# Principle of Marginal Rate of Substitution

### Marginal Rate of Substitution

Marginal rate of substitution (MRS) may be defined as the rate at which the consumer is willing to substitute one commodity for another without changing the level of satisfaction.

In other words, MRS can also be defined as the amount of a commodity that a consumer is willing to trade off for another commodity, as long as the second commodity provides same level of utility as the first one.

If we denote two commodities as X and Y, then MRS between X and Y can be expressed as the amount of Y a consumer is willing to give up so as obtaining one more unit of commodity X.

Mathematically, MRS is represented as

MRS=ΔY/ΔX

### Table 1: Indifference schedule

Combination Cigarette Coffee (cups) MRS
A 1 12
B 2 8 4
C 3 5 3
D 4 3 2
E 5 2 1

In the above indifference schedule are given 5 different combinations of two goods (cigarette and coffee), all of which produce same level of satisfaction.

We can see, combination A consists of 1 cigarette and 12 cups of coffee. When the consumer moves to combination B from A, he has to give up 4 cups of coffee in order to add 1 unit of cigarette, maintaining same level of satisfaction. Hence the marginal rate of substitution of cigarette for coffee is 4.

In the same way, when the consumer moves to combination C, he has to give up 3 more cups of coffee in order to add one more unit of cigarette and maintain the same utility level. Hence, marginal rate of substitution of cigarette for coffee here is 3.

Likewise, when the consumer moves to combination D and E, marginal rate of substitution is 2 and 1, respectively.

### Principle of Marginal Rate of Substitution

Marginal rate of substitution (MRS) is based on an important economic principle, i.e. MRS of X for Y diminishes more and more with each successive substitution of X for Y. This principle is known as diminishing marginal rate of substitution.

According to MRS, a consumer can let go off some of one commodity, say Y, in order to gain more of the other commodity X. However, as the consumer starts getting more and more of commodity X, he tends to forego less and less of good Y.

The rate at which the consumer substitutes X for Y is greater at the beginning. But, as he continues the substitution process, the rate of substitution begins to fall.

The diminishing marginal rate of substitution is also apparent from the table 1.

Initially, when the consumer moved to combination B from A, the MRS was calculated to be 4. In the same way, when he moved to combination C, the MRS was calculated to be 3. Likewise from combination C to D, MRS was 2. And, from D to E, MRS was 1.
Clearly, marginal rate of substitution diminished more and more as the consumer kept on substituting more and more cigarette for coffee.

The diminishing marginal rate of substitution can also be clearly visualized from the graphical representation of the indifference schedule.

#### Causes for diminishing marginal rate of substitution

Marginal rate of substitution is diminishing because of following reasons.

##### Goods are not perfectly substitutable

Goods can never be perfectly substitutable. If one good can perfectly substitute another good, both the goods are regarded as same. And, thus, increase or decrease in amount of any good will not cause effect in marginal substitution.