Marginal Rate of Technical Substitution

Updated on September 12, 2017

Meaning

The marginal rate of technical substitution (MRTS) is the rate at which one input can be substituted for another input without changing the level of output. In other words, the marginal rate of technical substitution of Labor (L) for Capital (K) is the slope of an isoquant multiplied by -1.

Since the slope of an isoquant is moving down, the isoquant is given by –ΔK/ΔL.

MRTS = –ΔK/ΔL = Slope of the isoquant.

Table 1

Combinations
Labor (L)
Capital (K)
MRTS (L for K)
Output
A
5
9
--
100
B
10
6
3:5
100
C
15
4
2:5
100
D
20
3
1:5
100

In the above table, all the four factor combinations A, B, C and D produce the same level of 100 units of output. They are all iso-product combinations. As we move from combination A to combination B, it is clear that 3 units of capital can be replaced by 5 units of labor. Hence, MRTSLK is 3:5. In the third combination, 2 units of capital are substituted by 5 more units of labor. Therefore, MRTSLK is 2:5.

In figure 1,

MRTSLK at point B = AE/EB

MRTSLK at point C = BF/FC

MRTSLK at point D = CG/GD

Isoquants and Returns to Scale

Let us now examine the responses in output when all inputs are varied in equal proportions.

Returns to scale refer to output responses to an equi-proportionate, change in all inputs. Suppose labor and capital are doubled, and then if output doubles, we have constant returns to scale. If output is less than double, we have decreasing returns to scale, and if output is more than double, we have increasing returns to scale.

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

For computing the returns to scale in a production function, we calculate the function co-efficient represented by the symbol ‘Ɛ’. The ratio of the proportionate change in output to a proportionate change in all inputs is called the function co-efficient Ɛ. That is Ɛ = (Δq/q)/(Δλ/λ) where the proportionate change in output and all inputs are shown by Δq/q and Δλ/λ. Then the returns to scale is classified as follows:

Ɛ < 1 = Increasing returns to scale

Ɛ = 1 = Constant returns to scale

Ɛ > 1 = Decreasing returns to scale

Increasing returns to scale

When output increases by a proportion that exceeds the proportion by which inputs increase, increasing returns to scale prevail.

The line OP is the scale line because a movement along this line shows only a change in the scale of production. The proportion of labor to capital along this line remains the same because it has the same sloe throughout. The operation of increasing returns to scale is shown by the gradual decrease in the distance between the isoquant. For example OA > AB > BC.

Causes of increasing returns to scale

Several technical and/or managerial factors contribute to the operation of increasing returns to scale.

1. Increasing specialization of labor

Increasing returns to scale can be the result of increase in the productivity of inputs caused by increased specialization and division of labor as the scale of operations increase.

2. Indivisibilities

In general, indivisibility implies that equipment is available only in minimum sizes or in definite ranges of size. Specialized machines are generally far more productive than less specialized machines. In large-scale operations the possibility of using specialized machines are higher, so productivity will also be higher.

3. Geometric necessity

For some production processes, it is a matter of geometric necessity. A larger scale of operation makes it more efficient. For example, to double the grazing area, a farmer need not have to double the length of fencing. Similarly, doubling the cylindrical equipment (like pipes and smoke stacks) and spherical equipment (like storage tanks) requires less than twice the quantity of metal.

Decreasing returns to scale

Decreasing returns to scale prevail when the distance between consecutive isoquants increase. For example, OA < AB < BC.

Decreasing returns arise when diseconomies are greater than economies. Difficulties in coordinating the operations of many factories and communication problems with employees may contribute to decreasing returns to scale. More than proportionate increases in managerial inputs may be required to expand output when an organization becomes very large. (see figure 3)

Constant returns to scale

Constant returns to scale prevail when output also increases by the same proportion in which input increases. In the case of constant returns to scale, the distance between successive isoquants remains constant. For example OA = AB = BC (see figure 4)

Constant returns arise when economies exactly balance with diseconomies. As economies of scale are exhausted, a phase of constant returns to scale may set in operation.

Comments

    0 of 8192 characters used
    Post Comment

    • profile image

      dossa 5 months ago

      i like the explanation of the marginal rate of technical substution

    working

    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, owlcation.com 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: "https://owlcation.com/privacy-policy#gdpr"

    Show Details
    Necessary
    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 googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
    Features
    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)
    Marketing
    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.
    Statistics
    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)