# Marginal Rate of Substitution

## Marginal Rate of Substitution Definition

The Marginal Rate of Substitution (MRS) is defined as the rate at which a consumer is ready to exchange a number of units good X for one more of good Y at the same level of utility.

The Marginal Rate of Substitution is used to analyze the indifference curve. This is because the slope of an indifference curve is the MRS.

## Marginal Rate of Substitution Example

To illustrate an example, we’re going to use the following table as points on our indifference curve. This table is known as the indifference schedule.

Combination | Good X | Good Y |

A | 2 | 10 |

B | 3 | 7 |

C | 4 | 5 |

D | 5 | 3 |

E | 6 | 2 |

From the table, at point A, we can see that the consumer is ready to exchange three units of Good Y for one additional unit of Good X. Therefore, at this stage, the consumer’s Marginal Rate of Substitution of X for Y is three.

The MRS of X for Y represents the amount of Y which the consumer has to give up for the gain of one additional unit of X so that his or her level of his or her utility (satisfaction) remains the same. We assume that any of the five combinations in the table have the same level of utility.

For example, if the consumer goes from D to E, then the marginal rate of substitution becomes 1.

## Marginal Rate of Substitution Formula

The Marginal Rate of Substitution of Good X for Good Y (MRSxy) = βY/ βX (which is just the slope of the indifference curve).

## The Principle of Diminishing Marginal Rate of Substitution

The MRS of Good X for Good Y diminishes as more and more of Good X is substituted for Good Y. In other words, as the consumer has more and more of good X he is prepared to give up less and less of Good Y.

The rate at which the consumer substitutes Good X for Good Y is greater at the beginning. But, as he continues the substitution process, the rate of substitution begins to fall.

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Hello. What if we do the calculations using Px and Py instead. Will the placements still be the same?

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