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# Law of Returns to Scale

## Meaning of Production Function

Before we discuss what the law of returns to scale states, let's be sure we understand the concept of production function. The production function is a highly abstract concept that has been developed to deal with the technological aspects of the theory of production. A production function is an equation, table or graph, which specifies the maximum quantity of output, which can be obtained, with each set of inputs. An input is any good or service that goes into production, and an output is any good or service that comes out of the production process. Prof. Richard H. Leftwich attributes that production function refers to the relationship between inputs and outputs at a given period. Here inputs mean all the resources such as land, labor, capital and organization used by a firm, and outputs mean any goods or services produced by the firm.

Suppose we want to produce apples. We need land, water, fertilizers, workers and some machinery. These are called inputs or factors of production. The output is apples. In abstract terms, it is written as Q = F(X1, X2… Xn). Where Q is the maximum quantity of output and X1, X2,… Xn are the quantities of the various inputs. If there are only two inputs, labor L and capital K, we write the equation as Q = F(L,K).

From the above equation, we can understand that the production function tells us the relationship between various inputs and outputs. However, it does not say anything about the combination of inputs. The optimal combination of inputs can be derived from the technique of isoquant and isocost line.

The concept of production function stems from the following two things:

1. It must be considered with reference to a particular period.

2. It is determined by the state of technology. Any change in technology may alter output, even when the quantities of inputs remain fixed.

## Law of Returns to Scale

In the long- run the dichotomy between fixed factor and variable factor ceases. In other words, in the long-run all factors are variable. The law of returns to scale examines the relationship between output and the scale of inputs in the long-run when all the inputs are increased in the same proportion.

Assumptions

This law is based on the following assumptions:

1. All the factors of production (such as land, labor and capital) but organization are variable
2. The law assumes constant technological state. It means that there is no change in technology during the time considered.
3. The market is perfectly competitive.
4. Outputs or returns are measured in physical terms.

Three phases of returns to scale

There are three phases of returns in the long-run which may be separately described as (1) the law of increasing returns (2) the law of constant returns and (3) the law of decreasing returns.

Depending on whether the proportionate change in output equals, exceeds, or falls short of the proportionate change in both the inputs, a production function is classified as showing constant, increasing or decreasing returns to scale.

Let us take a numerical example to explain the behavior of the law of returns to scale.

## Table 1: Returns to Scale

UnitScale of ProductionTotal ReturnsMarginal Returns

1

1 Labor + 2 Acres of Land

4

4 (Stage I - Increasing Returns)

2

2 Labor + 4 Acres of Land

10

6

3

3 Labor + 6 Acres of Land

18

8

4

4 Labor + 8 Acres of Land

28

10 (Stage II - Constant Returns)

5

5 Labor + 10 Acres of Land

38

10

6

6 Labor + 12 Acres of Land

48

10

7

7 Labor + 14 Acres of Land

56

8 (Stage III - Decreasing Returns)

8

8 Labor + 16 Acres of Land

62

6

The data of table 1 can be represented in the form of figure 1

RS = Returns to scale curve

RP = Segment; increasing returns to scale

PQ = segment; constant returns to scale

QS = segment; decreasing returns to scale

Increasing Returns to Scale

In figure 1, stage I represents increasing returns to scale. During this stage, the firm enjoys various internal and external economies such as dimensional economies, economies flowing from indivisibility, economies of specialization, technical economies, managerial economies and marketing economies. Economies simply mean advantages for the firm. Due to these economies, the firm realizes increasing returns to scale. Marshall explains increasing returns in terms of “increased efficiency” of labor and capital in the improved organization with the expanding scale of output and employment factor unit. It is referred to as the economy of organization in the earlier stages of production.

Constant Returns to Scale

In figure 1, the stage II represents constant returns to scale. During this stage, the economies accrued during the first stage start vanishing and diseconomies arise. Diseconomies refers to the limiting factors for the firm’s expansion. Emergence of diseconomies is a natural process when a firm expands beyond certain stage. In the stage II, the economies and diseconomies of scale are exactly in balance over a particular range of output. When a firm is at constant returns to scale, an increase in all inputs leads to a proportionate increase in output but to an extent.

A production function showing constant returns to scale is often called ‘linear and homogeneous’ or ‘homogeneous of the first degree.’ For example, the Cobb-Douglas production function is a linear and homogeneous production function.

Diminishing Returns to Scale

In figure 1, the stage III represents diminishing returns or decreasing returns. This situation arises when a firm expands its operation even after the point of constant returns. Decreasing returns mean that increase in the total output is not proportionate according to the increase in the input. Because of this, the marginal output starts decreasing (see table 1). Important factors that determine diminishing returns are managerial inefficiency and technical constraints.

Akshitha on October 10, 2019:

Ric on December 17, 2018:

Very usable information.

Sandy on November 28, 2018:

Aditya Shukla on November 11, 2018:

great explaination

Vinu on October 21, 2018:

It is very helpful article .l heartly said thank you.

Lone on September 13, 2018:

Nice explanation

Lakhan Chawla on April 28, 2018: