Front Page Titles (by Subject) Joint Production. - The Theory of Political Economy
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Joint Production. - William Stanley Jevons, The Theory of Political Economy 
The Theory of Political Economy (London: Macmillan, 1888) 3rd ed.
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In one of the most interesting chapters of his Principles of Political Economy, Book III., chap. xvi., John Stuart Mill has treated of what he calls "Some peculiar Cases of Value." Under this title he refers to those commodities which are not produced by separate processes, but are the concurrent or joint results of the same operations. "It sometimes happens," he says, "that two different commodities have what may be termed a joint cost of production. They are both products of the same operation, or set of operations, and the outlay is incurred for the sake of both together, not part for one and part for the other. The same outlay would have to be incurred for either of the two, if the other were not wanted or used at all. There are not a few instances of commodities thus associated in their production. For example, coke and coal-gas are both produced from the same material, and by the same operation. In a more partial sense, mutton and wool are an example; beef, hides, and tallow; calves and dairy produce; chickens and eggs. Cost of production can have nothing to do with deciding the values of the associated commodities relatively to each other. It only decides their joint value.... A principle is wanting to apportion the expenses of production between the two." He goes on to explain that, since the cost of production principle fails us, we must revert to a law of value anterior to cost of production, and more fundamental, namely, the law of supply and demand.
On some other occasion I may perhaps more fully point out the fallacy involved in Mill's idea that he is reverting to an anterior law of value, the law of supply and demand, the fact being that in introducing the cost of production principle, he had never quitted the laws of supply and demand at all. The cost of production is only one circumstance which governs supply, and thus indirectly influences values.
Again, I shall point out that these cases of joint production, far from being "some peculiar cases," form the general rule, to which it is difficult to point out any clear or important exceptions. All the great staple commodities at any rate are produced jointly with minor commodities. In the case of corn, for instance, there are the straw, the chaff, the bran, and the different qualities of flour or meal, which are products of the same operations. In the case of cotton, there are the seed, the oil, the cotton waste, the refuse, in addition to the cotton itself. When beer is brewed the grains regularly return a certain price. Trees felled for timber yield not only the timber, but the loppings, the bark, the outside cuts, the chips, etc. No doubt the secondary products are often nearly valueless, as in the case of cinders, slag from blast furnaces, etc. But even these cases go to show all the more impressively that it is not cost of production which rules values, but the demand and supply of the products.
The great importance of these cases of joint production renders it necessary for us to consider how they can be brought under our theory. Let us suppose that there are two commodities, X and Y, yielded by one same operation, which always produces them in the same ratio, say of m of X to n of Y. It might seem at first sight as if this ratio would correspond to the ratio of the degrees of productiveness, as shown a few pages above, that we might say
and thus arrive at the conclusion that things jointly produced would always exchange in the ratio of productiveness. But this would be entirely false, because that equation can only be established when there is freedom of producing one or the other, at each application of a new increment of labour. It is the freedom of varying the quantities of each that allows of the produce being accommodated to the need of it, so that the ratio of the degrees of utility, of the degrees of productiveness, and of the quantities exchanged are brought to equality. But in cases of joint production there is no such freedom; the one substance cannot be made without making a certain fixed proportion of the other, which may have little or no utility.
It will easily be seen, however, that such cases are brought under our theory by simply aggregating together the utilities of the increments of the joint products. If dx cannot be produced without dy, these being the products of the same increment of labour, dl, then the ratio of produce to labour cannot be written otherwise than as
It is impossible to divide up the labour and say that so much is expended on producing X, and so much on Y. But we must estimate separately the utilities of dx and dy, by multiplying by their degrees of utility and and we then have the aggregate ratio of utility to labour as
It is plain that we have no equation arising out of these conditions of production, so that the ratio of exchange of X and Y will be governed only by the degrees of utility. But if we compare X and Y with a third commodity Z, as regards its production, we shall arrive at the equation
In other words, the increment of utility obtained by applying an increment of labour to the production of Z, must equal the sum of the increments of utility which would be obtained if the same increment of labour were applied to the joint production of X and Y. It is evident that the above equation taken alone gives us no information as to the ratios existing between the quantities dx,dy, and dz. Before we can obtain any ratios of exchange we must have the further equation between the degrees of utility of X and Y, namely,
As a general rule, however, any two processes of production will both yield joint products, so that the equation of productiveness will take the form of a sum of increments of utility on both sides, which we may thus write briefly—
Such an equation becomes then a kind of equation of condition of which the influence may be very slight regarding the ratio of exchange of any two of the commodities concerned. And if in some cases the terms on one side of such an equation are reduced to one or two, it is probably because the other increments of produce are nearly or quite devoid of utility. As in the cases of cinders, chips, sawdust, spent dyes, potato stalks, chaff, etc. etc., almost every process of industry yields refuse results, of which the utility is zero or nearly so. To solve the subject fully, however, we should have to admit negative utilities, as elsewhere explained, so that the increment of utility from any increment dl of labour would really take the form
du1 ± du2 ± du3 ±...
The waste products of a chemical works, for instance, will sometimes have a low value; at other times it will be difficult to get rid of them without fouling the rivers and injuring the neighbouring estates; in this case they are discommodities and take the negative sign in the equations.