Marginal Rate of Substitution
A consumer remains indifferent between different combinations of goods on an indifference curve. Therefore, to remain on the same indifference curve the consumer has to substitute one commodity for another by just that much amount which keeps him at the same level of satisfaction. There rate at which the consumer is willing to substitute one commodity for another in order to maintain his level of satisfaction is known as the marginal rate of substitution.
In the above figure at point P on IC the consumer gets ON of good Y of OM of good X and point Q he gets ON1 (Y) and OM1 (X) since both points P and Q are on the same IC, therefore he is indifferent between them. This means the consumer sacrifice NN1 (Y) to get MM1 (X) in order to move from P to Q. The rate, which he is willing to substitute X for Y, is therefore.
This is Marginal rate of substitution of x for y. In short form it can be
Written as MRSxy = dY/dX