Returns to scale
Encyclopedia
In economics
, returns to scale and economies of scale
are related terms that describe what happens as the scale of production increases in the long run, when all input levels including physical capital
usage are variable (chosen by the firm). They are different terms and should not be used interchangeably.
The term returns to scale arises in the context of a firm's production function
. It refers to changes in output resulting from a proportional change in all inputs (where all inputs increase by a constant factor). If output increases by that same proportional change then there are constant returns to scale (CRS). If output increases by less than that proportional change, there are decreasing returns to scale (DRS). If output increases by more than that proportional change, there are increasing returns to scale (IRS). Thus the returns to scale faced by a firm are purely technologically imposed and are not influenced by economic decisions or by market conditions.
A firm's production function could exhibit different types of returns to scale in different ranges of output. Typically, there could be increasing returns at relatively low output levels, decreasing returns at relatively high output levels, and constant returns at one output level between those ranges.
Assuming that the factor costs are constant (that is, that the firm is a perfect competitor in all input markets), a firm experiencing constant returns will have constant long-run average costs
, a firm experiencing decreasing returns will have increasing long-run average costs, and a firm experiencing increasing returns will have decreasing long-run average costs. However, this relationship breaks down if the firm is not a perfect competitor
in the input markets. For example, if there are increasing returns to scale in some range of output levels, but the firm is so big in one or more input markets that increasing its purchases of an input drives up the input's per-unit cost, then the firm could have diseconomies of scale in that range of output levels. Conversely, if the firm is able to get bulk discounts of an input, then it could have economies of scale in some range of output levels even if it has decreasing returns in production in that output range.
resemble economies of scale, but they are not considered such because they are a function of the number of users of a good or service in an industry, not of the production efficiency within a business. Economies of scale external to the firm (or industry wide scale economies) are only considered examples of network externalities if they are driven by demand side economies.
is defined to have:
where K and L are factors of production, capital and labor, respectively.
functional form has constant returns to scale when the sum of the exponents adds up to one.
The function is:
where
and 
. Thus
But if the Cobb-Douglas production function has its general form
with
then there are increasing returns if b + c > 1 but decreasing returns if b + c < 1, since
which is greater than or less than
as b+c is greater or less than one.
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
, returns to scale and economies of scale
Economies of scale
Economies of scale, in microeconomics, refers to the cost advantages that an enterprise obtains due to expansion. There are factors that cause a producer’s average cost per unit to fall as the scale of output is increased. "Economies of scale" is a long run concept and refers to reductions in unit...
are related terms that describe what happens as the scale of production increases in the long run, when all input levels including physical capital
Capital (economics)
In economics, capital, capital goods, or real capital refers to already-produced durable goods used in production of goods or services. The capital goods are not significantly consumed, though they may depreciate in the production process...
usage are variable (chosen by the firm). They are different terms and should not be used interchangeably.
The term returns to scale arises in the context of a firm's production function
Production function
In microeconomics and macroeconomics, a production function is a function that specifies the output of a firm, an industry, or an entire economy for all combinations of inputs...
. It refers to changes in output resulting from a proportional change in all inputs (where all inputs increase by a constant factor). If output increases by that same proportional change then there are constant returns to scale (CRS). If output increases by less than that proportional change, there are decreasing returns to scale (DRS). If output increases by more than that proportional change, there are increasing returns to scale (IRS). Thus the returns to scale faced by a firm are purely technologically imposed and are not influenced by economic decisions or by market conditions.
A firm's production function could exhibit different types of returns to scale in different ranges of output. Typically, there could be increasing returns at relatively low output levels, decreasing returns at relatively high output levels, and constant returns at one output level between those ranges.
Example
When all inputs increase by a factor of 2, new values for output will be:- Twice the previous output if there are constant returns to scale (CRS)
- Less than twice the previous output if there are decreasing returns to scale (DRS)
- More than twice the previous output if there are increasing returns to scale (IRS)
Assuming that the factor costs are constant (that is, that the firm is a perfect competitor in all input markets), a firm experiencing constant returns will have constant long-run average costs
Cost curve
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 use these curves to find the optimal point of production , and profit maximizing firms can use them to decide output quantities to...
, a firm experiencing decreasing returns will have increasing long-run average costs, and a firm experiencing increasing returns will have decreasing long-run average costs. However, this relationship breaks down if the firm is not a perfect competitor
Perfect competition
In economic theory, perfect competition describes markets such that no participants are large enough to have the market power to set the price of a homogeneous product. Because the conditions for perfect competition are strict, there are few if any perfectly competitive markets...
in the input markets. For example, if there are increasing returns to scale in some range of output levels, but the firm is so big in one or more input markets that increasing its purchases of an input drives up the input's per-unit cost, then the firm could have diseconomies of scale in that range of output levels. Conversely, if the firm is able to get bulk discounts of an input, then it could have economies of scale in some range of output levels even if it has decreasing returns in production in that output range.
Network effect
Network externalitiesNetwork effect
In economics and business, a network effect is the effect that one user of a good or service has on the value of that product to other people. When network effect is present, the value of a product or service is dependent on the number of others using it.The classic example is the telephone...
resemble economies of scale, but they are not considered such because they are a function of the number of users of a good or service in an industry, not of the production efficiency within a business. Economies of scale external to the firm (or industry wide scale economies) are only considered examples of network externalities if they are driven by demand side economies.
Formal definitions
Formally, a production function is defined to have:
- constant returns to scale if (for any constant a greater than 0)
- increasing returns to scale if (for any constant a greater than 1)
- decreasing returns to scale if (for any constant a between 0 and 1)
where K and L are factors of production, capital and labor, respectively.
Formal example
The Cobb-DouglasCobb-Douglas
In economics, the Cobb–Douglas functional form of production functions is widely used to represent the relationship of an output to inputs. Similar functions were originally used by Knut Wicksell , while the Cobb-Douglas form was developed and tested against statistical evidence by Charles Cobb and...
functional form has constant returns to scale when the sum of the exponents adds up to one.
The function is:
where
and . ThusBut if the Cobb-Douglas production function has its general form
with
then there are increasing returns if b + c > 1 but decreasing returns if b + c < 1, sincewhich is greater than or less than
as b+c is greater or less than one.See also
- Diseconomies of scaleDiseconomies of scaleDiseconomies of scale are the forces that cause larger firms and governments to produce goods and services at increased per-unit costs. The concept is less well known than economies of scale.-Communication costs:...
- Economies of agglomerationEconomies of agglomerationThe term economies of agglomeration is used in urban economics to describe the benefits that firms obtain when locating near each other . This concept relates to the idea of economies of scale and network effects...
- Economies of scopeEconomies of scopeEconomies of scope are conceptually similar to economies of scale. Whereas 'economies of scale' for a firm primarily refers to reductions in average cost associated with increasing the scale of production for a single product type, 'economies of scope' refers to lowering average cost for a firm in...
- Experience curve effectsExperience curve effectsModels of the learning curve effect and the closely related experience curve effect express the relationship between equations for experience and efficiency or between efficiency gains and investment in the effort....
- Ideal firm sizeIdeal firm sizeThe ideal firm size is the theoretically most competitive size for any company, in a given industry, at a given time; which should ideally correspond with the highest possible per-unit profit.- Discussion :...
- MicroeconomicsMicroeconomicsMicroeconomics is a branch of economics that studies the behavior of how the individual modern household and firms make decisions to allocate limited resources. Typically, it applies to markets where goods or services are being bought and sold...
- Mohring effectMohring effectThe Mohring effect is a technical property of transit systems demonstrating increasing returns.In brief, as transit frequencies increase, wait times decrease, demand increases, and transit frequencies can increase again. This is because transit schedules occur over time...
- Moore's lawMoore's LawMoore's law describes a long-term trend in the history of computing hardware: the number of transistors that can be placed inexpensively on an integrated circuit doubles approximately every two years....
- Production, costs, and pricingProduction, costs, and pricingThe following outline is provided as an overview of and topical guide to industrial organization:Industrial organization – describes the behavior of firms in the marketplace with regard to production, pricing, employment and other decisions...
- W. Brian ArthurW. Brian ArthurWilliam Brian Arthur is an economist credited with influencing and describing the modern theory of increasing returns. He has lived and worked in Northern California for many years. He is an authority on economics in relation to complexity theory, technology and financial markets...
Further reading
- Susanto Basu (2008). "returns to scale measurement," The New Palgrave Dictionary of EconomicsThe New Palgrave Dictionary of EconomicsThe New Palgrave Dictionary of Economics , 2nd Edition, is an eight-volume reference work, edited by Steven N. Durlauf and Lawrence E. Blume. It contains 5.8 million words and spans 7,680 pages with 1,872 articles. Included are 1057 new articles and, from earlier, 80 essays that are designated as...
, 2nd Edition. Abstract. - James M. BuchananJames M. BuchananJames McGill Buchanan, Jr. is an American economist known for his work on public choice theory, for which he received the 1986 Nobel Memorial Prize in Economic Sciences. Buchanan's work initiated research on how politicians' self-interest and non-economic forces affect government economic policy...
and Yong J. Yoon, ed. (1994) The Return to Increasing Returns. U.Mich. Press. Chapter-preview links. - John Eatwell (1987). "returns to scale," The New Palgrave: A Dictionary of Economics, v. 4, pp. 165-66.
- Joaquim Silvestre (1987). "economies and diseconomies of scale," The New Palgrave: A Dictionary of Economics, v. 2, pp. 80-84.
- Spirros Vassilakis (1987). "increasing returns to scale," The New Palgrave: A Dictionary of Economics, v. 2, pp. 761-64.