law of diminishing returns

law of diminishing returns

diminishing returns, law of, in economics, law stating that if one factor of production is increased while the others remain constant, the overall returns will relatively decrease after a certain point. Thus, for example, if more and more laborers are added to harvest a wheat field, at some point each additional laborer will add relatively less output than his predecessor did, simply because he has less and less of the fixed amount of land to work with. The principle, first thought to apply only to agriculture, was later accepted as an economic law underlying all productive enterprise. The point at which the law begins to operate is difficult to ascertain, as it varies with improved production technique and other factors. Anticipated by Anne Robert Jacques Turgot and implied by Thomas Malthus in his Essay on the Principle of Population (1798), the law first came under examination during the discussions in England on free trade and the corn laws. It is also called the law of decreasing returns and the law of variable proportions.

See W. J. Spillman and E. Lang, The Law of Diminishing Returns (1924).

In economics, diminishing returns is also called diminishing marginal returns or the law of diminishing returns. According to this relationship, in a production system with fixed and variable inputs (say factory size and labor), beyond some point, each additional unit of variable input yields less and less output. Conversely, producing one more unit of output costs more and more in variable inputs. This concept is also known as the law of increasing relative cost, or law of increasing opportunity cost. Although ostensibly a purely economic concept, diminishing marginal returns also implies a technological relationship. Diminishing marginal returns states that a firm's short run marginal cost curve will eventually increase.

History

The concept of diminishing returns can be traced back to the concerns of early economists such as Johann Heinrich von Thünen, Turgot, Thomas Malthus and David Ricardo.

Malthus and Ricardo, who lived in 19th century England, were worried that land, a factor of production in limited supply, would lead to diminishing returns. In order to increase output from agriculture, farmers would have to farm less fertile land or farm with more intensive production methods. In both cases, the returns from agriculture would diminish over time, causing Malthus and Ricardo to predict population would outstrip the capacity of land to produce, causing a Malthusian catastrophe. (Case & Fair, 1999: 790).

A simple example

Suppose that one kilogram of seed applied to a plot of land of a fixed size produces one ton of crop. You might expect that an additional kilogram of seed would produce an additional ton of output. However, if there are diminishing marginal returns, that additional kilogram will produce less than one additional ton of crop (on the same land, during the same growing season, and with nothing else but the amount of seeds planted changing). For example, the second kilogram of seed may only produce a half ton of extra output. Diminishing marginal returns also implies that a third kilogram of seed will produce an additional crop that is even less than a half ton of additional output. Assume that it is one quarter of a ton.

In economics, the term "marginal" is used to mean on the edge of productivity in a production system. The difference in the investment of seed in these three scenarios is one kilogram — "marginal investment in seed is one kilogram." And the difference in output, the crops, is one ton for the first kilogram of seeds, a half ton for the second kilogram, and one quarter of a ton for the third kilogram. Thus, the marginal physical product (MPP) of the seed will fall as the total amount of seed planted rises. In this example, the marginal product (or return) equals the extra amount of crop produced divided by the extra amount of seeds planted.

A consequence of diminishing marginal returns is that as total investment increases, the total return on investment as a proportion of the total investment (the average product or return) also decreases. The return from investing the first kilogram is 1 t/kg. The total return when 2 kg of seed are invested is 1.5/2 = 0.75 t/kg, while the total return when 3 kg are invested is 1.75/3 = 0.58 t/kg.

Another example is a factory that has a fixed stock of capital, or tools and machines, and a variable supply of labor. As the firm increases the number of workers, the total output of the firm grows but at an ever-decreasing rate. This is because after a certain point, the factory becomes overcrowded and workers begin to form lines to use the machines. The long-run solution to this problem is to increase the stock of capital, that is, to buy more machines and to build more factories.

Returns and costs

There is an inverse relationship between returns of inputs and the cost of production. Suppose that a kilogram of seed costs one dollar, and this price does not change; although there are other costs, assume they do not vary with the amount of output and are therefore fixed costs. One kilogram of seeds yields one ton of crop, so the first ton of the crop costs one extra dollar to produce. That is, for the first ton of output, the marginal cost (MC) of the output is $1 per ton. If there are no other changes, then if the second kilogram of seeds applied to land produces only half the output of the first, the MC equals $1 per half ton of output, or $2 per ton. Similarly, if the third kilogram produces only ¼ ton, then the MC equals $1 per quarter ton, or $4 per ton. Thus, diminishing marginal returns imply increasing marginal costs. This also implies rising average costs. In this numerical example, average cost rises from $1 for 1 ton to $2 for 1.5 tons to $3 for 1.75 tons, or approximately from 1 to 1.3 to 1.7 dollars per ton.

In this example, the marginal cost equals the extra amount of money spent on seed divided by the extra amount of crop produced, while average cost is the total amount of money spent on seeds divided by the total amount of crop produced.

Cost can also be measured in terms of opportunity cost. In this case the law also applies to societies; the opportunity cost of producing a single unit of a good generally increases as a society attempts to produce more of that good. This explains the bowed-out shape of the production possibilities frontier.

Returns to scale

Note that the marginal returns discussed in this article refer to cases when only one of many inputs is increased (for example, the quantity of seed increases, but the amount of land remains constant). If all inputs are increased in proportion, the result is generally constant or increased output. (Cf. Economies of scale.)

Statement: As a firm in the long-run increases the quantities of all factors employed, other things being equal, the output may raise initially at a more rapid rate than the rate of increase in inputs, then output may increase in the same proportion of the input, and ultimately, output increases less proportionately.

Universal law?

Diminishing returns says that the marginal physical product of an input will fall as the total amount of the input rises (holding all other inputs constant). A standard qualification is that diminishing returns applies after a possible initial increase in marginal returns. So, on its own terms, it is less than a universal law.

There is evidence for possible increasing marginal returns in certain circumstances. A single fax machine is useless and returns nothing, but if two exist, they can exchange messages, increasing the network by 2 exchanges. A third allows each machine to send messages to two points, increasing the network by 4 exchanges (3*2-2). A fourth allows three points of exchange, with a marginal return of 8 exchanges, and so on. This law remains to be proven mathematically.

It's important to note that the "law of diminishing returns" says that there would be a moment when, for example, an increasing number of faxes will not improve productivity nor efficiency. If your company has a fax machine, it's good enough, having 2, would not improve your performance. It would not sense everyone having a fax machine. There is a moment when the efficiency starts to decrease.

See also

References

Sources

  • Johns, Karl E. & Fair, Ray C. (1999). Principles of Economics (5th ed.). Prentice-Hall. ISBN 0-13-961905-4.

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