Management Notes

# Management Notes

Reference Notes for Management

# Marginal Rate Of Substitution – Why does MRS Diminish? | Microeconomics

## Marginal Rate of Substitution

Marginal Rate of Substitution (MRS) is considered one of the very important concepts for the analysis of the indifference curve. Taking about the marginal rate of substitution, it is the rate that reflects the rate at which the consumer will be willing to replace /substitute the one commodity that he/she is using for another commodity in the market without compromising the level of satisfaction from it. Let us suppose two goods by A and B, then we can define MRS between A and B as the amount of B that the consumer is willing to give up so as to obtain one more unit of A good.

### Marginal Rate of Substitution Formula,

Expressing MRS mathematically,

MRS = ∆B/∆A

Using the following table,

 Various Combinations Good A Good Y MRS=B/A A 1 12 – B 2 8 4 C 3 5 3 D 4 3 2 E 5 2 1

From the above table, we can see that, for having one more unit of A commodity the consumer sacrificed four units of B commodity. Looking at the combination C, we can see that to get one more unit of commodity A, the consumer has sacrificed three units of commodity B. With these combinations the consumers will have the same level of satisfaction.

Using the figure,

### Marginal Rate of Substitution Graph, Marginal Rate of Substitution Diagram

Looking at the graphical figure of the marginal rate of substitution we can easily see that the consumer is ready to sacrifice four units of commodity B for one unit of commodity A in the combination B. In the same way if we look at the third combination we can see that the consumer is ready to sacrifice three units of commodity B for one more unit of commodity A. All these analyses reflects that when the consumer gets more units of commodity A, the desire for the commodity A will go diminishing/decreasing.

This will lead him to sacrifice fewer units of commodity B. These factors will cause a decline in MRS. As we can see in the figure that there is a downward slope of the Indifference curve which denotes the diminishing marginal rate of substitution. The reason behind diminishing MRS is because no goods are perfectly substitutable and the increment of one goodwill not satisfy the need/want to satisfy for the other goods.

### Diminishing Marginal rate of substitution

#### Why does MRS Diminish?

##### A) The particular want is satiable

The want for a particular commodity is satiable. As the consumer have more and more units of a commodity, the intensity of his want for that good goes on falling. Due to this reason, when the stock of a commodity, say X, increases with the consumer, he is willing to forgo less and less of another commodity, say Y, for every increase in X. In the beginning, when the consumer’s stock of good Y is relatively large and his stock of good X is relatively small, consumer’s marginal significance for good Y will be low while his marginal significance for good X will be high. Therefore, the consumer will be willing to give up a larger amount of Y for a unit increase in good X.

But as the stock of good X increases the marginal significance for good X will diminish. On the other hand, as the stock of good Y decreases, the marginal significance for good Y will go up. As a result, as the individual substitute more and more of X for Y he is prepared to give up less and less of Y for a unit increase in X.

##### B) Goods are not perfect substitute for each other

Marginal rate of substitution diminishes because goods are not perfect substitute for each
other. If the two goods are perfect substitute, the indifference curve will be a straight line with a negative slope. Since, goods are not perfect substitutes, the marginal utility attached to the additional quantity of a commodity decreases faster in relation to the other commodity whose total quantity decreases.

Therefore, when the quantity of one commodity (say, X) increases, the quantity of other (say, Y) decreases. It becomes increasingly costlier for the consumer to sacrifice more units of Y for one unit of X. Therefore, when a consumer is required to sacrifice additional unit of Y, he will require increasing units of X to maintain the level of his satisfaction. As a result, the MRS diminishes.

##### C) Increase in the quantity of one good does not increase the want satisfying of the other

The principle of diminishing marginal rate of substitution will hold good only if the increase in the quantity of one good does not increase the want satisfying power of the other. If with the increase in the stock of good X, the want satisfying power of good Y increases, the greater and greater amount of good Y will be required to be given up for a unit increase in good X. As a result, the consumer satisfaction remains same.

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