# Marginal Rate of Substitution (MRS) – Business Economics – BBA

Aug 24, 2021

## Marginal Rate of Substitution (MRS)

The concept of marginal rate substitution (MRS) was introduced by Dr. J.R. Hicks and Prof. R.G.D. Allen to take the place of the concept of diminishing marginal utility. Allen and Hicks are of the opinion that it is unnecessary to measure the utility of a commodity. The necessity is to study the behavior of the consumer as to how he prefers one commodity to another and maintains the same level of satisfaction.

The rate or ratio at which goods X and Y are to be exchanged is known as the marginal rate of substitution (MRS).

In the words of Hicks: “The marginal rate of substitution of X for Y measures the number of units of Y that must be scarified for unit of X gained so as to maintain a constant level of satisfaction”.

Marginal rate of substitution (MRS) can also be defined as: “The ratio of exchange between small units of two commodities, which are equally valued or preferred by a consumer”.

Formula:

MRSxy= ∆Y/∆X = Change in Y/ Change in X=Loss of Y/ Gain of X

MRSyx= ∆X/∆Y = Change in X/ Change in Y =Loss of X/ Gain of Y

In the table given above, all the five combinations of good X and good Y give the same satisfaction to the consumer. If he chooses first combination, he gets 1 unit of good X and 13 units of good Y. In the second combination, he gets one more unit of good X and is prepared to give 4 units of good Y for it to maintain the same level of satisfaction.

The MRS is therefore, 4:1. In the third combination, the consumer is willing to sacrifice only 3units of good Y for getting another unit of good X. The MRS is 3:1.Likewise, when the consumer moves from 4thto 5thcombination, the MRS of good X for good Y falls to one (1:1).

This illustrates the diminishing marginal rate of substitution. This behavior showing falling MRS of good X for good Y and yet to remain at the same level of satisfaction is known as diminishing marginal rate of substitution.

DMRS states diminishing quantities of one good must be sacrificed to obtain successive equal increases in the quantity of the other good.

An indifference curve exhibits a diminishing marginal rate of substitution:

1. The more of good x you have, the more you are willing to give up to get a little of good y.
2. The indifference curves
• Get flatter as we move out along the horizontal axis
• Get steeper as we move up along the vertical axis.

Importance of Marginal Rate of Substitution (MRS):

(i) Measures utility ordinally: The concept of MRS is superior to that of utility concept because it is more realistic and scientific than the theory of utility. It does not measure the utility of a commodity in isolation without reference to other commodities but takes into consideration the combination of related goods to which a consumer is interested to purchase.

(ii) A relative concept: The concept of marginal rate of substitution has the advantage that it is relative and not absolute like the utility concept given by Marshall. It is free from any assumptions concerning the possibility of a quantitative measurement of utility

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