Law of Returns to Scale

Updated on May 10, 2017

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.


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

Scale of Production
Total Returns
Marginal Returns
1 Labor + 2 Acres of Land
4 (Stage I - Increasing Returns)
2 Labor + 4 Acres of Land
3 Labor + 6 Acres of Land
4 Labor + 8 Acres of Land
10 (Stage II - Constant Returns)
5 Labor + 10 Acres of Land
6 Labor + 12 Acres of Land
7 Labor + 14 Acres of Land
8 (Stage III - Decreasing Returns)
8 Labor + 16 Acres of Land

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.


    0 of 8192 characters used
    Post Comment
    • profile image


      9 months ago

      Clear and helpful information

    • profile image


      19 months ago

      Very usable information.

    • profile image


      20 months ago

      Very helpfull

    • profile image

      Aditya Shukla 

      21 months ago

      great explaination

    • profile image


      21 months ago

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

    • profile image


      23 months ago

      Nice explanation

    • profile image

      Lakhan Chawla 

      2 years ago

      before reading this article i don't know anything about law of return to scale but after reading your article

      i have cleared all concept

      this is a nice article and i found it very helpful


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

    Show Details
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)
    ClickscoThis is a data management platform studying reader behavior (Privacy Policy)