Compensation Act and the National Insurance Act has been, from the point of view of employers, to diminish the number of employable persons in the community. Such possible effects of legislation intended to be " beneficent" must not be overlooked. CHAPTER V THE DIVISION OF INCOME BETWEEN A NUMBER OF FACTORS OF PRODUCTION. §1. We have seen that the absolute and relative sizes of the aggregate income from civil rights and from private gifts are mainly determined by collective action, through legislation or otherwise, and by altruistic individual action. In neither case do economic forces in the ordinary sense, that is to say the pursuit by individuals of the economic interests of themselves and their families, play any large part. We may now go on to consider that division of the aggregate income of any community, which is produced by economic forces in this sense. We may begin by considering in an abstract form in this chapter the general case of the division of the income created by the joint action of a number of factors of production. What are the causes which determine the absolute and relative shares of the total product accruing to such factors? We shall then consider in the five following chapters certain particular cases, which are included in this general case. In this group of chapters it will be convenient to ignore the fact that part of the income accruing to factors of production may be transferred from one person to another in the form of income from private gifts and to ignore also, except where the contrary is stated, transfers brought about by means of taxation and public expenditure. We may assume, provisionally, that, in the ordinary type of the modern capitalist system, the payment of each factor of production tends to be equal to its marginal net product and that the marginal net product of any factor tends to be the same in all employments.1 In a stationary state, where the conditions of demand and supply always remained the same for all factors, the absolute and relative shares of all factors would always remain the same. The absolute share of any factor would be equal to the number of units of that factor in employment multiplied by the marginal net product of any unit. The relative share of any factor would be equal to the proportion of this absolute share to the total product. In reality, in a non-stationary state, changes take place in the various conditions of demand and supply, and hence in the absolute and relative shares of various factors. The changes in these shares depend upon two sets of causes. They depend, in the first place, upon the various elasticities of demand and supply, or in other words, on the shapes of the various demand and supply curves. And they depend, in the second place, upon the way in which a movement of any one of these curves causes movements of the other curves. §2. The effects upon the share of any factor of a small increase in its supply have been expressed by Professor Pigou in two general propositions. The first is that the absolute share of any factor increases or diminishes, as a result of a small increase in its supply, according as its 1 We may also notice an application of what mathematicians know as Euler's Theorem to the theory of distribution between factors. This application was first made by Mr. Wicksteed in his Essay on the Co-ordination of the Laws of Distribution, who pointed out that, if the product of a number of factors, expressed as a function of their amounts, is a homogeneous function of the first degree, then the payment of each factor according to its marginal net product exactly absorbs the product. Compare Flux, Economic Principles, PP. 314-5 and Edgeworth, Quarterly Journal of Economics, Vol. 18, p. 182. But what happens if, as is very much more probable, the product is not a function of this narrowly limited type? This is a fine point in the marginal productivity theory, which none of its exponents seem yet to have satisfactorily explained. a Wealth and Welfare, pp. 92-93 (footnote). elasticity of demand is greater or less than one; the second is that its relative share increases or diminishes in like circumstances, according as its elasticity of demand is greater or less than the reciprocal of the relative share, before the increase, of all other factors taken together.1 The significance of the second proposition can be made clearer by a numerical example. Consider the effect upon the relative share of capital of a small increase in its supply. Suppose that, before this increase, capital's relative share was one-third of the whole. Then the relative share of all other factors taken together must have been two-thirds of the whole. The reciprocal of two-thirds is three-halves, that is to say, one and a half. The relative share of capital will, therefore, increase or diminish, according as the elasticity of demand for capital is greater or less than one and a half. Combining the two propositions set out above, we see that the effect of a small increase in the supply of any 1 If x is the number of units product, its absolute share is xy. by dy, its elasticity of demand of the factor, and y its marginal net If, when x increases by dx, y decreases yox = and its absolute share becomes xdy (x+dx) (y− ôy), or xy+yồx − xồy, if dx and dy are small. Therefore its absolute share increases or diminishes according as yox > or < xdy, that is to say according as the elasticity of demand is greater or less The relative share of the factor is *(*), where f (x) is the than one. I f(x) This relative share increases, when x total product and f'(x) : = y. x x f'(x) xf" (x) that is to say if the elasticity of demand is greater than the reciprocal of the relative share of all other factors taken together. Professor Pigou, owing to a misprint, (ibid. p. 92 n.) equates e to of to 1'(x) xf" (x)" These two propositions both assume that, as a result of the increased supply, no change takes place in the demand curve of the factor in question. factor will be (1) to diminish both its absolute and relative shares, if its elasticity of demand is less than one, (2) to increase its absolute, but to diminish its relative, share, if its elasticity of demand is greater than one, but less than the reciprocal of the relative share of all other factors taken together, (3) to increase both its absolute and its relative shares, if its elasticity of demand is greater than the reciprocal of the relative share of all other factors taken together. And, further, the increase, if any, in its share, whether absolute or relative, will be greater, the greater the elasticity of demand. The effect of a small increase in the demand for any factor, on the other hand, will be to increase its absolute share, except in the very unlikely event of its elasticity of supply being negative and less than minus one.1 We may assume that, in practice, the elasticity of supply of any factor will be positive, or in a few cases zero.2 On this assumption the relative share of any factor will also always be increased by a small increase in demand.3 And further, the increase in its share, whether absolute or relative, will be greater, the greater the elasticity of supply. §3. It is only, however, when changes in supply are small that the preceding propositions hold good. If the 1 That is to say, that its supply contracts as its supply price increases, and that the proportionate contraction is greater than the propor tionate increase in price. The most plausible hypothesis of a negative elasticity of supply of any factor is that, in certain circumstances, the amount of saving might increase as the rate of interest fell. Compare Marshall, Principles, pp. 234-5. • The condition that a small increase in the supply of a factor may increase that factor's relative share, may be applied, mutatis mutandis. Here e, the elasticity of supply, will be equal to f'(x) and not to -L'(x) xf" (x) I The condition, therefore, becomes e > and xf'(x) I xf" (x) the right hand side of this inequality is obviously a negative quantity. |