# Marginal Rate of Substitution – Meaning, Calculation, and Graph

## What is the Marginal Rate of Substitution?

Marginal rate of substitution (MRS) is an economic concept that helps in understanding human behavior. MRS is basically the amount of a commodity that a user is willing to forgo for new units of another commodity if they offer the same level of utility or satisfaction. Or, we can say that it is the number of new goods that a user will buy in place of a comparable commodity as long as the new goods meet the user’s needs.

MRS plays a vital role in analyzing consumer behavior in the indifference theory. If a consumer cannot decide between two commodities, then the MRS will be zero. This is because since they are indifferent between the two commodities, they will neither gain nor lose any utility or satisfaction.

## Formula for Marginal Rate of Substitution

We can calculate the MRS using three different formulas.

Suppose there are two commodities, X and Y, then MRS will be:

MRSxy = dY / dX

In this formula, we use the derivative of Y with respect to the X variable to get the rate of change.

MRSx,y = ΔY / ΔX

In this formula, we divide the change in the consumption of Y by the change in the consumption of X. This is the most used formula to calculate the MRS.

MRSx,y = MUy / MUx

MU here stands for marginal utility. In this formula, we divide the MU of Y by the MU of X.

## Example

Suppose Mr. A goes to a bakery and decides that four combinations of cake and pastries give him the same level of satisfaction. The following table shows the four combinations for Mr. A:

In this example, we will use the change in the quantity of cake and pastries to calculate the MRS for different combinations.

MRS for Combination B will be = Change in Pastries/Change in Cupcake = -4/1 = -4

MRS for Combination C will be = -2/1 = -2

And, MRS for Combination D will be = -1/1 = -1

In this example, the number of units of pastries that Mr. A is ready to replace decreases. So, this is the case of diminishing marginal rate of substitution.

## Types of Marginal Rate of Substitution

Though diminishing MRS is the most common, there can also be two other types of MRS.

### Diminishing Marginal Rate of Substitution

Diminishing or decreasing MRS will be when the two commodities are normal goods (or they are imperfect substitutes). In this case, the Indifference Curve will be convex to the origin, implying the consumption of one good increases, but the consumption drops for the other commodity. For example, in the case of oranges and mangoes, a user will normally reduce the consumption of one fruit if he consumes more of another fruit.

### Constant Marginal Rate of Substitution

Constant MRS will be when the two commodities are perfect substitutes. In this case, the indifference curve will be a straight line, implying the consumption of one good increases and the other good decreases in 1:1 proportion. Coca-Cola and Pepsi are considered to be perfect substitutes for each other. So, if a user is not having a Coke, he would have Pepsi. The change in units consumed in this case will always be 1. Thus, the MRS will be constant.

MRS will be infinite or zero when the two commodities are the perfect complement. In this case, the indifference curve will be L-shaped, implying an increase in the consumption of both commodities. For example, tea and biscuits are complementary products. So, if a user drinks more tea, then he will likely have more biscuits as well, and vice versa.

## Relation with Indifference Curve

MRS is a very important part of the indifference curve (IC). Every point on the indifference curve shows the different combinations of two goods that offer a consumer the same level of satisfaction. So, MRS represents the slope of the IC at any point on the curve.

Generally, indifference curves are convex. It is because a user will have to forgo units (or units) of one good to consume more of another. This means that the MRS will reduce as we move down the IC. We call this the law of diminishing marginal rate of substitution.

If the MRS is increasing, then the shape of the IC will be concave. This would imply that a consumer would increase the consumption of both commodities and vice versa.

## Limitations of Marginal Rate of Substitution

The biggest drawback of MRS is that it is used only for a pair of goods. It means that we can’t use it to analyze the impact of more than two commodities, as well as combinations of different commodities that a user could be willing to forgo for another combination of commodities, such as the combination of commodities A and B. Combination of commodities C and D. One can, however, overcome this shortcoming by calculating the MRS for different combinations of commodities.

Another drawback of MRS is that it assumes the marginal utility between two commodities to be the same. In reality, different commodities could offer different satisfaction levels to consumers. A better method would be to analyze the utility margins separately.

One more drawback is that the MRS ignores other factors that significantly impact the consumption pattern. For this reason, analysts use MRS in combination with other concepts, such as the frontier curve of demand. 