Calculate marginal rate of substitution from marginal utilities, Cobb-Douglas preferences, slope changes, or price ratios in economics.

MRS is measured in units of Y per unit of X at constant utility. The marginal-utility ratio uses MUx / MUy; the signed indifference-curve slope is its negative.

Marginal Rate of Substitution Formula

The following equation is used to calculate a marginal rate of substitution.

MRS = MUx / MUy
  • Where MRS is the marginal rate of substitution
  • MUx is the marginal utility of good x
  • MUy is the marginal utility of good y

To calculate a marginal rate of substitution, divide the marginal utility of one good or product by the marginal utility of another related good or product.

Marginal Rate of Substitution Definition

Marginal rate of substitution measures how many units of good Y a consumer is willing to give up for one additional unit of good X while keeping utility constant. For two desirable goods, MRS = MUx/MUy is the positive magnitude of the local indifference-curve slope.

Marginal Rate of Substitution Example

Example Problem #1:

First, determine the marginal utility of the first good. This will be considered good X.

In this case, the marginal utility of X is found to be .56.

Next, determine the marginal utility of the second good this will be compared to. This will be considered good Y.

For this example, the marginal utility of Y is .45.

Finally, calculate the marginal rate of substitution using the formula above:

MRS = MUx / MUy

MRS = .56 / .45

MRS = 1.24444

FAQ

What is a marginal rate of substitution?

Marginal rate of substitution is the amount of good Y a consumer is willing to give up for one additional unit of good X while holding utility constant. For positive marginal utilities, it equals MUx/MUy and the absolute local slope of the indifference curve.

What are the limitations of the marginal rate of substitution?

This calculator compares two goods while holding utility and other goods constant. MRS depends on the current consumption bundle; the marginal-utility ratio needs a nonzero denominator, and smooth tangency conditions do not cover every corner or kink.

How to calculate marginal rate of substitution?

  1. First, determine the marginal utility of good X.

    Calculate or determine the marginal utility of the first product or good. If you are unsure, navigate to the marginal utility calculator linked above.

  2. Next, determine the marginal utility of good Y.

    Just as in step 1, determine the marginal utility of the other product.

  3. Finally, calculate the MRS.

    Calculate the marginal rate of substitution by using the formula MUx/MUy.