Me 5

Production Analysis

Meaning of Production:

The term“Production”means transformation of physical “inputs” into physical “outputs”.

The term “inputs” refers to all those things which are required by the firm to produce a particular product.

The term “output” refers to finished products.

In the words of Prof J. R. Hicks, “Production means any activity whether physical or mental which satisfy the wants of other people through exchange”.

Production Function

Meaning of Production Function:

A production function refers to the functional relationship, under the given technology, between physical rates of input and output of a firm, per unit of time.

In other words, it shows for a given technology (technique) of production the output that can be obtained from various levels of factor inputs, during a given period of time.

Since it relates inputs to outputs it is also called as, “Input-Output Relation”.

In algebraic terms the production function may be written as,

Q = f (a, b, c, d, ……….n, T)

Where Q=physical quantity of output per unit of time.

f =functional relationship.

a, b, c, d, n = quantities of various inputs per unit of time.

T = prevailing state of technology or know how

Types of Factor Inputs:

• Fixed factors

• Variable factors

This distinction holds good in the short run. In the long run all factors will become variable in nature.

Types of Production Functions:

• Short run Production Function

• Long run Production function

Short run Production function

• In this case producers will keep all fixed factors as constant and change only a few variable factor inputs. In short run we have two production functions:

A. Quantities of all the inputs both fixed and variable will be kept constant and only one variable input will be varied.

Ex: The Law of Diminishing Returns.

B. In this case keeping all the inputs constant, only two variable factor inputs are varied.

Ex: Iso - Quants and Iso - Cost curves.

Long run Production Function

In this case producer will vary the quantities of all factor inputs in the same proportion.

Ex: The Law of Returns to Scale.

The Law of Variable Proportions(or) The Law of Diminishing Returns

The Law of Variable Proportion explains how variation in one factor input leads to variations in output, keeping the quantities of other factors fixed.

According to Prof. Benham, “As the proportion of one factor in a combination of factors is increased, after a point, first the marginal and then the average product of that factor will diminish”.

Assumptions of the Law

1) Only one factor unit is to be varied, while all other factors should be kept constant.

2) Different units of variable factors are homogenous.

3) Techniques of production remain constant.

4) The law will hold good only for short and given period.

5) It is possible to vary the proportion in which the various inputs are considered.

Trends in Output

From the above table we can observe the we can observe the following tendencies in TP, AP and MP:

1. Total output goes on increasing as long as MP is positive. It is the highest when MP is zero and TP declines when MP becomes negative.

2. MP increases in the beginning, reaches highest point and then diminishes at the end.

3. AP will have the same tendencies as the MP. In the beginning MP will be higher than AP but at the end AP will be higher than MP.

Explanation of diagrammatic representation

From the diagram it is clear that there are three stages:

I. First stage : The Law of Increasing Returns

II. Second stage : The Law of Diminishing Returns

III. Third stage : Negative Returns

Uses in Decision Making / Practical Importance

i. It helps to work out the more ideal combination of factor inputs or the least cost combination of factor inputs.

ii. It is useful to a businessman in the short run production planning at the micro level.

iii. The law gives guidance, that by making continuous improvements in technology, the producer can postpone the occurrence of diminishing returns.

Cobb-Douglas Production Function

This is more realistic in approach, as it consider two variable factor inputs at a time.

Q = f (L, k, )

Where L = Labour

K = Capital

= factor (fixed) component of input.

For empirical measurement, the Cobb-Douglas production function is presented with power terms as : Q = aLK

Where Q = total output

L = Labour units – input

K = Capital units – input

• It is widely used in empirical research on production.

• In estimating regression of a Cobb-Douglas production function, it showed the transformation into a linear form by using double log terms.

Log Q = log a + b log L + c log K

Iso-quants and iso-costs

There are a large number of combinations of factor inputs which can produce a given output and the producer has to select the most economical combination out of them.

Iso quant curve is a technique developed in recent years to show the equilibrium of a producer with two variable input.

Meaning and definitions:

The term ‘Isoquant’ consists of 2 words – ‘iso’ and ‘quant’. ‘Iso’ means ‘equal’ and ‘quant’ means ‘quantity’.

Therefore Isoquant curve means Iso-product curve or equal product curve or constant product curve.

Iso-product curve may be defined as “ A curve which shows the different combinations of two inputs producing the same level of output”.

• According to Prof. Keinstead, “ Iso-product

Curve represents all possible combinations of two factors that will give the same TP”.

The following table shows the various hypothetical combinations of 2 factor inputs-labour and capital, which are capable of producing the same quantity of output –100 units of a commodity.

Iso-Quant Map

• A catalogue of different combinations of inputs with different levels of output shown on a graph is called as Iso-quant map or equal-product map.

• In other words, a number of isoquants representing different quantities of output are known as Iso-quant map.

Diminishing Marginal Rate of Technical Substitution (DMRTS)

• The DMRTS measures the rate of reduction in one factor for an additional unit of another factor in the combination, without affecting any change in the quantity of output .

Properties Of Iso-Quants / Equal Product Curves

1. The Iso-quant curves slope downwards from left to right – This is so because, if one factor is increased, another factor must be reduced in order to produce the same quantity of output.

2. Iso-quant curves cant intersect each other – This is so because the amount of factors required to produce 100 units of a commodity

cant be equal to the amount of factors required to produce 200 units of a commodity.

3. Iso-product curve lying to the right or higher level indicates the higher level of output and vice versa.

4. The Iso-quant curves are convex to the point of origin . The convexity of the curve is due to the DMRTS.

5. An Iso-product curve will not touch either X or Y axis.

Iso – cost Curves or Lines:

An Iso-cost line is a line which shows various combinations of two inputs that the firm can buy at given prices with a given outlay. It shows two things:

1. Prices of two inputs

2. Total outlay of the firm.

• Factor X : Rs. 50/unit

• Factor Y : Rs. 40/unit

X Y

At Rs. 2000 50 40

At Rs. 3000 75 60

At Rs. 4000 100 80

Producers Equilibrium (Least cost combination of factors)

• The producing firm needs two instruments to find out the equilibrium position. They are:

1. Its Iso-quant map

2. Its Iso-cost line

An iso-product curve represents different possible combinations of two factor inputs with the help of which a given level of output can be produced. On the other hand, an Iso-cost line shows the total outlay of the producer and the prices of factors of production.

Laws of Returns to Scale

The Laws OF Returns To Scale

• The LRS explain the behavior of output in response to a proportional and simultaneous change in inputs.

Three technical possibilities:

Increasing returns to scale

Total output may increase more than proportionately.

Constant returns to scale

Total output may increase proportionately

Decreasing returns to scale.

Total output may increase less than proportionately .

1. Increasing Returns to Scale

When a certain proportionate increase in both the inputs K and L leads to more than proportionate increase in output ,it exhibits increasing returns to scale

The causes of increasing returns to scale:

• Higher degree of specialization

Certain inputs cannot be divided into parts to suit small scale production.

• Technical and managerial indivisibilities

Use of specialized labour and modern machinery increases productivity for variety of inputs.

• Dimensional relations

Length and Breadth

15*10=150 sqft

30*20=600 sqft

2. Constant Returns to Scale

When an increase in inputs results in proportionate increase in output , it is called constant returns to scale.

3.Decreasing Returns to Scale

When a certain proportionate increase in inputs K and L leads to less than proportionate increase in output ,it exhibits decreasing returns to scale.

• Causes:

Decrease in managerial efficiency

Exhaustibility of natural resources