Returns to a factor

Returns to a factor refers to the behaviour of physical output owing to change in physical input of a variable factor, fixed factors remaining constant.

In economics, returns to scale describe what happens to long run returns as the scale of production increases, when all input levels including physical capital usage are variable (able to be set by the firm). The concept of returns to scale arises in the context of a firm’s production function. 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 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 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
• 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).

Returns to factors are also called factor productivities. Productivity is the ratio of output to the input. Factor productivity refers to the short-run relationship of input and output. The productivity of one unit of a factor of production will be equal to the output it can generate. The productivity of a particular factor is measured with the assumption that the other factors are not changed or remain unchanged. Only that particular factor under study is changed.

Returns to factors refer to the output or return generated as a result of change in one or more factors, keeping the other factors unchanged. Given a percentage of increase or decrease in a particular factor such as labour, is it yielding proportionate increase or decrease in production? This is analysed in ‘returns to factors.’

The change in productivity can be measured in terms of

• Average productivity the total physical product divided by the number units of that particular factor used yields average productivity.
• Total productivity the total output generated at varied levels of input of a particular factor (while other factors remain constant), is called total physical product.
• Marginal productivity the marginal physical product is the additional output generated by adding an additional unit of the factor under study, keeping the other factors constant.

The total physical product increases along with an increase in the inputs. However, the rate of increase is varied, not constant. The total physical product at first increases at an increasing rate because of the law of increasing return to scale, and later its rate of increase declines because of the law of decreasing returns to scale.

Assumptions:

• Labour is the variable factor and capital is the fixed factor.
• There are only two factors of production, labour and capital.
• The production function is homogeneous.
• Both factors are variable in returns to scale.