Production Function: Concept, Assumptions & Law of Diminishing Return

1 year ago

Atiqur Rahman

11 minutes

Introduction

Production is the process of converting the inputs or raw materials into the outputs or the final goods. The rate at which the inputs can be converted into output is governed by the laws of production. Laws of production are also known as theory of production or laws of returns.

Theory of production explains the relationship between the inputs and the outputs and how the change in the inputs leads to a change in the outputs. There are various inputs which are required in the production but for simplicity economists have taken only four factors of production namely, land, labour, capital and entrepreneur, where each factor of production renders its services in order to produce the final good and in return it is paid factor payment.

Since nothing comes free, therefore, factors of production also have a cost and that cost is known as factor payment, where land earns rent, labour get wages, capital earns interest and entrepreneur gets profit.

Hence, the production of a commodity involves cost of production, which is in turn the main component of the supply of the commodity. Moreover, cost of production shows cost – output relationship i.e. how the change in the output leads to a change in the cost of production.

Concept of Production Function

Production function shows the relationship between the output and inputs. In other words it shows that output is a function of inputs (land, labour, capital and entrepreneur) and how the change in inputs affects the change in the output.

Mathematically:

Q = f (LA, L, K, E)

This is known as production function, where LA is land, L is labour, K is capital and E is entrepreneur.

Moreover, the production function also represents the technology of a firm, of an industry or of the economy as a whole. A production function may take the form of a schedule or table, a graphed line or curve, an algebraic equation or a mathematical model. But each of these forms of a production function can be converted into its other forms.

However, for the simplicity purpose, the economists have modified the above production function into:

Q = f (L, K)

Where the quantity of goods produced i.e. production depends on labour and capital.

Short-run and Long-run Production Functions

In short run some factors of production are fixed and some are variable, whereas in long run all factors are variable. Thus, a short run production function has inelastic capital i.e., the capital is fixed in short run and elastic labour i.e., labour is variable. In other words, output can be increased by increasing labour only because capital is fixed.

On the other hand, long run production function all the factors of production are variable i.e., output can be increased in long run by increasing either one or both of labour and capital.

Hence, in long run the supply of both labour and capital is elastic in nature. Therefore, the short run production is also known as single variable production function and it is termed as:

Q = f (¯K, L)

Here a bar on K represents that capital is fixed and the producer cannot infuse more capital in the production in short run, whereas labour, L, is variable and changeable.

Hence, the laws of production under short-run conditions is called ‘the law of variable proportions’, the ‘law of returns to a variable input’ and the ‘law of diminishing marginal returns’; whereas, in the long-run, it is known as the ‘law of returns to scale’.

Assumptions of Production Function

Both inputs and output are divisible.
Only two factors of production, i.e., labour and capital.
Labour and capital are imperfect substitutes.
Constant technology i.e. technology is given.
Inelastic supply of the fixed factors in the short run.
Elastic supply of the factors in the long run.
Producer is rational.

Law of Return to a Variable Proportions (Short-run Law of Production)

Assumptions of law of variable proportions:

Technology is given
Homogeneous labour
Capital is fixed/constant

The law of returns to a variable proportions states that when output is increased by using only one variable input, as the all other inputs is fixed, then initially the output increases as an increasing rate, then at a constant rate and finally it keep on increasing at a diminishing rate.

In other words, if more and more of labour is used then the output initially increases at an increasing rate, when more labour is again used then the output increases at a constant rate and then when again the labour is increased then the output increases but it increases at a diminishing rate. The ultimate law is that the marginal increase in total output eventually decreases when additional units of a variable factor are applied to a given quantity of fixed factors.

Accordingly, there are three laws of returns to variable inputs as follows-

(i) the law of increasing returns
(ii) the law of constant returns and
(iii) the law of diminishing returns.

In order to understand this law it is important to understand few concepts first.

Total product (TP_L) is defined as the total output produced with the help of labour.

Average product (AP_L) is defined as total product divided by the number of labour used in the production process.

Marginal product (MP_L) is defined as the additional output produced by employing / increasing one more labour. That is, TP_L – TP_L-1 = MPL.

Hence, given the number of workers and total product, average product and marginal product can be derived in the following way:

Table: Total, Marginal and Average Products

Three Stages in the Law of Diminishing Returns

As represented in the above table. In Stage-I, total product increases as an increasing rate as labour increases. This is indicated by the rising marginal product until the employment of the fifth worker; after that, the fifth and sixth labour represents a constant return to a variable factor.

In Stage-II, total product is still increasing but this time it is increasing at a diminishing rate which is indicated by a falling marginal product. This stage is hence known as the stage of diminishing returns to a variable factor, as in this stage when more of labour is used, the total product increases at a diminishing rate. In this stage the total product also reaches to its maximum, as in the table above, total product reaches to its maximum at 600 at tenth labour, but when the labour is increased from tenth to eleventh and twelfth then the total product started falling and correspondingly marginal product becomes negative. This is known as Stage-III of negative returns.

Hence the three stages represents that the total product initially increases at an increasing rate and marginal product also increases but when more labour is used then it start increasing at a diminishing rate and marginal product start falling but when the total product reaches to its maximum and then when the labour is still increased then the total product do not increase rather it falls and correspondingly the marginal product becomes negative. This can be represented in the following diagram:

Three Stages in the Law of Diminishing Returns

The above diagram can be summarized in the following points:

Increasing returns: Both TP and MP increases at an increasing rate.
Decreasing / diminishing returns: TP increases at a diminishing rate and MP starts falling.
Negative returns: TP reaches to its maximum and then falls and correspondingly MP reaches zero and then becomes negative.

Relationship Between AP and MP:

Increasing returns: Both AP and MP increases but MP increases at an increasing rate as compare to AP and reaches to its maximum.
Decreasing / diminishing returns: MP starts falling whereas AP increases at a diminishing rate and reaches to its maximum.
Negative returns: MP touches the x- axis i.e. becomes zero and goes to negative but AP continues to fall.

In other words, the features of the three stages of production may be described as follows:

● Stage I: The marginal product of the variable factor (labour) is higher than its average product, i.e., MP_L > AP_L

● Stage II: The marginal product of the variable factor (labour) falls below its average product, i.e., in Stage II, MP_L < AP_L, but both remaining greater than zero.

● Stage III: The marginal product of the variable factor (labour) turns negative, while average product remains greater than zero.

Factors Behind the Law of Returns to a Variable Factor

One of the main factors behind the increasing returns to a variable factor is the indivisibility if the fixed factor capital. It is because when more and more of labour is used with a given amount of capital then the utilization of capital increases along with the increase in the productivity of labour.

On the other hand, if the labour is less than the optimum number, then it results into underutilization of capital and lower productivity of labour because since the capital is indivisible so each unit of capital requires an optimum number of labours.

Another reason for the increase in labour productivity is that employment of additional workers gives the advantages of division of labour, until optimum capital–labour combination is reached.

However, once the optimum capital–labour ratio is reached, employment of additional workers amounts to substitution of capital with labour. But, technically, one factor can substitute another only to a limited extent.

Hence, to replace the same amount of capital, more and more workers will have to be employed because per worker marginal productivity decreases and this leads to diminishing returns to labour.

Production Function: Concept, Assumptions & Law of Diminishing Return

Introduction

Concept of Production Function

Short-run and Long-run Production Functions

Assumptions of Production Function

Law of Return to a Variable Proportions (Short-run Law of Production)

Three Stages in the Law of Diminishing Returns

Factors Behind the Law of Returns to a Variable Factor

Read More- Microeconomics

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Introduction

Concept of Production Function

Short-run and Long-run Production Functions

Assumptions of Production Function

Law of Return to a Variable Proportions (Short-run Law of Production)

Three Stages in the Law of Diminishing Returns

Factors Behind the Law of Returns to a Variable Factor

Read More- Microeconomics

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