The law of diminishing returns

Definition FACT

A one-hectare plot receives a first worker, then a second, then a tenth. The first additions achieve a great deal: work is divided, tasks become specialized, and the harvest grows rapidly. Beyond a certain number, each additional worker adds less than the previous one. This is not because the worker performs poorly: it is because the same plot must be shared with more and more people.

The law of diminishing returns is the standard hypothesis that, with technology unchanged and the other factors of production held fixed, the additional output obtained by adding one unit of the variable input eventually decreases as that input increases. It describes many technologies in the short run, but it is not a universal theorem.

Four qualifications are contained in this statement, and each is regularly overlooked.

• The law concerns additional output—the marginal product—not total output. Total output continues to grow as long as marginal product remains positive, even when the latter is declining.
• It says “eventually.” Nothing prevents marginal product from rising at first; the hypothesis states that after a certain threshold, marginal product decreases as the input increases.
• It requires the other inputs to remain fixed. Without this control, one is no longer measuring the marginal product of the input under study; varying all inputs together is a different question, namely that of returns to scale.
• It assumes unchanged technology. It describes the behavior of a given production function and never compares two different techniques.

Reading a production table FACT

Consider a one-hectare plot—the fixed input—to which identical workers, the sole variable input, are added. Total product $Q$Q is the harvest in quintals; marginal product $\mathrm{Pm}$Pm is the difference in the harvest attributable to the last worker; average product $\mathrm{PM} = Q/L$PM=Q/L is the harvest divided by the number of workers.

Three phases can be read in this marginal-product column, and they must not be confused.

• Up to the third worker, marginal product increases (10, then 14, then 15). The phase of diminishing marginal returns has not yet begun in this table.
• From the fourth to the seventh, it decreases (13, 10, 7, 4) while remaining positive: these are diminishing returns in the strict sense. Notice that the total harvest continues to rise—from 39 to 73 quintals. A decline in marginal product does not mean a decline in output.
• At the eighth, marginal product becomes negative: the total harvest falls from 73 to 72. This phase is distinct from the previous one; the law does not assert it. It says that marginal product decreases, not that it falls below zero.

The maximum total product, here 73 quintals, is reached with the last worker whose marginal product remains positive—the seventh, whose contribution is still 4 quintals. Indeed, the total can only decline once a negative quantity is added to it.

Marginal product and average product FACT

The table shows a regularity that is not specifically economic: it is true of every average.

As long as marginal product exceeds average product, it pulls the average upward. As soon as it falls below, it pulls the average downward. Average product therefore stops rising where marginal product meets and then crosses it: here, the maximum value 13,0 is reached with the third and fourth workers, and it is at the fourth that $\mathrm{Pm} = \mathrm{PM} = 13$Pm=PM=13.

This is the familiar property of every average: a grade above the current average raises that average, a grade below lowers it, and a grade equal to it leaves it unchanged. Nothing more is invoked here.

Two caveats accompany this reading. The exact coincidence between the crossing and the maximum is a result of differential calculus—the derivative of $Q/L$Q/L vanishes precisely when $\mathrm{Pm} = \mathrm{PM}$Pm=PM—and holds only approximately in a table of integers, where the maximum may extend across a plateau, as it does here. Moreover, the equality of the two quantities at the first worker ($\mathrm{Pm} = \mathrm{PM} = 10$Pm=PM=10) is an identity with no significance: with only one worker, the average product is the marginal product.

This distinction has a practical consequence. Average product can remain unchanged even though the law of diminishing returns already applies: between the third and fourth workers, marginal product fell from 15 to 13, while average product held at 13,0. Observing stable average productivity therefore does not prove that returns are not diminishing.

From marginal product to marginal cost FACT

This is where the law connects with price formation. Suppose labor is the only variable input, paid the same wage $w$w regardless of the number of workers hired—the employer takes the market wage as given—and treat labor as divisible, an approximation that permits continuous notation where the table counts only whole workers.

Obtaining one additional unit of output then requires $1/\mathrm{Pm}$1/Pm of an additional worker; it therefore costs

$\mathrm{Cm} = \frac{w}{\mathrm{Pm}}$Cm=Pmw​

where $\mathrm{Cm}$Cm is marginal cost, that is, the cost of one additional unit near the point considered. Under these assumptions and as long as $\mathrm{Pm}>0$Pm>0, marginal cost varies inversely with marginal product, up to the factor $w$w: when one decreases, the other increases.

With a wage of 100 € per worker:

In this example, marginal cost traces a U-shaped curve because marginal product first rises, reaches a maximum, and then falls. The law explains the rise in marginal cost when positive marginal product declines; it does not require a preceding downward phase. From the fourth worker onward in this table, each additional unit becomes increasingly costly to produce, without any rise in wages: the increase in cost comes from the decline in marginal product.

This leads to the connection with the supply curve. A producer who takes the market price as given will agree to supply one more unit only if that price covers what the unit costs; because this cost rises with quantity during the phase of diminishing returns, a higher price is needed to obtain a larger quantity. In this short-run model, the decline in marginal product causes marginal cost to rise and therefore, for a price-taking firm, causes the relevant portion of its supply curve to slope upward.

Three caveats delimit this conclusion. The reasoning assumes a price-taking producer. Under imperfect competition—notably for a monopoly—there is generally no supply curve independent of demand, because price and quantity are chosen jointly. For a perfectly competitive firm, only the portion of marginal cost above the minimum of average variable cost constitutes its short-run supply curve. At the market level, the slope of supply also depends on differences in costs among producers, which this reasoning ignores.

Do not confuse it with returns to scale FACT

The objection arises naturally: suppose a factory doubles both its machines and its workers, and its output also doubles. Would the law be false? No—the question being asked is not the same.

The two concepts are therefore not equivalent and can readily occur together within the same technology. Consider the production function $Q = L^{1/2}K^{1/2}$Q=L1/2K1/2, where $K$K denotes capital. Multiplying both inputs by $t$t gives

$(tL)^{1/2}(tK)^{1/2} = t\,L^{1/2}K^{1/2} = tQ$(tL)1/2(tK)1/2=tL1/2K1/2=tQ

which is exactly constant returns to scale: doubling everything doubles output. Yet, with capital $\bar K$Kˉ fixed, the marginal product of labor $\partial Q/\partial L = \tfrac{1}{2}L^{-1/2}\bar K^{1/2}$∂Q/∂L=21​L−1/2Kˉ1/2 decreases strictly with $L$L, starting with the very first unit.

What the example establishes is precise and sufficient to refute the objection: constant returns to scale in no way preclude diminishing marginal product when one input is held fixed. It does not prove that all technologies with constant returns to scale have this property; for example, $Q=L+K$Q=L+K also has constant returns to scale, but a marginal product of labor equal to 1.

In a differentiable formulation, the hypothesis states that there is a threshold $L^{*}$L∗ from which point onward $\partial^{2} Q/\partial L^{2} < 0$∂2Q/∂L2<0, with the quantity of the other inputs held fixed. In a table of integers, this corresponds to marginal differences that decrease beyond the threshold. It is a property of the production function with fixed inputs, not of its behavior when all inputs change together.

The status of the law FACT

Despite its name, the law is not a theorem deduced from axioms: it is a short-run production hypothesis whose validity depends on the technology under study. Bounded output merely rules out marginal product remaining indefinitely above a positive threshold; it is not enough to demonstrate a monotonic decline beyond a certain point.

The threshold $L^{*}$L∗ therefore cannot be deduced from a general principle: it is measured or estimated for a given technology and operating range. In the table constructed here, the decline begins with the fourth worker; a different organization, a different stock of fixed capital, or an innovation could shift, preserve, or eliminate this threshold within the observed range.

What the law assumes—and what it does not say FACT

• The other inputs remain fixed during the marginal variation. This is the necessary condition for attributing the measured change in output to the input under study. More generally, the short run is defined as the horizon over which at least one input cannot be adjusted; the marginal experiment described here nevertheless holds all inputs other than the one being varied constant.
• Technology does not change. An innovation changes the production function to which the hypothesis applies. A harvest that grows from one generation to the next is therefore not enough to refute the law, because the two observations may not concern the same function.
• The units of the variable input are homogeneous. If the workers added are progressively less skilled, this heterogeneity may alter marginal product and blur the measurement. Observation alone then does not isolate the effect of the fixed inputs. The law assumes interchangeable units so that, within the model, the variation can be attributed to the productive combination rather than to a change in the quality of the variable input.
• Inputs are used efficiently. The table compares points at which the maximum possible output is obtained from each combination. A decline caused by poor organization does not fall under the law.

Finally, it says nothing about the desirable level. Determining how far to increase the variable input requires comparing what the additional unit yields with what it costs—and therefore requires prices, which are absent from the statement. Diminishing returns describe a technology; they prescribe no quantity.

Summary

With technology unchanged, increasing one input while the others remain fixed often ultimately reduces its marginal product; if it is the only variable input, paid at a constant price, and as long as its marginal product remains positive, this decline raises marginal cost.

Main references FACT

• OpenStax — Production in the Short Run
• OpenStax — Costs in the Long Run
• OpenStax — Marginal Cost and the Firm's Supply Curve
• MIT OpenCourseWare — Production and Cost