The Return

Another hand can bring more work from a field, a bench or a machine. What it adds depends on what is already there, and on what else is allowed to change. The first worker may have equipment standing idle; the next may help keep it running; a later arrival may have to wait for someone else to finish. The question of diminishing returns concerns this changing contribution at the edge of production. It brings the margin from the buyer's wants to the means by which those wants can be met. Its answer begins by distinguishing a larger use of one resource from a larger operation altogether. Adding labor to a fixed workshop and building another workshop are different experiments. So are working the same acre more intensively and bringing another acre into cultivation. To say what the next hand or acre yields, we must first say which experiment we have in mind.

Marshall states the agricultural tendency in terms of additional capital and labor applied to land whose extent is held fixed. With the arts of cultivation unchanged, further applications eventually add less produce than earlier ones. The qualifications belong to the argument from its beginning. A field may initially receive too little attention to reveal its powers; clearing weeds or organizing the work can make an additional expenditure unusually productive. Marshall therefore allows increasing returns in the early stages, and even irregular movements before the diminishing tendency asserts itself. The marginal return is the additional produce attributable to an additional application, compared with what would have been obtained without it. His extra hoeing may be the expenditure that only just pays, although harvesting still comes later. “Last” means last at the profitable margin, rather than last on the calendar. This way of reckoning makes the counterfactual explicit: what would the crop have been if that particular addition had not been made? The answer concerns an increment of output, not a physically separable heap of grain made by one person's hands.¹

A simple production function can display the distinction between a total, an average and a marginal return. Suppose, for illustration, that output Q equals the square root of the product of equipment services K and labor services L, all measured in fixed units. Hold equipment at sixteen. Output is then four times the square root of labor. At one unit of labor, total output is four and output per unit of labor is four; the marginal product, the derivative of output with respect to labor, is two. At four units of labor, total output is eight, average output per labor unit is two, and marginal product is one. Total production has risen even though both the average and the marginal return have fallen. The derivative describes a small change around the specified employment level, so its value of one at four units is not a claim that the fourth whole unit produced exactly one. These distinctions matter in ordinary descriptions of productivity. A falling contribution from the next small addition can coexist with a growing harvest, and the output divided among all the workers need not equal the output attributable to the next increment.²

Diminishing marginal product with one input fixed does not imply diminishing returns to scale. In the illustrative technology, doubling both equipment and labor doubles output: the square root of four times the original product is twice the original square root. The same technology therefore combines diminishing marginal returns to either input on its own with constant returns to a proportionate enlargement of both. A different technology can allow a larger operation to exploit specialization, indivisible equipment or improved organization. Marshall examines these economies separately, distinguishing those available within a business from those arising in the surrounding industry. An improvement in technique changes the productive possibilities again: it can raise output at a given combination of resources, without requiring that the old fixed-input comparison was mistaken. The question about the next worker at today's machines, the question about a larger factory, and the question about a better process are each legitimate. They require different things to be held still. No one of them, by itself, establishes that growth must end because every additional effort yields less.³

The physical return becomes a cost of output once the price of the additional input is specified. Suppose labor is the only variable input in our workshop, equipment remains fixed, and each additional unit of labor costs six. Where output rises smoothly with labor, marginal cost is the wage per labor unit divided by the marginal product of labor. At one unit of labor, an additional small unit of output requires approximately half a unit of labor, so its marginal cost is three. At four units, the marginal product has fallen to one and marginal cost has risen to six. The same movement can be read from either side: less additional output from another unit of labor means more additional labor for another unit of output. This is one route from diminishing product to the rising supply blade in The Scissors. It depends on the stated input prices and productive conditions. A change in the wage, another variable input or a different process changes the calculation. An industry able to add complete plants is also facing a different choice from this workshop using the equipment it already has.⁴

The producer must then ask whether the output gained is worth the input sacrificed. If the output price is six as well, and the workshop can sell what it makes at that unchanged price, the additional revenue from a unit of labor is six times its marginal product. In the illustrative model the interior profit maximum is at four units of labor, where that additional revenue equals the labor cost of six. With equipment fixed, the concavity of the production function makes this a maximum of revenue less variable cost; whether to operate at all still requires the comparison of avoidable commitments explained in The Method. The rule is a comparison of available changes under prices the firm takes as given. It does not identify a portion of the finished product that one factor created unaided, or establish the justice of the resulting claims. Labor's marginal contribution depends on the equipment with which it works, just as the equipment's contribution depends on labor. The production is joint; the margin asks what changes when one specified part is varied within it.⁵

The return closes the volume by bringing the two sides of its inquiry into relation. On the side of wants, an additional unit permits an additional use, whose importance depends on what the person already has and what else can be chosen. On the side of production, an additional unit requires resources, whose contribution depends on the other means available and the technique employed. The resemblance is a shared method of comparison, not an identity between human preferences and a physical technology. Each must be established on its own terms. Once they are brought together, the margin asks whether the next unit is worth what must be given up to obtain it. That question locates a stopping point under the conditions we have examined; it also invites a larger reckoning. What of the units already exchanged, each worth more to its buyer than the sacrifice needed to supply it? The gains within that space are the subject of The Surplus. Its opening figure, The Triangle, turns the last unit's equality into a view of the gains that came before.