- The Marginal Rate of Technical Substitution Formula
- How The Marginal Rate of Technical Substitution Calculated?
- What Can You Understand By The Marginal Rate of Technical Substitution?
- What Are The Properties of MRTS?
- Solved Illustrations
- Cobb-Douglas Production Function
- Perfect Substitutes
- What causes the Marginal Rate of Technical Substitution to diminish?

# What Is the Marginal Rate Of Technical Substitution?

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 **ma****rginal 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

**Frequently Asked Questions**

Here are the most frequently asked questions that we have scouted over the internet and answered to further clarify your queries.

**1. What Is The Marginal Rate Of Technical Substitution Between Labor And Capital?
**The marginal charge of technical substitution (of exertions for the capital) is the charge in which capital may be decreased for each one unit boom in exertions, and maintaining output constant. It is described because the absolute price of the slope of the isoquant is drawn with exertions at the horizontal axis and capital at the vertical axis.

**2. Why Does Marginal Rate Of Technical Substitution Between Factor Diminish?
**The marginal charge of technical substitution diminishes while the manufacturer continues on substituting one useful resource of manufacturing with some other enter of manufacturing.

**3. What Is The Marginal Rate Of Commodity Substitution?
**In economics, the marginal charge of substitution (MRS) is the charge at which a customer can surrender a few quantities of 1 suitable in trade for every other suitable whilst keeping the equal stage of the utility. At equilibrium intake levels (assuming no externalities), or marginal quotes of substitution are of identical nature.

**4. How Do I Calculate Marginal Output?
**An enterprise calculates marginal sales with the aid of using dividing the alternate in overall sales with the aid of using the alternate in overall output quantity. Therefore, the sale fee of an unoccupied extra object offered equals marginal sales. For example, an enterprise sells its first one hundred gadgets for a complete of $1,000.

**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 overtime at the time of production.

**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.**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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