Diminishing returns

Diminishing returns is an economic principle stating that decreasing in marginal (incremental) output of a production process as the amount of a single factor of production is incrementally increased, holding all other factors of production equal (ceteris paribus).[1] The law of diminishing returns (also known as the law of diminishing marginal productivity) states that in productive processes, increasing a factor of production by one unit, while holding all other production factors constant, will at some point return a lower unit of output per incremental unit of input.[2][3] After the point of optimum production, excessively adding to the input variable will not only lead to a decrease in efficiency, but also to a negative return of production. A negative return might hurt the whole production process.[4]

The modern understanding of the law adds the dimension of holding other outputs equal, since a given process is understood to be able to produce co-products.[5] An example would be a factory increasing its saleable product, but also increasing its CO2 production, for the same input increase.[2] The law of diminishing returns is a fundamental principle of both micro and macro economics and it plays a central role in production theory.[6]

The concept of diminishing returns can be explained by considering other theories such as the concept of exponential growth.[7] It is commonly understood that growth will not continue to rise exponentially, rather it is subject to different forms of constraints such as limited availability of resources and capitalisation which can cause economic stagnation. This example of production holds true to this common understanding as production is subject to the four factors of production which are land, labour, capital and enterprise. These factors have the ability to influence economic growth and can eventually limit or inhibit continuous exponential growth.[8] Therefore, as a result of these constraints the production process will eventually reach a point of maximum yield on the production curve and this is where marginal output will stagnate and move towards zero.[9] However it should also be considered that innovation in the form of technological advances or managerial progress can minimise or eliminate diminishing returns to restore productivity and efficiency, and to generate profit.

Diminishing Returns Graph The graph highlights the concept of diminishing returns by plotting the curve of output against input. The areas of increasing, diminishing and negative returns are identified at points along the curve. There is also a point of maximum yield which is the point on the curve where producing another unit of output becomes inefficient and unproductive.

This idea can plays an important parts on the theory of rent and the theory of population and it should find it promulgated both by the reputed anticipator of Ricardo, James Anderson, and by Malthus' essay on the Principle of Population.[10] The population size on Earth is growing rapidly, but this will not continue forever (exponentially). Constraints such as resources will see the population growth stagnate at some point and begin to decline.[7] Similarly, it will begin to decline towards zero, but not actually become a negative value. The same idea as in the diminishing rate of return inevitable to the production process.

Figure 2: Output vs. Input [top] & Output per unit Input vs. Input [bottom] Seen in [top], the change in output by increasing input from L1 to L2 is equal to the change from L2 to L3. Seen in [bottom], until an input of L1, the output per unit is increasing. After L1, the output per unit decreases to zero at L3. Together, these demonstrate diminishing returns from L1.

History

The concept of diminishing returns can be traced back to the concerns of early economists such as Johann Heinrich von Thünen, Jacques Turgot, Adam Smith,[11] James Steuart, Thomas Robert Malthus, and [12] David Ricardo. However, classical economists such as Malthus and Ricardo attributed the successive diminishment of output to the decreasing quality of the inputs whereas Neoclassical economists assume that each "unit" of labor is identical. Diminishing returns are due to the disruption of the entire production process as additional units of labor are added to a fixed amount of capital. The law of diminishing returns remains an important consideration in areas of production such as farming and agriculture.

Proposed on the cusp of the First Industrial Revolution, it was motivated with single outputs in mind. In recent years, economists since the 1970s have sought to redefine the theory to make it more appropriate and relevant in modern economic societies.[5] Specifically, it looks at what assumptions can be made regarding number of inputs, quality, substitution and complementary products, and output co-production, quantity and quality.

The origin of the law of diminishing returns was developed primarily within the agricultural industry. In the early 19th century, David Ricardo as well as other English economists previously mentioned, adopted this law as the result of the lived experience in England after the war. It was developed by observing the relationship between prices of wheat and corn and the quality of the land which yielded the harvests.[13] The observation was that at a certain point, that the quality of the land kept increasing, but so did the cost of produce etc. Therefore, each additional unit of labour on agricultural fields, actually provided a diminishing or marginally decreasing return. There was many people who die of disease and famine as a result of the diminishing marginal returns especially the advances relate to storage, food production and transport.[14]

Example

Figure 2 [OLD]: Total Output vs. Total Input [top] & Output per unit Input vs. Total Input [bottom] Seen in TOP, the change in output by increasing output from L1 to L2 is equal to the change from L2 to L3. Seen in BOTTOM, until an output of L1, the output per unit is increasing. After L1, the output per unit decreases to zero at L3. Together, these demonstrate diminishing returns from L1.

A common example of diminishing returns is choosing to hire more people on a factory floor to alter current manufacturing and production capabilities. Given that the capital on the floor (e.g. manufacturing machines, pre-existing technology, warehouses) is held constant, increasing from one employee to two employees is, theoretically, going to more than double production possibilities and this is called increasing returns.

If we now employ 50 people, at some point, increasing the number of employees by two percent (from 50 to 51 employees) would increase output by two percent and this is called constant returns.

However, if we look further along the production curve to, for example 100 employees, floor space is likely getting crowded, there are too many people operating the machines and in the building, and workers are getting in each other's way. Increasing the number of employees by two percent (from 100 to 102 employees) would increase output by less than two percent and this is called "diminishing returns."

After achieving the point of maximum output, if we employ additional workers, this will give us negative returns.[15]

Through each of these examples, the floor space and capital of the factor remained constant, i.e., these inputs were held constant. However, by only increasing the number of people, eventually the productivity and efficiency of the process moved from increasing returns to diminishing returns.

To understand this concept thoroughly, acknowledge the importance of marginal output or marginal returns. Returns eventually diminish because economists measure productivity with regard to additional units (marginal). Additional inputs significantly impact efficiency or returns more in the initial stages.[16] The point in the process before returns begin to diminish is considered the optimal level. Being able to recognize this point is beneficial, as other variables in the production function can be altered rather than continually increasing labor.

Further, examine something such as the Human Development Index, which would presumably continue to rise so long as GDP per capita (in Purchasing Power Parity terms) was increasing. This would be a rational assumption because GDP per capita is a function of HDI. However, even GDP per capita will reach a point where it has a diminishing rate of return on HDI.[17] Just think, in a low income family, an average increase of income will likely make a huge impact on the wellbeing of the family. Parents could provide abundantly more food and healthcare essentials for their family. That is a significantly increasing rate of return. But, if you gave the same increase to a wealthy family, the impact it would have on their life would be minor. Therefore, the rate of return provided by that average increase in income is diminishing.

Mathematics

Signify ${\displaystyle Output=O\ ,\ Input=I\ ,\ O=f(I)}$

Increasing Returns: ${\displaystyle 2\cdot f(I)

Constant Returns: ${\displaystyle 2\cdot f(I)=f(2\cdot I)}$

Diminishing Returns: ${\displaystyle 2\cdot f(I)>f(2\cdot I)}$

Production Function

There is a widely recognised production function in economics: Q= f(NR, L, K, t, E):

• The point of diminishing returns can be realised, by use of the second derivative in the above production function.
• Which can be simplified to: Q= f(L,K).
• This signifies that output (Q) is dependent on a function of all variable (L) and fixed (K) inputs in the production process. This is the basis to understand. What is important to understand after this is the math behind Marginal Product. MP= ΔTP/ ΔL. [18]
• This formula is important to relate back to diminishing rates of return. It finds the change in total product divided by change in labour.
• The Marginal Product formula suggests that MP should increase in the short run with increased labour. However, in the long run, this increase in workers will either have no effect or a negative effect on the output. This is due to the effect of fixed costs as a function of output, in the long run.[19]

Link with Output Elasticity

Start from the equation for the Marginal Product: ${\displaystyle {\Delta Out \over \Delta In_{1}}={{f(In_{2},In_{1}+\Delta In_{1})-f(In_{1},In_{2})} \over \Delta In_{1}}}$

To demonstrate diminishing returns, two conditions are satisfied; marginal product is positive, and marginal product is decreasing.

Elasticity, a function of Input and Output, ${\displaystyle \epsilon ={In \over Out}\cdot {\delta Out \over \delta In}}$ , can be taken for small input changes. If the above two conditions are satisfied, then ${\displaystyle 0<\epsilon <1}$ .[20]

This works intuitively;

1. If ${\displaystyle {In \over Out}}$  is positive, since negative inputs and outputs are impossible,
2. And ${\displaystyle {\delta Out \over \delta In}}$  is positive, since a positive return for inputs is required for diminishing returns
• Then ${\displaystyle 0<\epsilon }$
1. ${\displaystyle {\delta Out \over Out}}$  is relative change in output, ${\displaystyle {\delta In \over In}}$  is relative change in input
2. The relative change in output is smaller than the relative change in input; ~input requires increasing effort to change output~
• Then ${\displaystyle {\delta Out \over Out}/{\delta In \over In}={In \over Out}\cdot {\delta Out \over \delta In}=\epsilon <1}$

Returns and costs

There is an inverse relationship between returns of inputs and the cost of production,[21] although other features such as input market conditions can also affect production costs. Suppose that a kilogram of seed costs one dollar, and this price does not change. Assume for simplicity that there are no fixed costs. One kilogram of seeds yields one ton of crop, so the first ton of the crop costs one dollar to produce. That is, for the first ton of output, the marginal cost as well as the average cost of the output is 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 (showing diminishing returns), the marginal cost would equal per half ton of output, or per ton, and the average cost is per 3/2 tons of output, or /3 per ton of output. Similarly, if the third kilogram of seeds yields only a quarter ton, then the marginal cost equals per quarter ton or per ton, and the average cost is per 7/4 tons, or /7 per ton of output. Thus, diminishing marginal returns imply increasing marginal costs and increasing average costs.

Cost is 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.

Justification

Ceteris Paribus

Part of the reason one input is altered ceteris paribus, is the idea of disposability of inputs.[22] With this assumption, essentially that some inputs are above the efficient level. Meaning, they can decrease without perceivable impact on output, after the manner of excessive fertiliser on a field.

If input disposability is assumed, then increasing the principal input, while decreasing those excess inputs, could result in the same 'diminished return', as if the principal input was changed certeris paribus. While considered as 'hard' inputs, like labour and assets, diminishing returns would hold true. In the modern accounting era where inputs can be traced back to movements of financial capital, the same case may reflect constant, or increasing returns.

It is necessary to be clear of the 'fine structure'[5] of the inputs before proceeding. In this, ceteris paribus is disambiguating.

References

Citations

1. ^ "Diminishing Returns". Encyclopaedia Britannica. Encyclopaedia Britannica. 2017-12-27. Retrieved 2021-04-22.
2. ^ a b Samuelson, Paul A.; Nordhaus, William D. (2001). Microeconomics (17th ed.). McGraw-Hill. p. 110. ISBN 0071180664.
3. ^ Erickson, K.H. (2014-09-06). Economics: A Simple Introduction. p. 44. ISBN 978-1501077173.
4. ^ "The Law of Diminishing Marginal Returns Definition | Indeed.com". Indeed Career Guide. Retrieved 2022-04-25.
5. ^ a b c Shephard, Ronald W.; Färe, Rolf (1974-03-01). "The law of diminishing returns". Zeitschrift für Nationalökonomie. 34 (1): 69–90. doi:10.1007/BF01289147. ISSN 1617-7134. S2CID 154916612.
6. ^ Encyclopædia Britannica. Encyclopædia Britannica, Inc. 26 Jan 2013. ISBN 9781593392925.
7. ^ a b "Exponential growth & logistic growth (article)". Khan Academy. Retrieved 2021-04-19.
8. ^ "What is Production? | Microeconomics". courses.lumenlearning.com. Retrieved 2021-04-19.
9. ^ Pichère, Pierre (2015-09-02). The Law of Diminishing Returns: Understand the fundamentals of economic productivity. 50Minutes.com. p. 17. ISBN 978-2806270092.
10. ^ Cannan, Edwin (1892-03-01). "The Origin of the Law of Diminishing Returns, 1813-15". The Economic Journal. 2 (5): 53–69. doi:10.2307/2955940. ISSN 0013-0133.
11. ^ Smith, Adam. The wealth of nations. Thrifty books. ISBN 9780786514854.
12. ^ Pichère, Pierre (2015-09-02). The Law of Diminishing Returns: Understand the fundamentals of economic productivity. 50Minutes.com. pp. 9–12. ISBN 978-2806270092.
13. ^ Cannan, Edwin (March 1892). "The Origin of the Law of Diminishing Returns, 1813-15". The Economic Journal. 2 (5): 53–69. doi:10.2307/2955940. JSTOR 2955940.
14. ^ "Google 翻譯". translate.google.com. Retrieved 2022-04-29.
15. ^ "The Law of Diminishing Returns - Personal Excellence". personalexcellence.co. 2016-04-12. Retrieved 2022-04-29.
16. ^ "Law of Diminishing Returns & Point of Diminishing Returns Definition". Corporate Finance Institute. Retrieved 2021-04-26.
17. ^ Cahill, Miles B. (October 2002). "Diminishing returns to GDP and the Human Development Index". Applied Economics Letters. 9 (13): 885–887. doi:10.1080/13504850210158999. ISSN 1350-4851. S2CID 153444558.
18. ^ Carter, H. O.; Hartley, H. O. (April 1958). "A Variance Formula for Marginal Productivity Estimates using the Cobb-Douglas Function". Econometrica. 26 (2): 306. doi:10.2307/1907592. JSTOR 1907592.
19. ^ "The Production Function | Microeconomics". courses.lumenlearning.com. Retrieved 2021-04-21.
20. ^ Robinson, R. Clark (July 2006). "Math 285-2 - Handouts for Math 285-2 - Marginal Product of Labor and Capital" (PDF). Northwestern - Weinberg College of Arts & Sciences -Department of Mathematics. Retrieved 1 November 2020.
21. ^ "Why It Matters: Production and Costs | Microeconomics". courses.lumenlearning.com. Retrieved 2021-04-19.
22. ^ Shephard, Ronald W. (1970-03-01). "Proof of the law of diminishing returns". Zeitschrift für Nationalökonomie. 30 (1): 7–34. doi:10.1007/BF01289990. ISSN 1617-7134. S2CID 154887748.

Sources

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