In
economics
Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and intera ...
, returns to scale describe what happens to long-run returns as the scale of production increases, when all
input levels including physical
capital
Capital may refer to:
Common uses
* Capital city, a municipality of primary status
** List of national capital cities
* Capital letter, an upper-case letter Economics and social sciences
* Capital (economics), the durable produced goods used f ...
usage are variable (able to be set by the
firm
A company, abbreviated as co., is a Legal personality, legal entity representing an association of people, whether Natural person, natural, Legal person, legal or a mixture of both, with a specific objective. Company members share a common p ...
). The concept of returns to scale arises in the context of a firm's
production function
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 ...
. It explains the long-run linkage of the rate of increase in output (production) relative to associated increases in the inputs (
factors of production
In economics, factors of production, resources, or inputs are what is used in the production process to produce output—that is, goods and services. The utilized amounts of the various inputs determine the quantity of output according to the rel ...
). In the long run, all factors of production are variable and subject to change in response to a given increase in production scale. While
economies of scale
In microeconomics, economies of scale are the cost advantages that enterprises obtain due to their scale of operation, and are typically measured by the amount of output produced per unit of time. A decrease in cost per unit of output enables ...
show the effect of an increased output level on unit costs, returns to scale focus only on the relation between input and output quantities.
There are three possible types of returns to scale: increasing returns to scale, constant returns to scale, and diminishing (or decreasing) returns to scale.
If output increases by the same proportional change as all inputs change then there are constant returns to scale (CRS). If output increases by less than the proportional change in all inputs, there are decreasing returns to scale (DRS). If output increases by more than the proportional change in all inputs, there are increasing returns to scale (IRS). 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 some range of output levels between those extremes.
In mainstream microeconomics, the returns to scale faced by a firm are purely technologically imposed and are not influenced by economic decisions or by market conditions (i.e., conclusions about returns to scale are derived from the specific mathematical structure of the production function ''in isolation'').
Example
When the usages of 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) and the production function is
homothetic, 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 does not face perfectly competitive factor markets (i.e., in this context, the price one pays for a good does depend on the amount purchased). 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.
Formal definitions
Formally, a production function
is defined to have:
*Constant returns to scale if (for any constant ''a'' greater than 0)
(Function F is
homogeneous
Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...
of degree 1)
*Decreasing returns to scale if (for any constant ''a'' greater than 1)