PRODUCTION FUNCTION

PRODUCTION FUNCTION
The production function is a statement of the relationship between a firm’s scarce resources (i.e. its inputs) and the output that results from the use of these resources. More specifically, it states technological relationship between inputs and output. The production function can be algebraically expressed in the form of an equation in which the output is the dependent variable and inputs are the independent variables. The equation can be expressed as:

                                        Q = f (a, b, c, d …….n)

Where ‘Q’ stands for the rate of output of given commodity and a, b, c, d…….n, are the diuerent factors (inputs) and services used per unit of time.

Assumptions of Production Function: There are three main assumptions underlying any production function.

First we assume that the relationship between inputs and outputs exists for a specific period of time. In other words, Q is not a measure of accumulated output over time.

Second, it is assumed that there is a given “state-of-the-art” in the production technology. Any innovation would cause change in the relationship between the given inputs and their output. For example, use of robotics in manufacturing or a more eflcient software package for financial analysis would change the input-output relationship.

Third assumption is that whatever input combinations are included in a particular function, the output resulting from their utilization is at the maximum level.

The production function can be defined as:
The relationship between the maximum amount of output that can be produced and the input required to make that output. It is defined for a given state of technology i.e., the maximum amount of output that can be produced with given quantities of inputs under a given state of technical knowledge. (Samuelson)
It can also be defined as the minimum quantities of various inputs that are required to yield a given quantity of output.

The output takes the form of volume of goods or services and the inputs are the diuerent factors of production i.e., land, labour, capital and enterprise. To illustrate, for a company which produces beverages, the inputs could be fixed assets such as plant and machinery; raw materials such as carbonated water, sweeteners and flavourings and labour such as assembly line workers, support-stau and supervisory personnel.

For the purpose of analysis, the whole array of inputs in the production function can be reduced to two; L and K. Restating the equation given above, we get:

Q = f (L, K). 

Where

 Q = Output

 L= Labour

K= Capital

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