# Understanding the Marginal Rate of Technical Substitution (MRTS)

![Marginal Rate of Technical Substution (MRTS) Economic Formula](https://www.investopedia.com/thmb/7qHUDk5HVc1zmTewaM03MclCsOk=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/marginal-rate-technical-substitution.asp-a44505b8c6d64a7e965eca1c1c046a37.png)

*— Investopedia / NoNo Flores*

## What Is Marginal Rate of Technical Substitution (MRTS)?

The marginal rate of technical substitution (MRTS) is the rate at which production inputs, typically labor and capital, can be substituted while maintaining the same level of output. Firms that want to maintain productivity while altering inputs need to have a practical understanding of MRTS. Calculating and applying MRTS is key to optimizing production efficiency.

The MRTS reflects the give-and-take between factors that allow a firm to maintain a level of productivity. MRTS differs from the [marginal rate of substitution (MRS)](https://www.investopedia.com/terms/m/marginal_rate_substitution.asp) in that MRTS is focused on producer [equilibrium](https://www.investopedia.com/terms/e/equilibrium.asp) and MRS is focused on consumer equilibrium.

An isoquant is a graph that shows all combinations of two inputs that result in the same output.  The slope of the isoquant, or MRTS, shows how much an input can be substituted by another while maintaining the same output.

### Key Takeaways

*   The marginal rate of technical substitution (MRTS) indicates how one input, like labor, can replace another, like capital, while keeping output constant.
*   Unlike the marginal rate of substitution (MRS), MRTS focuses on producer equilibrium for production inputs rather than consumer utility.
*   The MRTS is calculated as the negative ratio of the marginal products of labor and capital.
*   Isoquants illustrate combinations of inputs that result in the same level of output, with their slope representing the MRTS.
*   A diminishing MRTS shows a decrease in the number of input units needed to substitute another while maintaining the same output.

## Understanding the MRTS Formula

﻿ $\begin{aligned} &\text{MRTS(\textit{L}, \textit{K})} = - \frac{ \Delta K }{ \Delta L } = \frac{ \text {MP}_L }{ \text {MP}_K } \\ &\textbf{where:} \\ &K = \text{Capital} \\ &L = \text{Labor} \\ &\text{MP} = \text{Marginal products of each input} \\ &\frac{ \Delta K }{ \Delta L } = \text{Amount of capital that can be reduced}\\ &\text{when labor is increased (typically by one unit)} \\ \end{aligned}$﻿

## Calculating the Marginal Rate of Technical Substitution

An isoquant shows combinations of capital and labor that yield the same output. Its slope indicates the MRTS, showing how much capital is needed to replace one unit of labor while keeping output constant.  

For example, in an [isoquant graph](https://www.investopedia.com/terms/i/isoquantcurve.asp) with capital (K) on the Y-axis and labor (L) on the X-axis, the MRTS at any point is calculated as dL/dK.

## Insights from MRTS: What It Means for Production

The slope of the isoquant, or MRTS, shows how much one input can be substituted for another while maintaining output. The MRTS is the absolute value of the isoquant's slope at any point.  

A decline in MRTS along an isoquant for producing the same level of output is called the diminishing marginal rate of [substitution](https://www.investopedia.com/terms/s/substitute.asp). The figure below shows that when a firm moves down from point (a) to point (b) and uses one additional unit of labor, the firm can give up 4 units of capital (K) and yet remain on the same isoquant at point (b). So the MRTS is 4. If the firm hires another unit of labor and moves from point (b) to (c), the firm can reduce its use of capital (K) by 3 units but remains on the same isoquant, and the MRTS is 3.

![MRTS](https://www.investopedia.com/thmb/QN5JS4vAP55g5byuIT74H1X8gK4=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/marginal_rate_of_substitution_final2-893aa48189714fcb97dadb6f97b03948.png)

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## What Is the Role of MRTS?

MRTS helps producers maximize production within input constraints. For example, it helps a firm decide how to invest in inputs to achieve a target output. By using MRTS, a firm can estimate input costs and choose the least expensive combination to meet its output goals.  

## What Is the Difference Between MRS and MRTS?

Marginal rate of substitution is the rate at which a consumer is willing to forgo one good for another while maintaining a fixed level of utility. Marginal rate of technical substitution is the rate at which a producer can substitute one input factor for another while maintaining a fixed level of production.

## What Is the MRTS Indifference Curve?

The MRTS [indifference curve](https://www.investopedia.com/terms/i/indifferencecurve.asp) is simply a graphic representation of all the various combinations of inputs that would result in the same level of output. At any point along such a curve, productivity will remain unchanged, even as the specific combination of labor and capital fluctuates.

## The Bottom Line

The marginal rate of technical substitution (MRTS) is the rate at which one input can replace another without affecting output levels. For example, typical inputs in MRTS calculations are the usage of labor and capital. MRTS is visually represented by an isoquant curve on a graph.

Producers who want to optimize input combinations while maintaining output levels efficiently will need to understand MRTS. There is the risk of diminishing MRTS, which is when the substitutability of inputs decreases as production continues. Marginal rate of substitution is different than MRTS as the rate of a consumer is willing to forgo one good for another while maintaining a fixed level of utility.