# Production Function

23/02/2020

#### Meaning of Production Function

In simple words, production function refers to the functional relationship between the quantity of a good produced (output) and factors of production (inputs).

“The production function is purely a technical relation which connects factor inputs and output.” Prof. Koutsoyiannis

Defined production function as “the relation between a firm’s physical production (output) and the material factors of production (inputs).” Prof. Watson

In this way, production function reflects how much output we can expect if we have so much of labour and so much of capital as well as of labour etc. In other words, we can say that production function is an indicator of the physical relationship between the inputs and output of a firm.

The reason behind physical relationship is that money prices do not appear in it. However, here one thing that becomes most important to quote is that like demand function a production function is for a definite period.

It shows the flow of inputs resulting into a flow of output during some time. The production function of a firm depends on the state of technology. With every development in technology the production function of the firm undergoes a change.

The new production function brought about by developing technology displays same inputs and more output or the same output with lesser inputs. Sometimes a new production function of the firm may be adverse as it takes more inputs to produce the same output.

Mathematically, such a basic relationship between inputs and outputs may be expressed as:

Q = f( L, C, N )

Where Q = Quantity of output

L = Labour

C = Capital

N = Land.

Hence, the level of output (Q), depends on the quantities of different inputs (L, C, N) available to the firm. In the simplest case, where there are only two inputs, labour (L) and capital (C) and one output (Q), the production function becomes.

Q =f (L, C)

Definitions

“The production function is a technical or engineering relation between input and output. As long as the natural laws of technology remain unchanged, the production function remains unchanged.” Prof. L.R. Klein

“Production function is the relationship between inputs of productive services per unit of time and outputs of product per unit of time.” Prof. George J. Stigler

“The relationship between inputs and outputs is summarized in what is called the production function. This is a technological relation showing for a given state of technological knowledge how much can be produced with given amounts of inputs.” Prof. Richard J. Lipsey

Thus, from the above definitions, we can conclude that production function shows for a given state of technological knowledge, the relation between physical quantities of inputs and outputs achieved per period of time.

#### Features of Production Function

Following are the main features of production function:

1. Substitutability

The factors of production or inputs are substitutes of one another which make it possible to vary the total output by changing the quantity of one or a few inputs, while the quantities of all other inputs are held constant. It is the substitutability of the factors of production that gives rise to the laws of variable proportions.

1. Complementarity

The factors of production are also complementary to one another, that is, the two or more inputs are to be used together as nothing will be produced if the quantity of either of the inputs used in the production process is zero.

The principles of returns to scale is another manifestation of complementarity of inputs as it reveals that the quantity of all inputs are to be increased simultaneously in order to attain a higher scale of total output.

1. Specificity

It reveals that the inputs are specific to the production of a particular product. Machines and equipment’s, specialized workers and raw materials are a few examples of the specificity of factors of production. The specificity may not be complete as factors may be used for production of other commodities too. This reveals that in the production process none of the factors can be ignored and in some cases ignorance to even slightest extent is not possible if the factors are perfectly specific.

Production involves time; hence, the way the inputs are combined is determined to a large extent by the time period under consideration. The greater the time period, the greater the freedom the producer has to vary the quantities of various inputs used in the production process.

In the production function, variation in total output by varying the quantities of all inputs is possible only in the long run whereas the variation in total output by varying the quantity of single input may be possible even in the short run.

SHORT RUN AND LONG RUN PRODUCTION FUNCTION

A short-run production function refers to that period of time, in which the installation of new plant and machinery to increase the production level is not possible. On the other hand, the Long-run production function is one in which the firm has got sufficient time to install new machinery or capital equipment, instead of increasing the labour units.

The production function can be described as the operational relationship between the inputs and outputs, in the sense that the maximum amount of finished goods that can be produced with the given factors of production, under a particular state of technical knowledge. There are two kinds of the production function, short run production function and long run production function.

Short Run Production Function

The short run production function is one in which at least is one factor of production is thought to be fixed in supply, i.e. it cannot be increased or decreased, and the rest of the factors are variable in nature.

In general, the firm’s capital inputs are assumed as fixed, and the production level can be changed by changing the quantity of other inputs such as labour, raw material, capital and so on. Therefore, it is quite difficult for the firm to change the capital equipment, to increase the output produced, among all factors of production.

In such circumstances, the law of variable proportion or laws of returns to variable input operates, which states the consequences when extra units of a variable input are combined with a fixed input. In short run, increasing returns are due to the indivisibility of factors and specialisation, whereas diminishing returns is due to the perfect elasticity of substitution of factors.

Long Run Production Function

Long run production function refers to that time period in which all the inputs of the firm are variable. It can operate at various activity levels because the firm can change and adjust all the factors of production and level of output produced according to the business environment. So, the firm has the flexibility of switching between two scales.

In such a condition, the law of returns to scale operates which discusses, in what way, the output varies with the change in production level, i.e. the relationship between the activity level and the quantities of output. The increasing returns to scale is due to the economies of scale and decreasing returns to scale is due to the diseconomies of scale.

The difference between short run and long run production function can be drawn clearly as follows:-

1. The short run production function can be understood as the time period over which the firm is not able to change the quantities of all inputs. Conversely, long run production function indicates the time period, over which the firm can change the quantities of all the inputs.
2. While in short run production function, the law of variable proportion operates, in the long-run production function, the law of returns to scale operates.
3. The activity level does not change in the short run production function, whereas the firm can expand or reduce the activity levels in the long run production function.
4. In short run production function the factor ratio changes because one input varies while the remaining are fixed in nature. As opposed, the factor proportion remains same in the long run production function, as all factor inputs vary in the same proportion.
5. In short run, there are barriers to the entry of firms, as well as the firms can shut down but cannot exit. On the contrary, firms are free to enter and exit in the long run.

To sum up, the production function is nothing but a mathematical presentation of technological input-output relationship.

For any production function, short run simply means a shorter time period than the long run. So, for different processes, the definition of the long run and short run varies, and so one cannot indicate the two time periods in days, months or years. These can only be understood by looking whether all the inputs are variable or not.