Diminishing returns

Last updated
A 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. Diminishing Returns Graph.svg
A 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.

In economics, diminishing returns are the decrease 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] The law of diminishing returns does not cause a decrease in overall production capabilities, rather it defines a point on a production curve whereby producing an additional unit of output will result in a loss and is known as negative returns. Under diminishing returns, output remains positive, but productivity and efficiency decrease.

Contents

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. [4] 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. [5]

The concept of diminishing returns can be explained by considering other theories such as the concept of exponential growth. [6] 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. [7] 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. [8] These factors have the ability to influence economic growth and can eventually limit or inhibit continuous exponential growth. [9] 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. [10] 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. [11]

This idea can be understood outside of economics theory, for example, population. 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. [6] 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. Diminishing Returns Graphs.svg
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, [12] James Steuart, Thomas Robert Malthus, and [13] David Ricardo. The law of diminishing returns can be traced back to the 18th century, in the work of Jacques Turgot. He argued that "each increase [in an input] would be less and less productive." [14] In 1815, David Ricardo, Thomas Malthus, Edward West, and Robert Torrens applied the concept of diminishing returns to land rent. These works were relevant to the committees of Parliament in England, who were investigating why grain prices were so high, and how to reduce them. The four economists concluded that the prices of the products had risen due to the Napoleonic Wars, which affected international trade and caused farmers to move to lands which were undeveloped and further away. In addition, at the end of the Napoleonic Wars, grain imports were restored which caused a decline in prices because the farmers needed to attract customers and sell their products faster. [15]

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. [4] 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. [16] 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. [17]

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. Total, Average, and Marginal Product.svg
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 50 people are employed, 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.

Further along the production curve at, 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, employing additional workers, this will give negative returns. [18]

Through each of these examples, the floor space and capital of the factor remained constant, i.e., these inputs were held constant. 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. [19] 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. Even GDP per capita will reach a point where it has a diminishing rate of return on HDI. [20] 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

Increasing Returns:

Constant Returns:

Diminishing Returns:

Production function

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

Start from the equation for the Marginal Product:

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

Elasticity, a function of Input and Output, , can be taken for small input changes. If the above two conditions are satisfied, then . [23]

This works intuitively;

  1. If is positive, since negative inputs and outputs are impossible,
  2. And is positive, since a positive return for inputs is required for diminishing returns
  1. is relative change in output, 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~

Returns and costs

There is an inverse relationship between returns of inputs and the cost of production, [24] 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. [25] 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 "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" [4] of the inputs before proceeding. In this, ceteris paribus is disambiguating.

See also

Related Research Articles

In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. In older works, power is sometimes called activity. Power is a scalar quantity.

A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter design. The filter is sometimes called a high-cut filter, or treble-cut filter in audio applications. A low-pass filter is the complement of a high-pass filter.

Growth accounting is a procedure used in economics to measure the contribution of different factors to economic growth and to indirectly compute the rate of technological progress, measured as a residual, in an economy. Growth accounting decomposes the growth rate of an economy's total output into that which is due to increases in the contributing amount of the factors used—usually the increase in the amount of capital and labor—and that which cannot be accounted for by observable changes in factor utilization. The unexplained part of growth in GDP is then taken to represent increases in productivity or a measure of broadly defined technological progress.

<span class="mw-page-title-main">Profit maximization</span> Process to determine the highest profits for a firm

In economics, profit maximization is the short run or long run process by which a firm may determine the price, input and output levels that will lead to the highest possible total profit. In neoclassical economics, which is currently the mainstream approach to microeconomics, the firm is assumed to be a "rational agent" which wants to maximize its total profit, which is the difference between its total revenue and its total cost.

In economics, the marginal cost is the change in the total cost that arises when the quantity produced is increased, i.e. the cost of producing additional quantity. In some contexts, it refers to an increment of one unit of output, and in others it refers to the rate of change of total cost as output is increased by an infinitesimal amount. As Figure 1 shows, the marginal cost is measured in dollars per unit, whereas total cost is in dollars, and the marginal cost is the slope of the total cost, the rate at which it increases with output. Marginal cost is different from average cost, which is the total cost divided by the number of units produced.

<span class="mw-page-title-main">Cobb–Douglas production function</span> Macroeconomic formula that describes productivity

In economics and econometrics, the Cobb–Douglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the amounts of two or more inputs and the amount of output that can be produced by those inputs. The Cobb–Douglas form was developed and tested against statistical evidence by Charles Cobb and Paul Douglas between 1927 and 1947; according to Douglas, the functional form itself was developed earlier by Philip Wicksteed.

<span class="mw-page-title-main">Production function</span> Used to define marginal product and to distinguish allocative efficiency

In economics, a production function gives the technological relation between quantities of physical inputs and quantities of output of goods. The production function is one of the key concepts of mainstream neoclassical theories, used to define marginal product and to distinguish allocative efficiency, a key focus of economics. One important purpose of the production function is to address allocative efficiency in the use of factor inputs in production and the resulting distribution of income to those factors, while abstracting away from the technological problems of achieving technical efficiency, as an engineer or professional manager might understand it.

In economics, average cost (AC) or unit cost is equal to total cost (TC) divided by the number of units of a good produced :

<span class="mw-page-title-main">Marginal product</span> Change in output resulting from employing one more unit of a particular input

In economics and in particular neoclassical economics, the marginal product or marginal physical productivity of an input is the change in output resulting from employing one more unit of a particular input, assuming that the quantities of other inputs are kept constant.

In mechanics, virtual work arises in the application of the principle of least action to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement is different for different displacements. Among all the possible displacements that a particle may follow, called virtual displacements, one will minimize the action. This displacement is therefore the displacement followed by the particle according to the principle of least action.

The work of a force on a particle along a virtual displacement is known as the virtual work.

<span class="mw-page-title-main">Marginal revenue</span> Additional total revenue generated by increasing product sales by 1 unit

Marginal revenue is a central concept in microeconomics that describes the additional total revenue generated by increasing product sales by 1 unit. Marginal revenue is the increase in revenue from the sale of one additional unit of product, i.e., the revenue from the sale of the last unit of product. It can be positive or negative. Marginal revenue is an important concept in vendor analysis. To derive the value of marginal revenue, it is required to examine the difference between the aggregate benefits a firm received from the quantity of a good and service produced last period and the current period with one extra unit increase in the rate of production. Marginal revenue is a fundamental tool for economic decision making within a firm's setting, together with marginal cost to be considered.

In machine learning, backpropagation is a gradient estimation method used to train neural network models. The gradient estimate is used by the optimization algorithm to compute the network parameter updates.

The marginal revenue productivity theory of wages is a model of wage levels in which they set to match to the marginal revenue product of labor, , which is the increment to revenues caused by the increment to output produced by the last laborer employed. In a model, this is justified by an assumption that the firm is profit-maximizing and thus would employ labor only up to the point that marginal labor costs equal the marginal revenue generated for the firm. This is a model of the neoclassical economics type.

In economics, a cost curve is a graph of the costs of production as a function of total quantity produced. In a free market economy, productively efficient firms optimize their production process by minimizing cost consistent with each possible level of production, and the result is a cost curve. Profit-maximizing firms use cost curves to decide output quantities. There are various types of cost curves, all related to each other, including total and average cost curves; marginal cost curves, which are equal to the differential of the total cost curves; and variable cost curves. Some are applicable to the short run, others to the long run.

The Solow–Swan model or exogenous growth model is an economic model of long-run economic growth. It attempts to explain long-run economic growth by looking at capital accumulation, labor or population growth, and increases in productivity largely driven by technological progress. At its core, it is an aggregate production function, often specified to be of Cobb–Douglas type, which enables the model "to make contact with microeconomics". The model was developed independently by Robert Solow and Trevor Swan in 1956, and superseded the Keynesian Harrod–Domar model.

<span class="mw-page-title-main">Supply (economics)</span> Amount of a good that sellers are willing to provide in the market

In economics, supply is the amount of a resource that firms, producers, labourers, providers of financial assets, or other economic agents are willing and able to provide to the marketplace or to an individual. Supply can be in produced goods, labour time, raw materials, or any other scarce or valuable object. Supply is often plotted graphically as a supply curve, with the price per unit on the vertical axis and quantity supplied as a function of price on the horizontal axis. This reversal of the usual position of the dependent variable and the independent variable is an unfortunate but standard convention.

In finance, bootstrapping is a method for constructing a (zero-coupon) fixed-income yield curve from the prices of a set of coupon-bearing products, e.g. bonds and swaps.

In economics, the marginal product of capital (MPK) is the additional production that a firm experiences when it adds an extra unit of input. It is a feature of the production function, alongside the labour input.

In economics, the marginal product of labor (MPL) is the change in output that results from employing an added unit of labor. It is a feature of the production function and depends on the amounts of physical capital and labor already in use.

The AK model of economic growth is an endogenous growth model used in the theory of economic growth, a subfield of modern macroeconomics. In the 1980s it became progressively clearer that the standard neoclassical exogenous growth models were theoretically unsatisfactory as tools to explore long run growth, as these models predicted economies without technological change and thus they would eventually converge to a steady state, with zero per capita growth. A fundamental reason for this is the diminishing return of capital; the key property of AK endogenous-growth model is the absence of diminishing returns to capital. In lieu of the diminishing returns of capital implied by the usual parameterizations of a Cobb–Douglas production function, the AK model uses a linear model where output is a linear function of capital. Its appearance in most textbooks is to introduce endogenous growth theory.

References

Citations

  1. "Diminishing Returns". Encyclopaedia Britannica. 2017-12-27. Retrieved 2021-04-22.
  2. 1 2 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. CreateSpace Independent Publishing Platform. p. 44. ISBN   978-1501077173.
  4. 1 2 3 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.
  5. Encyclopædia Britannica. Encyclopædia Britannica, Inc. 26 Jan 2013. ISBN   9781593392925.
  6. 1 2 "Exponential growth & logistic growth (article)". Khan Academy. Retrieved 2021-04-19.
  7. "What Is Stagflation, What Causes It, and Why Is It Bad?". Investopedia. Retrieved 2023-04-23.
  8. "What are the Factors of Production". www.stlouisfed.org. Retrieved 2023-04-23.
  9. "What is Production? | Microeconomics". courses.lumenlearning.com. Retrieved 2021-04-19.
  10. Pichère, Pierre (2015-09-02). The Law of Diminishing Returns: Understand the fundamentals of economic productivity. 50Minutes.com. p. 17. ISBN   978-2806270092.
  11. "Knowledge, Technology and Complexity in Economic Growth". rcc.harvard.edu. Retrieved 2023-04-23.
  12. Smith, Adam. The wealth of nations. Thrifty books. ISBN   9780786514854.
  13. Pichère, Pierre (2015-09-02). The Law of Diminishing Returns: Understand the fundamentals of economic productivity. 50Minutes.com. pp. 9–12. ISBN   978-2806270092.
  14. "Anne-Robert-Jacques Turgot (1727–1781)", The Concise Encyclopedia of Economics , Library of Economics and Liberty (2nd ed.), Liberty Fund, 2008, archived from the original on 2 December 2019, retrieved 16 July 2013
  15. Brue, Stanley L (1993-08-01). "Retrospectives: The Law of Diminishing Returns". Journal of Economic Perspectives. 7 (3): 185–192. doi: 10.1257/jep.7.3.185 . ISSN   0895-3309.
  16. 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.
  17. "Law of Diminishing Marginal Returns: Definition, Example, Use in Economics". Investopedia. Retrieved 2023-04-23.
  18. "The Law of Diminishing Returns - Personal Excellence". personalexcellence.co. 2016-04-12. Retrieved 2022-04-29.
  19. "Law of Diminishing Returns & Point of Diminishing Returns Definition". Corporate Finance Institute. Retrieved 2021-04-26.
  20. 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.
  21. 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.
  22. "The Production Function | Microeconomics". courses.lumenlearning.com. Retrieved 2021-04-21.
  23. 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.
  24. "Why It Matters: Production and Costs | Microeconomics". courses.lumenlearning.com. Retrieved 2021-04-19.
  25. 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.