Production Function
A production function relates
physical output of a production process to physical inputs or production. The
primary 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.
Production in this way is defined
as the transformation of input into output.
Product Function is
Y
= f (L, K, S)
Here Y = Yield (production), L = Labor,
K =Capital S= Land
Factor inputs are classified into fixed
factors and variable factors.
Where as fixed factors are not
related to the level and volume of the profit and these factors remains fixed
whether the volume of product is more or less or even zero.
And variable factors are factors
which are directly related to the volume of output such as labor, fuel, and raw
material.
The distinction between fixed and
variable factor is restricted to short period only. In the long period, all
factors are supposed to be variable.
Cobb–Douglas production function
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, particularly physical
capital and labor, and the amount of output that can be produced by those
inputs. In its most standard form for production of a single good with two
factors, the function is
Where:
Y = total production (the real
value of all goods produced in a year)
α and β are the output elasticities of capital
and labor, respectively. These values are constants determined by available
technology.
Output elasticity measures the
responsiveness of output to a change in levels of either labor or capital used
in production, ceteris
paribus. For example if α = 0.45, a 1% increase in capital usage
would lead to approximately a 0.45% increase in output.
Further, if
α + β = 1,
the
production function has constant returns to scale, meaning that doubling the usage of
capital K and labor L will also double output Y. If
α + β <
1,
returns to
scale are decreasing, and if
α + β >
1,
returns to
scale are increasing. Assuming perfect competition and α + β = 1, α and β can be shown to be capital's
and labor's shares of output.
