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# Marginal rate of technical substitution

## What is the marginal rate of technical substitution – MRTS?

The marginal rate of technical substitution (MRTS) is an economic theory that illustrates the rate at which one factor must decrease in order for the same level of productivity to be maintained when another factor is increased.

The MRTS reflects the trade-offs between factors, such as capital and labor, that allow a firm to maintain constant production. The MRTS differs from the marginal rate of substitution (MRS) in that the MRTS focuses on the producer balance and the MRS focuses on the consumer balance.

Key points to remember

• The marginal rate of technical substitution indicates the rate at which you can substitute one input, such as labor, for another input, such as capital, without changing the level of the resulting output.
• The isoquant, or curve on a graph, shows all of the various combinations of the two inputs that give the same amount of output.

## The MRTS formula is



MRTS (L, K)

=

??

K

??

THE

=

deputy

THE

deputy

K

or:

K

=

Capital city

THE

=

Workforce

deputy

=

Marginal products of each input

??

K

??

THE

=

Amount of capital that can be reduced

when the work is increased (usually by one unit)

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 (usually by one)} end {aligned}

MRTS (THE, K)=??THE??K=deputyKdeputyTHEor:K=Capital cityTHE=Workforcedeputy=Marginal products of each input??THE??K=Amount of capital that can be reducedwhen the work is increased (usually by one unit)

## How to calculate the marginal rate of technical substitution – MRTS

An isoquant is a graph showing combinations of capital and labor that will produce the same output. The slope of the isoquant indicates the MRTS or at any point along the isoquant how much capital would be required to replace a unit of labor at that point of production.

For example, in the graph of an isoquant where capital (represented by K on its Y axis and labor (represented by L) on its X axis, the slope of the isoquant, or the MRTS at any point, is calculated as dL / dK.

## What does the MRTS tell you?

The slope of the isoquant, or the MRTS, on the graph shows the rate at which a given input, whether labor or capital, can be substituted for the other while keeping the same level of output. The MRTS is represented by the absolute value of the slope of an isoquant at a chosen point.

A decrease in the MRTS along an isoquant to produce the same level of production is called the declining marginal rate of substitution. The figure below shows that when a company goes down from point (a) to point (b) and uses an additional unit of labor, the company can give up 4 units of capital (K) while remaining on the same isoquant in point (b). So the MRTS is 4. If the company hires another labor unit and moves from point (b) to (c), the company can reduce its use of capital (K) by 3 units but remains on the same isoquant, and the MRTS is 3.

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