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Marginal Rate of Substitution (All You Need To Know)

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What is the marginal rate of substitution formula?

How do you find the MRS?

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What Is Marginal Rate of Substitution (MRS)

The Marginal Rate of Substitution, also referred to as the MRS, is a notion used in economics to refer to a consumer’s willingness to purchase certain goods in relation to other goods when the goods provide the consumer with equal satisfaction. 

In other words, in an attempt to analyze how consumers behave, economists use the concept of the marginal rate of substitution to assess a consumer’s inclination to replace one good with another when both goods provide the consumer the same level of satisfaction.

For example, let’s say that we want to evaluate how consumers will choose cereal over oats and in what quantity they will be indifferent to purchase a cereal breakfast over oatmeal.

To calculate the MRS, economists must find out from the consumer the combination of cereal versus oats giving them an equal level of satisfaction.

The results are plotted on an indifference curve showing the consumer’s behavior in switching from one good to another as the quantities consumed of one good increase.

The most common type of indifference curve that we’d expect is that of diminishing marginal substitution rate where the more a consumer consumes cereal, the less oats they are willing to consume.

Marginal Rate of Substitution Definition

According to Investopedia, the marginal rate of substitution is defined as follows:

Marginal rate of substitution is the willingness of a consumer to replace one good for another good, as long as the new good is equally satisfying.
Author

As you can see from this definition, the marginal rate of substitution is characterized as follows:

  • It’s an economic model 
  • Attempting to understand consumer behavior
  • To understand a consumer’s willingness to switch one product for another
  • If the substitution of the product provides the consumer with equal satisfaction

In neoclassical economics, you calculate marginal rate of substitution by placing two goods on an indifference curve representing the quantify of one good a consumer is indifferent in substituting for another equally satisfying good.

Marginal Rate of Substitution Formula

The marginal rate of substitution formula is the following:

  • “x” represents one good
  • “y” represents another good
  • Dy / Dx = represents the derivative of y with respect to x
  • MU = represents the marginal utility of two goods

How To Find The Marginal Rate of Substitution

To find the marginal rate of substitution, you’ll need to place two goods on an indifference curve depicting a consumer’s indifference in the utility of “Good X” versus “Good Y”.

The slope that you’ll obtain in charting a consumer’s indifference is a curve showing how much the consumer is willing to purchase Good X in relation to Good Y (or vice versa).

The marginal rate of substitution graph shows a consumer’s indifference to consume or purchase a certain quantity of one good (depicted on the X-axis) versus another good (depicted on the Y-axis).

Fundamentally, a consumer’s MRS (or indifference between two goods) is any single point on the MRS curve.

When the indifference curve forms a downward, convex, and negative sloping curve, it means that the consumer will have a diminishing marginal rate of substitution for one good over another good.

The diminishing MRS is the most common depiction of consumer behavior as it means that a consumer will consume less of one good by increasing his or her consumption of another equally satisfying good.

When you have an increasing marginal rate of substitution, the indifference curve will have a more concave curve which means that a consumer would consume more of one good as he or she consumes more of another good.

An increasing MRS is not a common type of indifference curve depicting what economists anticipate to represent a consumer’s typical behavior.

The Indifference Curve

The indifference curve, as the name suggests, represents a graphical representation of a consumer’s willingness to consume more of one good (Good X) in relation to another (Good Y) to the extent the consumer is equally satisfied.

For example, you can chart a consumer’s willingness to consume more hamburgers in relation to hot dogs.

The indifference curve will show you that the more a consumer consumes hamburgers, the less they are going to derive utility by consuming hot dogs.

When the consumption of one good increases in relation to another, the indifference curve will have a downward, negative, and concave slope.

At any single point on the indifference curve, you can say that the consumer is indifferent in substituting Good X for Good Y as he or she will achieve the same level of utility.

Coming back to our hamburger and hot dog example, you can calculate the marginal rate of substitution and may conclude that for every one hamburger, a consumer may be willing to give up an “x” amount of hot dogs.

MRS Drawbacks

The MRS notion has some drawbacks that you should be mindful of.

The first limitation is that the MRS considers the relative utility of two individual goods preferred by a consumer as opposed to a combination of goods.

You’ll need to adapt your calculation if you are looking to find the relationship between two bundles of goods or a combination of goods relative to another.

The second drawback is that you are limited to charting the relationship between two variables only.

In other words, you will not have the ability to consider the marginal substitution effect for more than two variables acting as a function of another.

Finally, to calculate MRS, you are assuming that two goods are comparable or provide an equal utility to the consumer. 

However, in reality, two goods may not provide a consumer with the same level of utility.  

“Marginal Rate of Substitution” Takeaways 

So, what is MRS?

How to calculate marginal rate of substitution?

What is the marginal rate of substitution?

In this article, we’ve broken down the notion of MRS so you can have a better understanding.

In a nutshell, you can consider the marginal rate of substitution as the trade-off of goods by a consumer.

What is a consumer’s willingness to trade one good for another while maintaining the same level of satisfaction?

Finding marginal rate of substitution will help us answer the above question and attempt to predict the consumer’s spending behavior.

The MRS formula can be depicted as follows:

Let’s look at a summary of our findings.

Define Marginal Rate of Substitution

  • The marginal rate of substitution is an economic depiction of the rate at which a consumer is willing to give up one product in relation to another to the extent the consumers maintain the same level of utility and satisfaction
  • MRS is the quantity of one good that a consumer can substitute (or forego) in order to consume more quantity of another good (and achieve the same level of utility)
  • In economics, calculating marginal rate of substitution and the marginal rate of substitution equation is used to analyze consumer spending behavior
Consumer behavior theory 
Cross elasticity of demand 
Fisher Effect
Implicit differentiation 
Indifference curve 
Indifference theory 
Isoquant curve 
Law of diminishing marginal utility 
Marginal productivity 
Marginal utility 
Moral suasion 
Substitution effect
Utility function
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