Fritz Machlup, “On the Meaning of the Marginal Product” (1937)

Machlup’s essay is a theoretical clarification of marginal productivity analysis. It does not deny the usefulness of the concept of marginal product; it argues that the concept becomes meaningful only when economists specify exactly what is being varied, how it is measured, and under what market and temporal assumptions the resulting product is valued.

It is with the meaning of the terms employed, especially with the units in which factor and product are expressed or measured, that we shall be concerned.

The first problem is the unit of the factor. A productive service is never merely a thing; it is a quantity of a service applied during some interval. Labor, land, and machinery therefore require units such as labor-hours, acre-seasons, or machine-days, and the appropriate unit depends on technical conditions, institutional arrangements, and divisibility. Machlup stresses that divisibility is not a simple physical fact. Some services can be hired in tiny time slices, while others are practically available only in large contractual blocks.

The divisibility with respect to time of highly qualified labor deviates particularly from that of the more common types of labor—inasmuch as certain qualified services may be bought by the minute at the one extreme, by five-year contracts only at the other.

This unit problem leads directly to heterogeneity. Marginal productivity presupposes comparable units, yet workers, plots of land, machines, and entrepreneurial services differ in quality, location, complementarity, and timing. “Efficiency units” can be useful, but they are dangerous when efficiency is inferred from the value of the product. A theory intended to explain factor prices cannot first define factor quantities by those prices without circularity. Machlup therefore treats many supposedly single factors as collections of distinct services unless there is a defensible independent basis for aggregation.

Product units create the next ambiguity. Physical marginal products are technically important, but they are not normally the relevant object in distribution theory. The decisive magnitude for a firm is not simply extra tons, yards, or bushels, nor even the market value of those units at an unchanged price. It is the expected change in the firm’s receipts, allowing for the market situation in which the added output is sold. A perfectly competitive seller may treat price as unaffected; a monopolist or imperfect competitor may not. Thus the “marginal product” relevant to factor demand is a value or money product framed by a definite competitive environment.

Time makes the concept still less mechanical. Inputs and outputs are not simultaneous, and products arriving at different dates cannot be added as if they were homogeneous physical units.

This third dimension is, then, the time interval between the application of any productive service, say a labor-hour, and the enjoyment of its product.

Consequently marginal products must be discounted, and uncertain products must be estimated. For the individual firm, Machlup insists, the schedule relevant to hiring decisions is an anticipated money schedule: the entrepreneur compares the money outlay on an additional factor unit with the expected money contribution, adjusted for time, risk, and the need for complementary inputs. At the level of an industry or the economy, one may construct real or money schedules, but each choice brings further assumptions about prices, monetary conditions, and the scope of adjustment.

The final clarification concerns the phrase “other things equal.” In many short-run situations an added unit of one factor produces nothing unless additional complementary services are also supplied. The relevant measure is then a marginal net product: the value attributable to the added factor after allowing for the extra complementary costs required to make it effective. Machlup’s conclusion is therefore not that marginal productivity is empty, but that it is conditional. A precise marginal product is an expected, dated, discounted, value or money net product of a specified unit of a specified service, calculated for a specified market situation and adjustment horizon.