 # Marginal Rate of Substitution (MRS): Formula, Curve & Principle

The Marginal Rate of Substitution (MRS) is the rate at which a person is willing to trade one good for another. It is used to measure the relative value of two goods. To calculate the MRS, you divide the amount of one good that a person is willing to trade for another by the amount of the other good that they are given.

The MRS can be used to determine how much a person values one good relative to another. For example, if a person is willing to trade 2 apples for 1 banana, then their MRS for apples is 2/1 or 2. This means that the person values apples twice as much as bananas.

The MRS can also be used to find out how much a person would be willing to give up in order to get more of something else.

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

The Marginal Rate of Substitution (MRS) is the rate at which a consumer is willing to trade one good for another. It is determined by the relative prices of the two goods and the consumer’s preferences. The MRS can be used to measure how much a consumer would be willing to sacrifice one good in order to get more of the other good.

For example, if a consumer is given the choice between two different types of fruit, they will have a different MRS for each type of fruit. If they are given a choice between an apple and an orange, they may be willing to give up 2 oranges in order to get 1 apple. However, if they are given a choice between an apple and a grape, they may only be willing to give up 1 orange in order to get 1 grape.

### MRS Formula

The Marginal Rate of Substitution (MRS) is a formula used to calculate the change in the quantity of one good that is willing to be given up in order to receive an additional unit of another good.

It is calculated by dividing the marginal utility of the second good by the marginal utility of the first good. The MRS can help individuals and businesses make decisions about what goods to produce and how much of each to produce.

MRSxy  =dy/dx = MUy/MUx’

• 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 Marginal Rate of Substitution (MRS) is the rate at which a consumer is willing to trade one good for another. The MRS is found by taking the slope of the indifference curve. The slope of the indifference curve measures how much the consumer values one good over the other.

The MRS can be used to find the optimal mix of goods that a consumer should purchase. To find this, you must first find the point on the indifference curve where the MRS is equal to the ratio of prices (P1/P2). Once you have found this point, you can purchase goods in amounts that will produce the greatest satisfaction or utility for the consumer.

## The Principle of Diminishing Marginal Rate of Substitution

In economics, the principle of diminishing marginal rate of substitution (DMS) states that as individuals increase the quantity of one good they consume relative to another, they find that the additional satisfaction they gain from each successive unit of the first good diminishes. In essence, this means that people are willing to trade off less and less of one good for another as they consume more of both.

The principle is often used to explain why people tend to prefer a variety of goods and services over time. For example, someone might start out by preferring a lot of sugary snacks but eventually trade some of those snacks for healthier foods as their preference for sugar diminishes.

This is because as people consume more and more sugary snacks, they find that the additional satisfaction from each one decreases, making them less likely to want them overall.

## Limitations of the Marginal Rate of Substitution

The Marginal Rate of Substitution is a key concept in Economics and is used to measure how much one good can be substituted for another. The Marginal Rate of Substitution is the rate at which a person is willing to trade one good for another, keeping all other things constant.

However, there are limitations to the Marginal Rate of Substitution. One limitation is that it does not take into account the cost of trading goods. Another limitation is that it does not take into account the availability of goods. Finally, the Marginal Rate of Substitution does not always reflect people’s actual behavior.

## Example of Marginal Rate of Substitution (MRS)

For example, if someone is offered a choice between a candy bar and a piece of fruit, the MRS would be equal to the number of candy bars that could be traded for a piece of fruit before the person’s preference for candy bars over fruit changes. If someone is only willing to trade one candy bar for half a piece of fruit, then their MRS would be 2. Previous post Buy Low, Sell High Strategy: Does it Make Any Difference? Next post Fixed Asset Turnover Ratio: Formula, Limitations & Examples