LAWS OF RETURNS: PRODUCTION FUNCTION

 

LAWS OF RETURNS

PRODUCTION FUNCTION

A production function shows the maximum quantity of a commodity that can be produced per unit of time with the given amount of inputs, when the best production technique available is used.

For example, a production function for a shoe-making factory may indicate that a certain (maximum) quantity of shoes can be produced per day with given quantities of leather, glue, workers, machinery, etc.

A production function may be expressed in the form of a table graph or an algebraic equation. In the form of an algebraic equation, the production function for a good may be expressed as:

Qx = f(f1,f2……fn)

Where Qx is the quantity of output of commodity X; and f1,f2….fn are the quantities of different inputs used to produce the commodity X.

If we assume that there are only two inputs, viz. labor(L) and capital(K), then the simple production function can be stated as:

Qx = f(L,K)

In this simple production function, the quantity of commodity X produced is the function, ie. depends upon the quantity of L and K.

Features of Production Function

1.      A Production function is expressed with reference to a particular period of time, say a day or a month since both inputs and output involve flow.

2.      It expresses a physical relation because both inputs and outputs are expressed in physical terms.

3.      Production function describes a purely technological relation because what can be produced from a given amount of inputs depends upon the state of technology.

SHORT RUN AND LONG RUN

Short Run

Short run refers to the period of time over which the amount of some inputs, called the ‘fixed factors’ cannot be changed.

For example, the amount of plant and equipment, etc, is fixed in the short run. This implies that an increase in output in the short run can be brought about by increasing those inputs that can be varied, known as ‘variable inputs’.

 

Long Run

Long Run is defined as the time period during which all factors of production can be varied.

A firm installs a new plant or raises a new factory building. Long run is the period during which the size of the plant can be changed. Thus all the factors are variable in the long run; meaning that their quantities can be changed.

Types of Production Functions

·       Short run Production Function: A short run production function refers to a situation when only one input is variable and all other inputs are assumed to be constant.

Here, we study the effect of change in the quantity of one input on the total output by keeping all other inputs constant.

Short run production function is the subject matter of law of variable proportions, or what the classical economists have named as ‘laws of returns’.

·       Long run Production Functions: A long run production function refers to a situation when all the inputs are variable. It shows the changes in outputs when all inputs used in production of a commodity are changed simultaneously and in the same proportion.

Long run production function is the subject matter of ’returns to scale’.

 

Some Basic Concepts-Total ,Average and Marginal Physical Products

·       Total Product(TP): Total product or total physical product refers to the total amount of a commodity produced during some period of time by combining a particular quantity of a variable factor with the fixed factor. It is also called total returns.

·       Average Product(AP): Average product or average physical product of a available factor refers to the output per unit of a variable factors. It is also called ‘average returns’.

It is found simply by dividing the total product by the total number of variable factor, which is labor in our example.

APL=TPL/L or Qvf

·        Marginal Product (MP): Marginal product or marginal physical product may be defined as the change in the total product resulting from one additional unit of a variable factor. It is also called marginal returns.

MPL = ΔTP/ΔL

Where ,                       MPL  is the marginal product of a variable factor, labor

TP is the change in the total product

L is the change in variable factors

In other words,

MPnth = TPn - TP(n-1)

 

Returns to a Factor –Laws of returs to a Variable Factor

Returns to a factor means change in the physical output of a good when the quantity of one factor is increased while that of the other factors is increased while that of the other factors remains constant.

It is a short run phenomenon.

 

Variation of output in the Long Run-Returns to Scale

When all inputs are changed in the same proportion, we call this as change in scale of production. The way total output changes due to change in scale of production is known as the ‘law of returns to scale’.

 

Economies of scale refer to the situation on which increase in the scale of production gives rise to certain benefits to the producers.

Economies of scale are generally classified into

·        Internal economies

·        External economies

 

Internal economies

Internal economies are those economies which arise from the expansion of the plant size of the firm.

·       They are internal in the sense that they accrue to the firm when its output or scales increases.

·       They are specific to firms, and they are enjoyed only by those firms which expensed their scales.

·       Some of the internal economies are: use of better techniques, greater specialization, good management, marketing economies, economies of transport etc.

External economies

External economies are those economies which arise as a result of expansion of the whole industry.

·       These economies are external in the sense that they accrued to a firm because of the factors that are entirely outside the firm.

·       The economies are general and common to all the firms in an industry.

·       Some of the external economies are : availability of cheaper inputs, availability of improved technologies, supply of skilled labor, development of ancillary industries, economies of localization in a particular area.

Internal diseconomies

Internal diseconomies are those diseconomies which are experienced by a particular firm which increases its production or scale beyond a point.

Some of the internal diseconomies are: difficulty of management, inefficiency of labor, technical diseconomies.

External diseconomies

External diseconomies are those disadvantages which arise because of the expansion of the scale of production of the industry beyond management limits.

These diseconomies are general and are common to all the firms. Some of the external diseconomies are: costlier transport, shortage of skilled labours, powe etc.

 

LAWS OF VARIABLE PROPORTIONS

LAW OF RETURNS TO A FACTOR OR LAW OF VARIABLE PROPORTIONS

The Law of diminishing returns is actually the old name of the Law of Variable Proportions. The Law of Returns to factors means change in physical output of a good when the quantity of one factor is increased while that of the other factors remains constant. It is a short run phenomenon.

The Law states, “That as more and more units of a variable factor are applied to a given quantity of a fixed factor, the total product may initially increase at an increasing rate, but eventually it will increase at diminishing rate. This Law was formulated by Prof. Joan Robinson and other modern economists. This law is applicable to all sectors of an economy.

The Law of returns to factor expressed in terms of Average Product(AP) and Marginal Product(MP) and it seen that MP and AP of the variable factor i.e. labour will eventually decrease after increasing initially as the amount of fixed i.e. capital is held constant.

The assumptions of the Law are as follows:

(1)    The state of technology is given and remains constant.

(2)    Some inputs are kept and others are varied.

(3)    The technology should be such that it is possible to change factor proportions.

The law will not apply where the factors are used in fixed proportions.

(4)    All units of the variable factor i.e. labour should be homogenous and equally efficient.

 

The Law can be divided into three distinct stages:

(1)   Increasing returns to a Factor.

(2)   Diminishing returns to a factor.

(3)   Negative returns to a factor.

 

The law can be explained with the help of a table and illustrations:

No.  of units of   labour	Marginal product	Total product	Average
1 2 3 4 5	100 120 140 160 130	100 220 360 520 650	100 110 120 130 130	Stage-1
6 7 8 9	100 90 40 0	750 840 880 880	125 120 110 97.7	Stage-2
10 11	-50 -60	830 770	83 77	Stage-3

 

It has been assumed that capital (5 machines) is a fixed factors and its quantity remains unchanged at 5 units, whereas labour is a variable factor and it increases from 1 to 11.

(1)    The table shows that as the amount of labour increases, the total product (TP) Increases up to the 8^th unit. Initially TP increases at an increasing rate because MP rises- this tendency can be observed up to the employment of the 4^th unit of labour.

(2)    From employment of the 5^th unit of labour, TP increases at a diminishing rate as MP starts falling.

(3)    On the employment of the 9^th unit of labour TP reaches the maximum as MP becomes zero.

(4)    If the producer tries to employ any further units of TP declines.

Thus the law proves that as additional units of; labourers are employed without expanding capital, MP decreases.

 

 

 

DIAGRAM -1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DIAGRAM-2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Diagram-2 shows MP and AP curves which we get by plotting MP and AP on the Y-axis and units of the labour on the X-axis.

Stage-1

·       Thus, we see that TP increses at an increases rate upto point M in diagram-1, where MP is maximum as shown in diagram-2 upto the employment of L₁ units of labour.

·       Beyond point M, in diagram-2 as MP starts falling as in shown by the negative slope of the MP curve, we see that TP increases in diminishing manner beyond M as shown in diagram-1 upto the employment of L₂, units of labour when the MP curve cuts the AP curve at the highest point of AP as shown in diagram-1 i.e. point A.

     Stage-2

·       When the labour employment exceeds L₂ as shown in diagram-2 AP and MP falls continuosly, till MP is equal to zero. At this point it is seen that TP reaches its maximum at point T in diagram-1, i.e. when L₃ units of labour are employed, MP coincides with X-axis.

Stage-3

·       Beyond the employment of L3 units of labour MP becomes negative as shown by MP curve going below the X-axis in diagram-2 when TP declines as is shown in diagram-1.

Thus the law proves that as more and more units of a variable factor are employed beyond optimum point, the factor proportion becomes unsuitable and inefficient, hence, MP declines.

Relation between Marginal Product and Total Product can be summarized as:

·        When MP rises and the MP curve is positively inclined, TP increases in an increasing manner.

·        When MP falls and the MP curve is negatively inclined, TP increses in a diminishing manner

·        When MP is zero and the MP curve touches th-axis, TP is at its maximum point.

·        When MP is negative and the MP curve goes below the X-axis, TP declines and becomes negatively inclined.

Relation between  Average Product and Marginal Product

·       When AP rises MP curve is above it because MP is greater than AP while rising (MP>AP).

·       When AP is at maximum point MP falls,while falling they intersects at that pint where they both are equal to one another(MP=AP).

·       When AP falls, MP curve goes below it, as MP is less than AP while falling (MP<AP).

Diffrentiate Between:

Returns to a variable factor	Returns to scale
1.      Applies in the short run	Apllies in the long  run
2.     In this law levelof production is changed	In this law scale of production is changed
3.     In this law, only the units of the variable factors are changed while the units of fixed actors remains unchanged	In this law, all factors of productin are changed in the same proportion
4.     This law shows increasing decresing and negative returns to a factor	The law shows increasing, diminishing and constant return to a scale.
5.     This law becmes operative because of the efficient utilization of the fixed factors at the initial stages and the employment of variable factor beyond the optimum proportion (K/L) at the subsequent stage.	This law becmes operative because of economies of large scale production at the first stage and some diseconomies of large scale production at the subsequent stage.
6.     in this case, the factor proportions are changed i.e K/L ratio changes which means L changes with K constant.	In this case K/L ratio remains unchanged, since both K and L are increased by same percentage.

Causes of increasing Returns to a Factor

Following are the reasons for increasing returns to a factor-

(1)    Fuller utilization of fixed factors- Fixed factors are generally indivisible, i.e. we cannot divide them as per our requirement. Due to technical reasons, certain minimum quantity of factors has to be used whatever be the level of the output. Thus certain minimum labour is required to make optimum use of the fixed factor. If fewer workers are used, some machinery will remain unutilised. This is what happens in the first stage. In the beginning the amount of fixed factor is too large, while the amount of variable factor is too small. Therefore the fixed factors remain unutilized. Therefore if the numbers of workers is increased, the machine (fixed factors) is utilized better and more effectively.

(2)    Division of labour- as the number of variable factor is increased in stage I, the efficiency of variable factor itself increases. This is because of the division of labour and specialization. With more labourers (variable factor), it is possible to divide the work among the labourers according to their skill and aptitude. These results in specialization and increases in efficiency.

 

Causes of diminishing returns

Diminishing returns to a factor arise due to following reasons:

(1)   Disturbing the optimum proportion. As more and more quantity of the variable utilized. But there is a limit up to which it happens. There is an optimum combination of fixed and variable factors when the fixed factors is fully and efficiently utilized. If more and more workers are put on the fixed factor, optimum factor combination is disturbed. This leads to a fall in the average and marginal product.

(2)   Imperfect substitutability of factors of production. Upto some stage, we can substitute one factor for another factor. For example, more labour can be employed in place of capital. But there is a limit to which one input can be substituted for another. Therefore, diminishing returns will operate because we cannot effectively substitute labour for capital.

Causes for Negative Returns

(a)   Overcrowding. If we keep on adding variable factor (labour) with the given quantity of a fixed factor, this will lead to overcrowding on the fixed factor i.e. excessive variable factor (labour) on the given quantity of a fixed factor. There will be lower availability of tools and equipments per worker. This will cause a fall in productivity. Moreover, if there are too many workers on the given amount of fixed factors, they will come in each other’s way and disturb others. “Too many cooks spoil the broth” aptly applies to this situation.

(b)   Management Problem. Use of too much of variable factors like labour also creates the problem of effective management. When there are too many workers, they may shift responsibility to others. It becomes difficult to manage them. The labourers may avoid work. All this leads to decrease in efficiency.