Production theory can be divided into short run theory or long run theory.
Hence, a production function is defined as the maximum amount of output that can be produced (through the use of a given production technology) with a given amount of input.
A production function indicates the highest output (Q) that a firm can produce for every specified combinations of inputs (physical relationship between inputs and output), while holding technology constant at some predetermined state.
In other words, Production Function is a mathematical expression which defines the various combination between the input that help in producing optimum output.
Mathematically, we represent a firm’s production function as: Q = f (L, N,K,T, t)
Q= Production function
L= Land, K= Capital, N= Labour, T= Technology and t= Time
The production function is based on the assumptions:
Technology is invariant– It means that it won’t change as per the production.
Firm’s utilise their input at maximum level of efficiency.
We assume that all units of L and K are homogeneous or identical
The Production Function in the Short Run
The short run is a time period in which the quantity of some inputs, called fixed factors, cannot be increased. So, it does not correspond to a specific number of months or years. A fixed factor is usually an element of capital (such as plant and equipment).
Therefore, in our production function capital is taken to be the fixed factor and labor the variable one. This aspect of Production function is known as Law of Variable Proportion.
The Production Function in the Long Run
The long run is a time period in which all inputs may be varied but in which the basic technology of production cannot be changed. This aspect of Production function is known as Law of Returns to scale.
The long run corresponds to a situation that the firm faces when is planning to go into business (to expand the scale of its operations) Like the short run, the long run does not correspond to a specific length of time
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