# Marginal Rate of Technical Substitution

Reviewed by Annapoorna | Updated on Sep 30, 2020

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## What is the Marginal Rate of Technical Substitution?

The marginal rate of technical substitution (MRTS) is an economic theory that describes the rate at which one factor will decrease to be able to maintain the same level of efficiency when another factor rises.

The MRTS illustrates the gift-and-take between factors that enable a firm to maintain a constant production, such as capital and labour. MRTS varies from the marginal rate of substitution (MRS) since MRTS focuses on product balance and MRS focuses on market equilibrium.

## How to Calculate MRTS?

The MRTS is the slope of a graph representing one element on every axis. The slope of the MRTS is an isoquant or a curve connecting the two input points as long as the output stays the same.

The formula is as follows: MRTS(K,L): -( ∆K÷∆L) = MP(K)÷MP(L)

• K = Capital
• L = Labor
• MP = Marginal products of each input
• (∆K÷∆L) = Amount of capital that can be reduced when labour is increased (typically by one unit)

Let's take a graphical illustration to understand the concept. An MRTS graph that has the capital (depicted by K) on its Y-axis and labour (represented by L) on its X-axis is computed as dK / dL.

The isoquant shape depends upon whether input values are exact substitutes, resulting in a straight line, or complements, which creates an L shape. When input values are not precise substitutes, the line is curved.

## Uses and Application of MRTS

The isoquants in an MRTS graph display the rate at which the other can be substituted for a given input, either labour or capital, thus retaining the same output level.

A decrease in MRTS along an isoquant is called the declining marginal rate of substitution for generating the same level of output.

Producer equilibrium is a term in which all producers aim for the least amount of cost to achieve the maximum amount of profit. By bringing output factors together in a combination that needs the least amount of money, the producer gets equilibrium.

Therefore, the manufacturer is responsible for determining the combination of the factors of production, which best achieve this result. The decision made by the producer relates to the MRTS and the substitution principle.

It must be noted that only two factors of production are present in a plant, i.e. factor A and factor B. The factor A can produce a higher quantity of output than factor B. It can be done with an equal amount of capital being spent on both. It would result in the producer choosing factor A for factor B instead.