# The Laws of Returns to Scale

 The Laws Of Returns to Scale

 Introduction

The Laws of returns to scale and Economies of Scale are related terms that describe what happens as the scale of production increases in the long run.The term returns to scale arises in the context of a firm's Production Function.In the long run production function, all factors are variable. Therefore in the long run output can be increased by increasing all the factors of production.A firm's production function could exhibit different types of returns to scale in different ranges of output.Typically, there could be Increasing returns to scale,Constant returns to scale and Diminishing returns to scale. In this section we will use the isoquants to analyse the input output relationships under the condition that both the inputs (labour and Capital) are variable and their quantity is changed proportionately and simultaneously.

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 Definition of Law

In the long run production function, all factors are variable. Therefore in the long run output can be increased by increasing all the factors of production. br> The Laws of Production that pertain to the input-output relationship under the condition of changing scale of production are called the Laws of returns to scale.
statement of the Law: "Other things being equal in the long run, as the firm increases the quantities of all factors employed, the output may rise initially at a more rapid rate than the rate of increase in inputs, then the output may increase in the same proportion and ultimately the output increases less proportionately".
Symbolically, the long run production function can be written as:
Two factor model: Qx = f(L,K)
'N' factor model:
$Qx = {f(a/b,c,d,e....n,}\bar{T})$

 KEY WORDS

Returns to Scale
Long run production function

 Assumptions

1. Returns are measured in physical terms.
2. All units of factors are homogeneous.
3. Techniques of production remains constant.

 Stages of Laws of Returns to Scale

1. The Increasing Returns to Scale
2. The Constant Returns to Scale
3. The Diminishing Returns to Scale

 Explanation of Different Stages of Laws of Returns to Scale

1. The Increasing Returns to Scale:
There are increasing returns to scale when a given percentage increase in input leads to a greater relative percentage increase in output. It shows that output doubles itself even before the inputs can be doubled.It follows that in Fig. 9.15 the units oflabour is measured on X-axis and units of capital on Y axis. The scale line OS is drawn which shows the expansion path of a firm. In this case the distance between every successive isoquants becomes smaller and smaller i.e. OA > AB > BC. In case of increasing returns to scale, the production function is homogeneous of degree greater than one.
Example:
100 units (IQ1 at A) = 3L+ 3K
200 units (IQ2 at B) = 5L + 5K
300 units (IQ3 at C) = 6L + 6K

Diagramatic Representation:

It shows that output doubles itself even before the inputs can be doubled.It follows that in Fig. 9.15 the units of labour is measured on X-axis and units of capital on Y axis. The scale line OS is drawn which shows the expansion path of a firm. In this case the distance between every successive isoquants becomes smaller and smaller i.e. OA > AB > BC. How to read example(1):To produce 100 units of output requires three units of labour and three units of capital.

Causes of Increasing Returns to Scale:

a.Internal economies of scale
b.Efficiency of labour and capital
c.Improvement in large scale operation
d.Division of labour and specialization
e.Use of better and sophisticated technology
f.Economy of organisation
g.External economies of scale

2.Constant Returns to Scale:

There are constant returns to scale when a given percentage increase in input leads to an equal percentage increase in output. It shows that if inputs are doubled then the output also gets doubled. If inputs are trebled then the output also trebles

Symbolically:

Diagramatic Representation:

In Fig.2 the units of labour is measured on X-axis and units of capital on Y-axis. as is the scale of operation line. In this case the distance between every successive isoquant remains equal i.e. OL = LM = MN. It means if units of labour and capital are doubled, the output also doubles. In case of constant returns to scale, production function is homogenous of degree one.
Example:
100 units (IQ1 at L) = 3L + 3K
200 units (IQ2 at M) = 6L + 6K
300 units (IQ3 at N) = 9L + 9K

Causes of Constant Returns to Scale:
a)Internal economics of scale is equal to internal diseconomies of scale.
b)Balancing of external economics and diseconomies of scale
c)Factors of production are perfectly divisible substitutable, homogenous and their supply is perfectly elastic at given prices.

3.Decreasing Returns to Scale:

There are decreasing returns to scale when a given percentage increase in input leads to a smaller percentage increase in output.
Symbolically:

Diagramatic Representation:

In Fig.3 shows that there is decreasing returns to scale, when, to get an equal increase in output, a larger proportionate increase in both labour and capital are required. In case of decreasing returns to scale the distance between every successive isoquant on expansion path becomes larger and larger, i.e. OP < PQ < QR. In this case, production function is homogenous of degree less than one.
Example:

100 units (IQ, at P) = 3L + 3K
200 units (IQ2 at Q) = 7L + 7K
300 units (IQ3 at R) = 12L +12K
Causes of Decreasing Returns to Scale:

a.Internal diseconomies of scale
b.External diseconomies of scale
d.Lack of entrepreneurial efficiency
e.Unhealtny management and organization
f.Imperfect factor substitutability
g.Transport bottlenecks and Marketing difficulties.

 Activity

 Recapitalisation