Marginal Rate of Substitution: Definition, Formula & Example

Marginal Rate of Substitution: Definition, Formula & Example
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  • 0:03 Marginal Rate of Substitution
  • 1:23 The Exchange
  • 3:39 What Is Satisfaction?
  • 4:32 Lesson Summary
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Lesson Transcript
Instructor: Toni Bonton

Toni has taught personal finance and is currently pursuing a doctorate in business administration.

The amount of satisfaction derived from a good determines how much of that good the consumer needs to be fully satisfied. This lesson discusses the combination of goods needed for that satisfaction.

Marginal Rate of Substitution

Brandy loves to shop for shoes and bags. In fact, she spends most of her free time and allowance on shopping sprees for more shoes and bags. While loading up on handbags during a sale at the mall, Brandy hears the store manager's voice over the intercom announcing an impromptu discount on shoes, but there's a catch. Customers may only receive a maximum of $500 in discounts per purchase. Brandy is now faced with dilemma. She must decide how many handbags she is willing to give up in exchange for each pair of shoes and still be satisfied with her purchase.

This combination exchange is called the marginal rate of substitution. The marginal rate of substitution is the number of units a consumer is willing to give up of one good in exchange for units of another good and remain equally satisfied. The substitution doesn't indicate a preference in goods, only that the consumer is willing to give up units of one good for additional units of another good. In this case, Brandy is willing to give up a certain amount of handbags for each additional pair of shoes she would like to buy, as long as she doesn't have to compromise her total satisfaction. If her chosen combinations were graphed, it would look like this:

mrs_graph

Each combination of handbags and shoes will generate the same amount of satisfaction for Brandy.

The Exchange

Now that Brandy is willing to give up a certain amount of handbags for additional pairs of shoes that she would like to purchase, we can figure out the marginal rate of substitution. To calculate the marginal rate of substitution, the change in good x is divided by the change in good y:

mrs_formula

MRS(x,y) = the marginal rate of substitution between both goods

dx = the change in good x, the number of units a consumer is willing to give up

dy = the change in good y, the number of units a consumer gains by giving up units of good x

If that sounds like a foreign language, let's bring it all together so that it makes sense.

Listed below is the combination of handbags and shoes Brandy is willing to accept to be satisfied and still fall within her allowed discounts:

mrs_table

The marginal rate of substitution begins at Combination B because it shows what Brandy had to give up in order to purchase an additional pair of shoes. At Combination B, Brandy had to give up three handbags (7 - 4 = 3) to gain one additional pair of shoes (2 - 1 = 1). Let's calculate the marginal rate of substitution:

MRS(x,y) = 3 (the change in good x) / 1 (the change in good y)

MRS(x,y) = 3 / 1

MRS(x,y) = 3

The marginal rate of substitution is 3, or 3:1. When the marginal rate of substitution is written as a ratio, it points out how many of good x were given up for good y.

Now, Brandy has four handbags and two pair of shoes, but she has her eyes on another pair of shoes that she would love to have in her collection. This time Brandy's willing to give up two more handbags in order to buy one additional pair of shoes and still remain completely satisfied. Let's figure out the marginal rate of substitution for Combination C:

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