Diminishing returns

In economics, diminishing returns (also called lawof diminishing returns,[1][2] law of variable pro-portions,[3] principle of diminishing marginal pro-ductivity,[2] or diminishing marginal returns[4]) isthe decrease in the marginal (incremental) output of aproduction process as the amount of a single factor ofproduction is incrementally increased, while the amountsof all other factors of production stay constant.The law of diminishing returns states that in all produc-tive processes, adding more of one factor of production,while holding all others constant ("ceteris paribus"), willat some point yield lower incremental per-unit returns.[5]The law of diminishing returns does not imply that addingmore of a factor will decrease the total production, a con-dition known as negative returns, though in fact this iscommon.For example, the use of fertilizer improves crop produc-tion on farms and in gardens; but at some point, addingincreasingly more fertilizer improves the yield by less perunit of fertilizer, and excessive quantities can even reducethe yield. A common sort of example is adding moreworkers to a job, such as assembling a car on a factoryfloor. At some point, adding more workers causes prob-lems such as workers getting in each other’s way or fre-quently finding themselves waiting for access to a part. Inall of these processes, producing one more unit of outputper unit of time will eventually cost increasingly more,due to inputs being used less and less effectively.[6]

The law of diminishing returns is a fundamental princi-ple of economics.[5] It plays a central role in productiontheory.[7]

1 History

The concept of diminishing returns can be traced backto the concerns of early economists such as Johann Hein-rich von Thünen, Jacques Turgot, Adam Smith,[8] JamesSteuart, Thomas Robert Malthus and David Ricardo.However, classical economists such as Malthus and Ri-cardo attributed the successive diminishment of outputto the decreasing quality of the inputs. Neoclassicaleconomists assume that each “unit” of labor is identical.Diminishing returns are due to the disruption of the entireproductive process as additional units of labor are addedto a fixed amount of capital. The law of diminishing re-turns remains an important consideration in farming.

2 Diminishing marginal returns

As labor usage increases from L1 to L2, total output (measuredvertically in the top graph) increases by the amount shown. But iflabor usage is increased by the same amount again, output goesup by less, implying diminishing marginal returns to the use oflabor as an input. The marginal product of labor (measuredvertically in the bottom graph) is diminishing everywhere to theright of point A.

The defining feature of diminishing marginal returns isthat as total investment increases, the total return on in-vestment as a proportion of the total investment (the aver-age product or return) decreases. Suppose, for example,that 1 kilogram of seed applied to a certain plot of landproduces one ton of crop, that 2 kg of seed produces 1.5tons, and that 3 kg of seed produces 1.75 tons. In formu-laic terms, the i th kg of seeds produces 1

2i−1 additional

1

2 6 SOURCES

tons of crop. The return from investing the first kilogramis 1 t/kg. When 2 kg of seed is invested, the return is1.5/2 = 0.75 t/kg, and when 3 kg is invested, the return is1.75/3 = 0.58 t/kg.In formulaic terms, for this example, the diminishedmarginal return is:D = 1

X

∑Xi=1

12i−1

where X = seed in kilograms, and 12i−1 = additional crop

yield in tons, for the i th kilogram of seed.Substituting 3 for X and expanding yields:D = 1

3

∑3i=1

12i−1

= 13 ·

(1

21−1 + 122−1 + 1

23−1

)= 1

3 ·(

120 + 1

21 + 122

)= 1

3 ·(11 + 1

2 + 14

)= 1.75

3

= 0.583t/kgAnother example is a factory that has a fixed stock ofcapital, or tools and machines, and a variable supply oflabor. As the firm increases the number of workers, thetotal output of the firm grows but at an ever-decreasingrate. This is because after a certain point, the factory be-comes overcrowded and workers begin to form lines touse the machines. The long-run solution to this problemis to increase the stock of capital, that is, to buy moremachines and to build more factories.

3 Returns and costs

There is an inverse relationship between returns of inputsand the cost of production. Suppose that a kilogram ofseed costs one dollar, and this price does not change. Al-though there are other costs, assume they do not vary withthe amount of output and are therefore fixed costs. Onekilogram of seeds yields one ton of crop, so the first ton ofthe crop costs one dollar to produce. That is, for the firstton of output, themarginal cost of the output is $1 per ton.If there are no other changes, then if the second kilogramof seeds applied to land produces only half the output ofthe first, the marginal cost would equal $1 per half tonof output, or $2 per ton. Similarly, if the third kilogramof seeds yields only a quarter ton, then the marginal costequals $1 per quarter ton, or $4 per ton. Thus, diminish-ing marginal returns imply increasing marginal costs andrising average costs.Cost can also be measured in terms of opportunity cost.In this case the law also applies to societies – the op-portunity cost of producing a single unit of a good gen-erally increases as a society attempts to produce moreof that good. This explains the bowed-out shape of theproduction possibilities frontier.

4 See also• Diminishingmarginal utility, also not to bemistakenfor 'diminishing returns’

• Diseconomies of scale, does not assume fixed inputs,thus differing from 'diminishing returns’

• Economies of scale

• Increasing returns

• Learning curve and Experience curve effects

• Marginal value theorem

• Opportunity cost

• Pareto principle

• Submodular set function

• Tendency of the rate of profit to fall

• Liebig’s Law of the minimum

5 References[1] “diminishing returns”. dictionary.reference.com. Re-

trieved 12 August 2014.

[2] “diminishing returns”. Encyclopaedia Britannica OnlineAcademic Edition. Encyclopædia Britannica Inc. 2014.

[3] “AGlossary of Political Economy Terms; Diminishing re-turns, law of”. auburn.edu. Auburn University. Retrieved12 August 2014.

[4] Saiduzzaman, Selim. “THE THEORY OF DIMINISH-ING RETURN”. academia.edu. Retrieved 12 August2014.

[5] Samuelson, Paul A.; Nordhaus, William D. (2001). Mi-croeconomics (17th ed.). McGraw-Hill. p. 110. ISBN0071180664.

[6] George, Henry. The Science of Political Economy. NewYork: Robert Schalkenbach Foundation.

[7] Encyclopedia Britannica. Encyclopædia Britannica, Inc.26 Jan 2013. ISBN 9781593392925.

[8] Smith, Adam. The wealth of nations. Thrifty books.ISBN 9780786514854.

6 Sources• Case, Karl E.; Fair, Ray C. (1999). Principles ofEconomics (5th ed.). Prentice-Hall. ISBN 0-13-961905-4.

3

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