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Home > Performance Management Calculations > Marginal Rate of Substitution

Performance Management Calculations

# Marginal Rate of Substitution

## What It Measures

Sometimes referred to as MRS, the marginal rate of substitution measures the rate at which an individual must give up one asset to obtain a single additional unit of a second asset, while keeping overall utility constant. MRS can measure physical goods, but also assets such as labor or time. The result is generally plotted on an “indifference curve,” which shows the utility value for each combination of assets. MRS is also often used to show the rate at which a consumer will substitute one product or service with an alternative.

## Why It Is Important

MRS enables businesses to analyze how a rational user/consumer/organization chooses between two goods. For example, how will a change in the wage rate affect the choice between leisure time and work time? How far will price increases affect a consumer’s choice of drinking water?

## How It Works in Practice

To calculate MRS, we begin by creating an indifference curve, a line showing all the possible combinations of two goods/assets. The line plots the combinations that result in the same utility or value to the consumer.

In Figure 1, the graph shows a person receives the same utility from 4 hours of work and 6 hours of leisure as from 7 hours of work and 3 hours of leisure.

MRS is the amount of one asset (leisure) that needs to be sacrificed to obtain one unit of the second asset (work) while achieving the same utility (satisfaction).

The simple equation to calculate MRS is as follows:

Marginal rate of substitution = –dy ÷ dx

where d = change in good, and x and y represent different goods, products, or services. This calculation assumes utility remains constant.

For example, if the MRS is 2 then the consumer will give up 2 units of y to obtain one additional unit of x.

Using the example above, the marginal rate of substitution between the two selected variables is:

–(6 – 3) ÷ (4 – 7) = –3 ÷ –3

= 1

• Marginal rate of substitution diminishes over time because there is a principle of diminishing marginal utility—so the more units are consumed, the less additional satisfaction each addition creates (in other words, the more we consume something, the more willing we are to substitute it away).

• It is possible to create graphs showing more than one indifference curve—in this case, the resulting graph is called an “indifference curve map.”

• A key limitation of MRS is that the relationship between two goods remains constant. In reality, it may be that as a worker increases their salary, they desire more leisure time because they have more disposable income. An increase in tea consumption may decrease the marginal utility of coffee.

• It is common to add a budget line to MRS graphs, to separate affordable and unaffordable consumption possibilities.

## Further reading on Marginal Rate of Substitution

### Book:

• Pindyck, Robert S., and Daniel L. Rubinfeld. Microeconomics. 7th ed. Upper Saddle River, NJ: Pearson/Prentice Hall, 2008.