## Lesson 15. LAW OF RETURN

Module 3. Theory of production
Lesson 15
LAW OF RETURN

15.1 Introduction

Earlier economists differentiated between three laws of returns also referred to as laws of production viz., law of diminishing, increasing and constant returns. Modern economists are of the view that these three laws are really three aspects of same law viz., the Law of variable proportions. This chapter explains law of return.

15.2 Laws of Production

Laws of production explain the phenomena of production by organizations. These laws are classified into following categories.

a. Traditional View Point: Output can be produced by one or some factors fixed while other are kept variable. Law of diminishing marginal utility is based upon this traditional view point.

b. Modern View Point: Only one factor is variable while other factors are kept constant. Law of variable proportion is based upon this modern view point.

c. A type of production function in which quantities of all inputs can be changed to produce output of different quantities. This law is referred to as law of returns to scale.

15.2.1 Short run and long run production function

Production function is stated with reference to a particular period of time. In economics we are concerned with two types of production function : (i) the production function when the quantities of some inputs are constant and the quantity of one input is varied. This type of input-output relationship forms the subject-matter of the law of variable proportion. Secondly the productions function with all factors variable. This type of input-output relationship forms the subject-matter of the law of returns to scale.In case of short-run production function (variable proportion) some factors held constant and other factors are combined with varied proportion. The ratio of variable factor to that of the fixed factor goes on increasing on the quantity of the variable factor is increased. When all factors are increased in the same proportion the increase in output so obtained represents returns to scale. In the long run all factors are varied.

15.3 The Law of Diminishing Marginal Returns

This law was traditionally associated with agricultural production. In case of agricultural production land is a constant factor and other factor can be varied, when variable factors were varied during the experiments. Proportionate increase in output was not observed. Based upon this observation, law of diminishing marginal return was propounded which state that ' An increase in factors of capital and manpower applied to cultivation of land causes in general a less than proportionate increase in the amount of produce from the land, unless it is obtained by application of new improved scientific methods of agriculture’. This law was initially associated with only agricultural production but later on it was observed that it is applicable to all other field viz mining, fishing construction etc.

15.4 The Law of Variable Proportions

This is modern view point of traditional law of diminishing marginal returns. According to the law "As additional input of one factor in equal installment is carried out while keeping all other factor input constant, after a certain point, the output of the product also decreases i.e. the marginal product will decrease. To be more specific, "In the short run, as the amount of variable factors increase, other things remaining equal, output will increase more than proportionately to the amount of variable input in the beginning, then it may increase in the same proportion and ultimately it will increase less than proportionate.

15.4.1 Explanation of the law of variable proportion

(a) Total product: Total number of units of output obtained in a unit time by using all input factors.

(b) Average Product: Total product per unit of a given variable factor.

Marginal Product: The new additional total product obtained on addition of a unit of variable factor to the production process, keeping all other factors constant.

Table 15.1 Production with one variable input The above table indicates phenomena of law of variable proportion. The capital is fixed at 10 units and shown in first column. The labour units increase from zero to 10 units, shown in second column. The third column show the total output. The data of the table indicates that there is no production when labour unit is zero. Then as labour input increases, keeping the capital fixed, output increases first at an increasing rate and then at a decreasing rate, up to seventh unit of labour. At eighth unit, there is no increase in output. At seventh and eighth labour unit the output remains same as 448 units. Beyond eighth unit more units of labour is Counter Productive because output decrease as labour is increased. The average product shown in fourth column also increases initially then falls after fourth unit. The marginal product shown in fifth column also increases initially, then decreases and ultimately becomes negative, reason being use of variable input too intensively with the fixed input.

15.4.2 Example to illustrate law of diminishing returns

Agriculture economics department of agricultural university is conducting experiments on field to study various laws associated with economics. In one of the experiments, authorities have applied capital and labour in certain fixed quantities referred to as set. The number of such set are varied (increased) and its effect on output is judged which is shown in table below. The cost of each set is Rs 1000/-. The output from the farm and marginal output are shown in the table below.

Table 15.2 Total and marginal output  Fig. 15.1 Total and Marginal output

The experiment revealed that with increase in set, the additional returns in the form of marginal output goes on decreasing as shown in third column. The total output shown in second column increases but not at the same rate. It increases at diminishing rate. For example on application of one set, the output is 15 kg but on application of two sets, the output is 25 kg and not doubles. The total output also decreases after reaching a particular stage. In the above experiment, after sixth set the output decreases.

15.5 Law of Increasing Returns

This law is opposite to the law of diminishing returns. Here the return is more than proportionate. It results in lower cost per unit as production increases. In case of industries in which all input factor of production are available in abundant quantity all the time so that no defective combination of input factors occurs, the law of increasing returns applies. This law is also applicable up to the optimum point; beyond which laws of diminishing returns apply. Thus the law of increasing return is stated as "As the proportion of one factor in a combination of factors is increased, up to a point, the marginal product of the factor will increase.

15.5.1. Illustration

Suppose Ice Cream Cup manufacturing industry increases its investment in equal installments of Rs. 5000 each, the output of cups and its associated cost is shown in following table

Table 15.3 Law of increasing return From the table it can be said that as the Ice Cream Cup manufacturer goes on increasing investment by Rs. 5000 each, the total output goes on increasing, the cost of cup goes on decreasing and the marginal output goes on increasing. Fig. 15.2 Application of law of increasing returns

The law of increasing returns is applicable in manufacturing industries. Due to use of continuous machinery, specialized labour and lack of natural interferences like agriculture makes it possible to apply the law. Moreover due to large scale operations in industries, it is possible to realize internal and external economics in purchase, administration etc which facilitate cost savings.

15.6 Law of Constant Returns

This law states that irrespective of scale of production, the cost of product per unit remains the same. Here the return remains same weather business is expanded or contracted. The law of increasing return state that marginal return increases up to optimum level. If at this optimum level, operations are stabilized than law of constant return is achieved.

The milk can manufactures inverts Rs. 1 Lakhs in equal installments. The number of cans, cost and can and marginal output of cans is shown in table below.

Table 15.4 Investment and marginal output  Fig. 15.3 Investment and marginal output

The table and figure indicates that with increase in investment in equal proportion, the number of cans manufactured is also increased in equal proportion.

The law of diminishing marginal returns is application in sectors like agriculture when influence of nature is significant. The law of increasing return is applicable where man plays dominant role. In situations where the influence of both nature and man is balances, the law of constant returns is applicable.

In all industries influence of nature and men is evident. Nature influences raw material availability and man influences the production side. In dairy industry, the two aspects of agriculture and industry are combined and thus it is possible to apply the law constant returns.

In actual practice instead of three differed laws, only one law of variable proportion is applicable in all the industries. The stage of diminishing, increasing and constant return will vary. A rational manufacturer will manage the three stages optimally to derive maximum profit.

15.7 Expansion Path

The level of optimal factor proportions may change when output or factor-price ratio changes. Let us assume that the input prices do not change, but size of available budget to be spent on the input does change. Since input prices do not change, the relative input price structure is not affected. This means that the slope of the iso-cost curve remains the same. Under these circumstances, any change in the level of expenditure on inputs and hence in the level of output can effectuate a shift in the iso-cost curve. For example, if the top management decides to spend more on inputs: labour and capital, and if wage rate and interest rate have not changed, then there will be a parallel rightward shift in the iso-cost curve. As the there will be a parallel downward shift in the iso-cost curve. As the iso-cost curve thus shifts upward or downward, the point of producer’s equilibrium, satisfying the decision rule of proportionality may also change. For example, in Figure V. 9a when the iso-cost curve shifts from ML to M’L’, the equilibrium point shifts from e to e’; when the iso-cost curve shifts from ML to M”L”, the equilibrium points shifts from e to e" Fig. 15.4 Expansion path

The locus of these equilibrium points is traced out by a curve called the expansion path which shows how factor proportions change when output or expenditure changes, input prices remaining constant throughout. If expenditure has gone up such that the producer can buy either MM’ of additional capital or LL’ of additional labour-then the factor combination has changed form (OK+ON) to (OK’ + ON’). In case of constant returns to scale, the expansion path OE will be a straight line, which reflects that factor proportions are independent of the level of output. The shape of the expansion path changes depending upon the type of returns to scale prevalent. It is the expansion path which is critical in determining the long-run costs of production.