 # Marginal Rate of Substitution (MRS)

The quantity of one good that a consumer can forego for additional units of another good at the same utility level

## What is the Marginal Rate of Substitution (MRS)?

The marginal rate of substitution (MRS) is the quantity of one good that a consumer can forego for additional units of another good at the same utility level. MRS is one of the central tenets in the modern theory of consumer behavior as it measures the relative marginal utility.

Marginal rates of substitutions are similar at equilibrium consumption levels and are calculated between commodity bundles at indifference curves. Combinations of two different goods that give consumers equal utility and satisfaction can be plotted on a graph using an indifference curve. The MRS is based on the idea that changes in two substitute goods do not alter utility whatsoever.

### Summary

• The marginal rate of substitution (MRS) is the rate at which a consumer would be willing to forgo a specific quantity of one good for more units of another good at the same utility level.
• MRS, along with the indifference curve, is used by economists to analyze consumer’s spending behavior.
• The marginal rate of substitution is represented as a slope on the indifference curve, and each point along the curve shows the number of units of each good that would be substitutable for another.

### Understanding the Marginal Rate of Substitution (MRS)

In economics, MRS is used to show the quantity of good Y and good X that is substitutable for another. Another way to think of MRS is in terms of two commodity bundles that give a notion of compensation, which is founded in the feature of the uniform property.

In the mathematical field of topology, the uniform property is an invariant property of uniform space considering uniform isomorphism. The uniform property and MRS share a preference relation, which is represented by a differentiated utility function.

MRS includes bounded rationality in which consumers make purchasing decisions to satisfy their needs rather than to achieve an optimal solution. It is linked to the indifference curve, from where consumer behavior is analyzed.

### MRS Formula

The marginal rate of substitution is calculated using this formula: • Where:
• X and Y represent two different goods
• d’y / d’x = derivative of y with respect to x
• MU = marginal utility of two goods, i.e., good Y and good X

### MRS and Indifference Curve

The indifference curve is central in the analysis of MRS. Each point along the curve represents goods X and Y that a consumer would substitute to be exactly as happy after the transaction as before the transaction.

Goods and services are divisible without interruption, according to the neoclassical economics’ assumption. Such a notion implies that the direction of the indifference curve; notwithstanding, MRS will be the same and correspond to its slope. Most indifference curves change slopes as one moves along them, rendering MRS a changing curve.

There are three common types of graphs that employ indifference curves to analyze consumer behavior:

1. The first graph is used to define the utility of consumption for a specific economic agent. MRS moves to zero as it diminishes the number of units of good X, and to infinity, as it diminishes the number of units of good Y.
2. The second type of graph involves perfect substitutes of both goods X and Y. The MRS, along the indifference curve, is equal to 1 because the lines are parallel, with the slopes forming a 45° angle with each axis. MRS is defined as a fraction because the slope is different when considering different substitutes of goods. MRS will be constant for perfect substitutes.
3. The third type of graph represents complementary goods, with each indifference curve’s horizontal fragment showing an MRS of 0.

### The Principle of Diminishing Marginal Rate of Substitution

In the case of substitute goods, diminishing MRS is assumed when analyzing consumers’ expenditure behavior using the indifference curve. The assumption of diminishing MRS posits that when a consumer substitutes commodity X for commodity Y, the stock of X decreases, and that of Y decreases, while the MRS decreases.

In other words, the consumer is prepared to forego commodity Y as he owns more of commodity X. The concept can be illustrated by an indifference curve where the MRS of the two commodities continues to decrease along the indifference curve. However, in the case of perfect goods and complementary goods, this law is not applicable.

### Limitations of the Marginal Rate of Substitution

One of the weaknesses associated with the marginal rate of substitution is that in its evaluation, it does not account for a combination of goods that a consumer would happily substitute with another combination. For this reason, analysis of MRS is restricted to only two variables. Additionally, MRS treats the utility of two substitute goods equally even though this might not be the case; hence, it does not examine marginal utility in the actual sense.

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