diminishing returns

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 additional 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. It is possibly among the best-known economic "laws."

A simple example

Suppose that one kilogram (kg) 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.

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 1.333 to 1.71 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.

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, and at some point while the number of exchanges continues to exponentially increase, the usefulness of those exchanges may not(a third fax machine in the same room is not nessessarialy useful)( In this case time factors in. How long does it take to start and complete a fax? Eventually this will result in grid lock as the faxes stack up and connection attempts fail.)^[1]

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.

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 existing land 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).

See also

• Diseconomies of scale, does not assume fixed inputs, thus differing from 'diminishing returns'
• Diminishing marginal utility, also not to be mistaken for 'diminishing returns'
• Law of Accelerating Returns
• Opportunity cost
• Increasing returns
• Tendency of the rate of profit to fall

References

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

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