 Marginal Rate of Technical Substitution, abbreviated as MRTS, is defined as an economic theory that explains the rate at which one factor decreases to keep the level of productivity constant or unchanged when another factor increases. The marginal rate of technical substitution reflects the give-and-take relationship that the factors share between them.

For example, the relationship between the factors labor and capital helps a business maintain the steady flow of output, i.e., if capital needs to be increased, keeping the production level the same, producers must decrease labor use. The MRTS will determine the rate that will reduce the use of labor.

To put it in simple words, the marginal rate of technical substitution shows the rate at which one production input can be replaced for different inputs without altering the level of the resulting production quantity. The curve on a graph called the isoquant will help us show all the possible combinations of the two factors that will give the same level of output. What has been explained to you above is just a brief about the MRTS concept. For a more detailed understanding of this Economics related topic, continue reading about the different sub-topics falling under this concept.

## The Marginal Rate of Technical Substitution Formula

The marginal rate of the technical substitution formula has been given below, followed by an explanation.

MRTS (L, K) = −AB= MPB / MPA

Where:  A = Capital Input

B = Labor Input

MP = Marginal products of each input

A / B= The quantity of capital that can be substituted/decreased when another input B, labor, is increased (usually by one unit).

## How The Marginal Rate of Technical Substitution Calculated? As mentioned above, with the help of a curve on a graph called an isoquant, we can learn about the different combinations of the inputs, labor, and capital that will produce the same amount of output. The slope of the isoquant represents the marginal rate of technical substitution. Or you can also say that at any point along the curve, how much labor would be needed to substitute one unit of capital, keeping the level of production unchanged, can be seen from the slope of the isoquant.

Assume, in an isoquant graph, the Y-axis represents labor (shown as B), and the X-axis represents capital (shown as A). Therefore, the isoquant slope or the marginal rate of technical substitution at any one point on the slope can be calculated as a change in A divided by a change in B (A/B). When the inputs are perfect substitutes, the shape of the isoquant will be a straight line; when the inputs are perfect complements, the shape of the curve will be L-shaped, and when the inputs are not a perfect substitute, the shape of the isoquant will be a curve.

## What Can You Understand By The Marginal Rate of Technical Substitution?

The MRTS or the slope of the isoquant graphically indicates the rate at which a given production input, either capital or labor, can be replaced with the other information when the production level is kept the same. The absolute value of the slope of an isoquant at a specific point represents the marginal rate of technical substitution.

When the output level is the same, there is a decline in the MRTS along the curve or an isoquant, which is called the diminishing marginal rate of technical substitution. The reduction in one input and a constant level of output is termed as the principle of diminishing marginal rate of technical substitution. For example, an organization plots the inputs, labor, and capital on a graph. A movement from point C to D on the graph indicates a reduction in the capital by 1 unit to increase labor by 4. Further, moving from point D to E would mean decreasing capital by 1 unit to raise labor quantity by 2. Therefore, if the marginal rate of technical substitution = K/L, the MRTS from point C to D would be four, and from point D to E, it will be 2.

## What Are The Properties of MRTS?

The marginal rate of technical substitution has the following properties:

• When both the marginal products turn out to be positive, the slope of the isoquant shall be negative.
• If the increase in the quantity of labor along an isoquant declines the MRTS, the isoquants are convex to the origin in shape.
• A positive slope for an isoquant is not possible.

## Solved Illustrations

### Cobb-Douglas Production Function

Calculate MRTS, if Q = F(L,K) = L3/4 K1/4

Solution:

MPL = 3/4 (K / L)1/4

MPK = 1/4 (L / K)3/4

∴MRTS = L/K= 3 K / L

### Perfect Substitutes

Calculate MRTS, if Q = F(L,K) = L + 2K.

Solution:

MPL = 1

MPK = 2

## What causes the Marginal Rate of Technical Substitution to diminish?

There is a diminishing marginal rate of technical substitution when a manufacturer keeps replacing one production input with another input. The following are the reasons that make the MRTS diminish over time at the time of production.

1. When the factors of production are not a perfect substitution for one another: One factor of production cannot perfectly substitute the use of the other one because each input has its specialty in the production process that they only can fulfill effectively.
2. When there is a scarcity of the factors of production: If one input is replaced by another input continuously, the input being replaced regularly will not be able to deliver its best in the production system, resulting in inadequacy.

Hence, the marginal rate of technical substitution plays an essential role in the production process and there in the economy. If done effectively, MRTS can be a powerful way to achieve the same production level with reduced production inputs

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##### Arnab

Arnab Das is a passionate blogger who loves to write on different niches like technologies, dating, finance, fashion, travel, and much more.