Marginal Rate of Substitution Formula

MRS is used to study consumer preferences that are represented as a utility function, which can be used to examine buyer’s behavior where the rate is the exchange between two units of goods equally preferred by the buyer.

It is the rate at which the buyer is ready to replace one with another. In such a condition, if we lower the units of goods of type, we will have to compensate it by increasing the number of units of goods of the other type.

Hence, the rate calculates the decline in the number of units of one good remunerated by growth in another. 
Mathematically, MRS is represented as - MRS=ΔA/ΔB

For example- The consumer can let go of coffee if the consumer cigarette more. It means if the consumer starts buying more cigarettes, the number of coffee consumed declines.

A similar relationship can be seen between biofuel and biodiesel, and crude oil production. With changing patterns of commodity production and consumption, many goods are not perfectly substitutable and can never be completely replaced, so a lower or higher demand will not affect the marginal substitution.

Further, buying one item like coffee may not satisfy the need for cigarettes or vice versa.  The law only states that one commodity may sacrifice for the other to grow and as the utilization of one increases, there can be a decline in the demand for others.