## What is Production Function?

Meaning of Production Function: – Production function is the equation that expresses the relationship between the quantities of productive factors (such as labour and capital) used and the amount of product obtained. It states the amount of product that can be obtained from every combination of factors, assuming that the most efficient available methods of production are used.

Production is the result of four factors of production i.e., land, labor, capital and organization support. This is evident from the fact that no single commodity can be produced without the help of one of these four factors of production.

Therefore, the manufacturer combines all four factors of production to technical ratios. Profit maximization is the only aim of the producer. For this, he decides to maximize production at the lowest cost through the best combination of factors of production.

The manufacturer achieves the best combination by applying the principles of same-marginal return and substitution. According to the principle of equilateral returns, the maximum output of any product can be achieved, when the marginal return of all the means of production is equal to each other.

## What is the relationship between Input and Output?

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

Thus, the production function shows how much production we can expect if we have too much labor and so much capital as well as labor. In other words, we can say that the production function is an indicator of the physical relationship between the two inputs and outputs of a firm.

Mathematically, such a basic relationship between input and output can be expressed as: –

Q = f(L, C, N)

Where ‘Q’ = quantity of output

‘L’ = labor

‘C’ = capital

‘N’ = land.

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

Q = F (L, C)

## Definition of production function by different professors

Prof. Koutsoyiannis: – Defined as, “The production function is purely a technical relation which connects factor inputs and output.”

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

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

Prof. Richard J. Lipsey: – “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.”

Thus, from the above definitions, we can conclude that the production function reflects the relationship between the physical quantity of inputs and outputs obtained over a period of time, for a certain state of technical knowledge.

## What are the features of Production Function?

The main features of production function are as follows: –

1. Substitutability: – Thus the quantity of any output can vary with changes in the quantity of even one input while keeping other factors constant.
2. Complementary: – Therefore, a producer can produce the output by mixing the factor inputs together. If the quantity of any input is zero, the output cannot be produced.
3. Specificity: – For example, raw materials, specialized labor, machines, and equipment can be used for the production of the specific product. However, all these factors of production are not completely specialised as they can also be used in the production of other products.
4. Production Time: – Production of any type of product requires time. Production can only be possible in the long run. In the production function, the variation in total output is due to the variation in input quantity. The quantity of a single input may be possible in a short period of time.

## What are the characteristics of Production Function?

The characteristics of Production Function are as follows: –

1. A production function is a representation of the functional relationship between the amount of input employed and the amount of output produced.
2. This shows the technical relationship between inputs and outputs which are in physical form.
3. It also denotes the flow of input that will produce the flow of output over a specific period of time.
4. The state of technology affects production. A change in the state of technology will also change the production function. Improvement in the level of technology will increase the output level, even if the amount of input remains the same.
5. A production function has no monetary significance; It only shows the physical relationship.

## What are the types of production functions?

There are two types of production operations; they are short run and long runs: –

1. Short Run Production Function:
1. In short time period, the factors of production are fixed and variable.
2. In short run, it is not possible to change factors of production because of very less time.
3. A manufacturer cannot change the amount of capital such as machines, tools, equipment, factory houses, etc.
4. The manufacturer may change variable factors of production such as units of labor.
5. Factors of production that are given in quantity in the short term are known fixed factors of production.
6. Factors of production whose quantity can be changed are called variable factors of production.
7. Short-run refers to a period of time that is too short to allow a manufacturer to change its plant capacity, yet it is sufficient to change the level at which the fixed plant is used.
8. The short-term production function is written as: – Q = f (L) where, ‘Q’= Quantity of output and ‘L’= Labour
9. For example, an agricultural firm has 10 units of labor and 6 acres of land. Here, land is the constant factor and labor is the variable factor. The firm initially uses only one unit of labor (variable factor) on its land (constant factor). Hence the land-labor ratio is 6: 1. If the firm uses 2 units of labor, the land-labor ratio becomes 6: 2 or 3: 1.
1. Long Run Production Function: –
1. In long-term production, all functions, factors of production are variable.
2. In a long-run output, all inputs are variable in a single output.
3. When long term is used to explain, it is called the law of returns on the scale.
4. In long run we measure that by how much proportion the output changes if we change the proportion of input.
5. From the point of view of existing firms, the long term refers to the period that is sufficient to allow these firms to change the quantities of all resources which are employed in the production, including plant capacity.
6. The producer can convert all inputs and establish the necessary plant capacity to maximize profit.
7. Long run production can be written as: – Q= f(L,C) Where, ‘Q’= Quantity of output, ‘L’= Labour and ‘C’= Capital
8. All production resources or inputs are variable over the long term.
9. For example, the builder can build a new building or expand an existing building, buy more new machines and equipment, open more branches of a production unit, buy more land to expand the firm’s size, can hire more and skilled workers, change production and managerial technology, etc.