Production is the act of transforming inputs into output. Production function relates inputs to output; it describes the technological relationship between the physical inputs that a firm uses and the physical output that it produces. This functional relationship between inputs and output, or the production function can be written as
Q = f (a, b, c, d .........n)
Where Q is the quantity of a good produced and a, b, c, d…..n are the quantities of various inputs used. The functional relationship is shown by letter f that shows the dependence of Q on inputs which means that Q is dependent variables, and a change in these independent variables causes a change in the dependent variable Q.
If capital and labour are the only two factors (inputs) used in the production process, then the production function can be written as
Q = f (L, K)
Where L is the quantity of labour used in production with K as the amount of capital. The production function is thus the algebraic expression of the relationship between the quantities of input and the resultant quantity of output of any given product.
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