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Micro Economics

Notes of operation in the long run. In the long run, technology generally improves so that more output
can be obtained from a given quantity of inputs, or the same output can be obtained from fewer
inputs.

7.2 Production Function

A production function is a function that specifies the output of a firm, an industry, or an entire

economy for all combinations of inputs. In other words, it shows the functional relationship
between the inputs used and the output produced.
Mathematically, the production function can be shown as:
Q = f (X , X ..................X )
1 2 K
where,
Q = Output,
X .............. X = Inputs used.
1 K
For purposes of analysis, the equation can be reduced to two inputs X and Y. Restating,
Q = f (X, Y)
where,
Q = Output

X = Labour
Y = Capital

A more complete definition of production function can be:
‘A production function defines the relationship between inputs and the maximum amount that

can be produced within a given period of time with a given level of technology’.
A production function can be stated in the form of a table, schedule or mathematical equation.
But before doing that, two special features of a production function are given below:

1. Labour and capital are both unavoidable inputs to produce any quantity of a good, and
2. Labour and capital are substitutes to each other in production.
Production function can be written in many ways, but the multiplicative form is most widely
used

a
Q = Ak L b
This is also referred to as the Cobb-Douglas production function. So a Cobb-Douglas Production
function with parameters A = 100, a = 0.5 and b = 0.5 will be

0.5
Q = 100 K L 0.5
Q = 100 KL

Given this production function, if two units of labour and four units of capital are used, maximum
production is 283 units of output.
Another form is the Constant Elasticity of Substitution, CES function,
Q = B[gL + (1 – g)K] –1/h
–h
where h > –1 and B, g and h are constants.

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