The production function is a purely technical relation, which related factor inputs and outputs. It describes the law of proportion, that is, the transformation of factor inputs into products (outputs) at any particular time period. The production function represents the technology of a firm or an industry, or of the economy as a whole. It gives us the maximum amount of output that can be obtained by employing different inputs.
A method of production (process or activity) is a combination of the factor inputs required for the production of one unit of output. Usually a good may be produced by various methods of production. For example, a unit of good X may be produced by any of the following processes:
|Process 1||Process 2||Process 3|
|Units of labor required||10||15||05|
|Units of capital required||15||15||20|
A process of production is technically efficient if uses less of at least one factor and no more from the other factors, compared to any other process of production. In our above example we see that the process 2 is technically inefficient compared to the process 1.
Let us consider a single production process in which an entrepreneur utilizes two variable inputs, labor (L) and capital (K) and one or more fixed inputs in order to produce a single output, Q. His production function states the quantity of his output Q as a function of the quantities of his variable inputs L and K.
Q = f (L, K)
The production function is constructed based on the assumption that the state of the technology is given and output can be increases by increasing inputs. When the technology changes, the production function itself changes. Further, it is assumed that the inputs are utilized in the best possible way, i.e. optimum utilization of inputs. The best utilization of any particular input combination is a technical, not an economic problem. Selection of the best-input combination for the production of a particular output level depends upon input and output prices and is the subject of economic analysis.
Graphically, the production function is usually presented as a curve where the changes of the relevant variables are shown either by movements along the curve or by shifts of the curve. For example, while representing the production function graphically we refer to the total productivity of labor in the production of Q that can be secured from input L, if capital is assigned a fixed value K0 or, Q = f(L, K0).