## What is Marginal Rate of Substitution?

Marginal rate of substitution (MRS) refers to the rate at which one commodity can be substituted for another commodity maintaining the same level of satisfaction.

The MRS for two substitute goods X and Y may be defined as the quantity of commodity X required to replace one unit of commodity Y (or quantity of commodity Y required to replace one unit of X) such that the utility derived from either combinations remains the same.

This implies that the utility of X (or Y) is equal to the utility of additional units of Y (or X) added to a combination. MRS of X and Y is denoted as ΔY/ ΔX as it continues to diminish as the consumer continues to substitute X for Y or vice versa.

According to the **ordinal utility approach**, MRS_{y,x} (or MRS_{x,y}) decreases which means that the quantity of a commodity an individual is willing to give up for an additional unit of the other commodity continues to decrease with each substitution. MRS_{y,x} derived from different combinations of commodities X and Y are given in Table

Indifference points | Combinations Y+X | Change in Y (ΔY) | Change in X (ΔX) | MRS_{y,x} (ΔY/ ΔX) |
---|---|---|---|---|

a | 25 + 3 | – | – | – |

b | 15 + 5 | -10 | 2 | -5.00 |

c | 8 + 9 | -7 | 4 | -1.75 |

d | 4 + 17 | -4 | 8 | -0.50 |

e | 2 + 30 | -2 | 13 | -0.15 |

As the consumer moves from combination a to b on IC, he/she sacrifices 10 units of commodity Y and gets 2 units of commodity X. Therefore,

**MRS _{y,x} = –5**

Similarly when the consumer moves from combination b to c, he/she sacrifices 7 units of Y and gets 4 units of X. Therefore,

**MRS _{y,x} = –1.75**

This shows that as the consumer moves down the IC from point a to b to c, MRS diminishes from -5 to -1.75.

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