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# Marginal Rate of Technical Substitution (MRTS):

## Definition:

Prof. R.G.D. Alien and J.R. Hicks introduced the concept of MRS (marginal rate of substitution) in the theory of demand. The similar concept is used in the explanation of producers equilibrium and is named as marginal rate of technical substitution (MRTS).

Marginal rate of technical substitution (MRTS) is:

"The rate at which one factor can be substituted for another while holding the level of output constant".

The slope of an isoquant shows the ability of a firm to replace one factor with another while holding the output constant. For example, if 2 units of factor capital (K) can be replaced by 1 unit of labor (L), marginal rate of technical substitution will be thus:

MRS = ΔK  = 2 = 2

ΔL     1

## Explanation:

The concept of MRTS can be explained easily with the help of the table and the graph, below:

### Schedule:

 Factor Combinations Units of Labor Units of Capital Units of Output of Commodity X MRTS of Labor for Capital A 1 15 150 - B 2 11 150 4:1 C 3 8 150 3:1 D 4 6 150 2:1 E 5 5 150 1:1

It is clear from the above table that all the five different combinations of labor and capital that is A, B, C, D and E yield the same level of output of 150 units of commodity X, As we move down from factor A to factor B, then 4 units of capital are required for obtaining 1 unit of labor without affecting the total level of output (150 units of commodity X).

The MRTS is 4:1. As we step down from factor combination B to factor combination C, then 3 units of capital are needed to get 1 unit of labor. The MRTS of labor for capital 3:1. If we further switch down from factor combination C to D, the MRTS of labor for capital is 2:1. From factor D to E combination, the MRTS of labor for capital falls down to 1:1.

## Formula:

MRTSLK = ΔK

ΔL

It means that the marginal rate of technical substitution of factor labor for factor capital (K) (MRTSLK) is the number of units of factor capital (K) which can be substituted by one unit of factor labor (L) keeping the same level of output. In the figure 12.8, all the five combinations of labor and capital which are A, B, C, D and E are plotted on a graph.

### Diagram/Graph:

The points A, B, C, D and E are joined to form an isoquant. The iso-product curve shows the whole range of factor combinations producing 150 units of commodity X. It is important to point out that ail the five factor combination of labor and capital on an iso-product curve are technically efficient combinations. The producer is indifferent towards these, combinations as these produce the same level of output.

## Diminishing Marginal Rate of Technical Substitution:

The decline in MRTS along an isoquant for producing the same level of output is named as diminishing marginal rates of technical education. As we have seen in Fig. 12.8, that when a firm moves down from point (a) to point (b) and it hires one more labor, the firm gives up 4 units of capital (K) and yet remains on the same isoquant at point (b). So the MRTS is 4. If the firm hires another labor and moves from point (b) to (c), the firm can reduce its capital (K) to 3 units and yet remain on the same isoquant. So the MRTS is 3. If the firm moves from point (C) to (D), the MRTS is 2 and from point D to e, the MRTS is 1. The decline in MRTS along an isoquant as the firm increases labor for capital is called Diminishing Marginal Rate of Technical Substitution.

## Relevant Articles:

» What is Production Function
» Short Period Analysis of Production
»

## Long Run Production With Variable Inputs

» Isoquants
» Properties of Isoquants
» Isocost Lines
» Marginal Rate of Technical Substitution
» Optimum Factor Combination

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