Supply and Demand

by Sir Hubert Douglas Henderson

Suppose a crossbred sheep yields 10 units of mutton and 8 units of wool.

Suppose, further, that a merino sheep and a crossbred sheep each cost the same sum, say, for convenience, £10, to rear and maintain; and that there are no special costs assignable to the wool and the mutton respectively, as, of course, in fact there are.

Then 10 merino sheep, yielding 90 units of mutton + 100 unitsof wool, cost £100; while 9 crossbred sheep, yielding 90 units of mutton + 72 units of wool, cost £90.

Hence you could obtain an extra 28 units of wool for an extra cost of £10, by maintaining 10 merino sheep rather than 9 crossbred sheep. The marginal cost of wool is thus £ 10/28 per unit.

Similarly 8 merino sheep, yielding 72 units of mutton + 80 units of wool, cost £80; while 10 crossbred sheep, yielding 100 units of mutton + 80 units of wool, cost £100.

Hence you could obtain an extra 28 units of mutton for an extra cost of £20, by maintaining 10 crossbred sheep in place of 8 merinos. The marginal cost of mutton is thus £ 20/28 per unit.

So long as the price obtainable for wool exceeds £ 10/28, and that obtainable for mutton does not exceed £ 20/28 per unit, it will pay to substitute merino for crossbred; and conversely. If the price of wool exceeds £ 10/28 and the price of mutton also exceeds £ 20/28, it will be profitable to expand the supply of both breeds, until as the result of the increased supply, one of the above conditions ceases to obtain. Conversely, if the prices of both products are less than the figures indicated, sheep farming of both kinds will be restricted. The resultant of the processes of expansion or restriction, and substitution, will be that, unless one of the breeds is eliminated, the prices of mutton and wool will equal their respective marginal costs. These marginal costs may, of course, alter as the process of substitution extends. For the relative cost of maintaining merinos and crossbreds will not be the same for every farmer. Here again it is the costs at the "margin of substitution" that matter.

§2. Marginal Utility under Joint Demand. On the side of demand there exist as a rule similar possibilities of variation. Some machinery, some labor, some materials of various kinds, are all indispensable in the production of any manufactured commodity. But the proportions in which these factors are combined together can be varied, and are frequently varied in practice as the result of the ceaseless pursuit of economy by business men. To produce pig-iron, you need both coal and iron ore; but, if coal becomes more costly, it is possible to economize its use. Machinery and labor must be used together, in some cases in proportions which are absolutely fixed. But there is in nearly every industry a debated question as to whether the introduction of some further labor-saving machine would be worth while, or some improved machine which would represent the substitution of more capital plus less labor for less capital plus more labor. A farmer can cultivate his land, to use a common expression, more intensively or less intensively; in other words, he can apply larger or smaller quantities of capital and labor (the proportion between which he can also vary) to the same amount of land. The problem is essentially the same as that of the substitution of the crossbred for the merino. We can take the various possible combinations of the factors of production, and contrast two cases in which different quantities of one factor are employed, together with equal quantities of the others. The extra product which will be yielded in the case in which the larger quantity of the varying factor is employed can then be regarded as the marginal product (or marginal utility) of the extra quantity of that factor; and we can say that the employment of this factor will be pushed forward to the point where this marginal product will be roughly equal to the price that must be paid for it. We can thus lay down the most important proposition that the relation between marginal utility and price holds good generally of the ultimate agents of production; that the rent of land, the wages of labor, and, we can even add, the profits of capital tend to equal their (derived) marginal utilities, or, as it is sometimes expressed, their marginal net products.

Whenever, therefore, the proportions in which two or more things are produced or used together can be varied, the relations of joint supply and joint demand are perfectly consistent with a specific marginal cost and marginal utility for each commodity.

§3. A contrast between Cotton and Cotton-seed, and Wool and Mutton. But it sometimes happens that such variations cannot be made. Thus, it has not been found possible (so far as I am aware) to alter the proportions in which cotton lint and cotton-seed are yielded by the cotton plant. Roughly speaking, you get about 2 pounds of cotton-seed for every 1 pound of cotton lint (or raw cotton), and though this proportion may vary somewhat from plantation to plantation, it is upon the knees of the gods, and not upon the will of the planter that the variation depends. We cannot, therefore, speak with accuracy of the separate marginal costs of raw cotton and cotton-seed. It is true that some plantations are so far distant from any seed-crushing mill that it is not worth while to sell the seed as a commercial product; and it might seem, therefore, as though we might regard the entire costs of cotton growing on such plantations as constituting the marginal costs of raw cotton. But planters, so situated, derive a considerable value from their cotton-seed by using it as fodder for their live stock or as a manure. You can, of course, argue that proper allowance is automatically made for this factor, as a deduction from the costs of raw cotton, when you add up the expenses of the plantation. In the same way you can deduct the price which a planter who sells his cotton-seed obtains for it, from the total costs of the plantation, and call the remainder the costs of the raw cotton. But this is really to reason in a circle. For in either case the magnitude of the deduction depends on the marginal utility of the cotton-seed. And the notion of the cost of anything becomes blurred and blunted if we so use it that it must be deduced from the utility of something else, which is not an agent in the production of the thing in question.