demand in a market is great or small according as the amount demanded increases much or little for a given fall in price." This conception is then developed in a footnote, with the aid of a diagram, as follows: Speaking more exactly we may say that the elasticity of demand is one, if a fall of one per cent. in price will make an increase of one per cent. in the amount demanded; that it is two or a half, if a fall of one per cent. in price makes an increase of two or one-half per cent. respectively in the amount demanded. The elasticity of demand can be best traced in the demand curve with the aid of the following rule :

Let a straight line touching the curve at any point P meet Ox in T and Oy in t, then the measure of the elasticity at the point P is the ratio of PT to Pt. If PT were twice Pt, a fall of one per cent. in price would cause an increase of two per cent. in the amount demanded; the elasticity of demand would be two. If PT were one-third of Pt, a fall of one per cent. in price would cause an increase of one-third per cent. in the amount demanded; the elasticity of demand would be one-third; and so on." But to this account it may be objected that elasticity at a point on a curve can tell us nothing of the elasticity corresponding to fnite changes in price. In order to know the size of the elasticity in this latter sense, we need to know not merely the position of the tangent at P and the ratio of PT to Pt, but also the position of neighbouring points on the curve DD'. Hence Marshall's statement that, "if PT were twice Pt, a fall of one per cent. in price would cause an increase of two per cent. in the amount demanded," is not necessarily true, though it may often be a close approximation to the truth. Elasticity at a point, a conception derived from the differential calculus, is only the elasticity corresponding to infinitesimal changes in demand price and amount demanded.

§2. The distinction, on which I have here insisted, is between elasticity at a point and elasticity across a finite arc, or, as we may say more shortly, between point elasticity and arc elasticity. It may be thought that, in the practical application of the conception of elasticity, this distinction is trivial and that no important ambiguity can arise from it. It appears to me that this is not the case.

Referring again to Marshall's Principles (p. 839) we read, "if the elasticity of demand be equal to unity for all prices of the commodity, any fall in price will cause a proportionate increase in the amount bought, and therefore will make no change in the total outlay which