For a consumer to be in equilibrium, why Marginal Rate of Substitution be equal to the ratio of prices of two goods?

Dear Student

Under indifference curve approach, a consumer is in equilibrium when MRS = P₁ / P_{2 .}

Marginal Rate of Substitution (MRS) refers to the rate at which the consumer is willing to forego a commodity to obtain more and more of other commodity.

The ratio of prices, on the other hand denote the rate at which the consumer has to sacrifice a commodity  to obtain more and more of other commodity.


A consumer cannot opt for any bundle on IC3 as it will be beyond his reach, as his budget line is given. 
A consumer can opt for any combination on IC1, but that will not give him maximum utility as it lies on lower indifference curve. 
A consumer will be at equilibrium at point E, as it is tangent to budget line and here MRS = P₁ / P_{2 .}

Regards