Production function

In economics, Production function may be defined as the functional relationship between physical inputs (i.e., factor of production) and physical outputs (i.e., the quantity of good produced). Production function shows technological or engineering relationship between output of a commodity and its inputs. The act of production involves the transformation of input into output. The word production in economics in not merely confined to effecting physical transformation in matter, it also covers the rendering of services. The production function can be expressed symbolically as,

Q = ƒ(X, Ld, L, C, M, T, t)


Q = Quantity of output,
ƒ = Unspecified function
X = Output of commodity
Ld = Land and Bulding
L = Labour
C = Capital
M = Management
T = Technology
t = Time

There are two types of production function:

  • Short run production function

The short run is defined in economics as a period of time where at least one factor of production is assumed to be in fixed supply i.e. it cannot be changed. We normally assume that the quantity of capital inputs (e.g. plant and machinery) is fixed and that production can be altered by suppliers through changing the demand for variable inputs such as labour, components, raw materials and energy inputs. Often the amount of land available for production is also fixed.

The time periods used in textbook economics are somewhat arbitrary because they differ from industry to industry. The short run for the electricity generation industry or the telecommunications sector varies from that appropriate for newspaper and magazine publishing and small-scale production of foodstuffs and beverages. Much depends on the time scale that permits a business to alter all of the inputs that it can bring to production.

In the short run, the law of diminishing returns states that as we add more units of a variable input (i.e. labour or raw materials) to fixed amounts of land and capital, the change in total output will at first rise and then fall. Diminishing returns to labour occurs when marginal product of labour starts to fall. This means that total output will still be rising – but increasing at a decreasing rate as more workers are employed. As we shall see in the following numerical example, eventually a decline in marginal product leads to a fall in average product.

  • Long run production function

Long run is the period where the fixed factor is changed. If the demand for the firm’s product increases, the firm can increase its output by enlarging the size of its plant or increasing the scale of its operations. So in the long run there is enough time to effect changes in the scale operations or to introduce other adjustment in the organization setup of the firm. In fact the firm in the long period, can build any desired scale of plant. All factors are variable none is fixed. In the long run, then, there are number of decisions that a firm will have to make about the scale of its operations, the location of its operations and the techniques of production it will use. In this concept it explains the laws of return to scale.