5.9:
Calculating Marginal Rate of Substitution
The marginal rate of substitution, or MRS, is the rate at which a consumer is ready to give up one product in exchange for another while maintaining the same satisfaction.
John enjoys meals at a restaurant and watching movies in a theater. The table shows various combinations of these that satisfy him equally.
MRS of watching movies in a theater for meals at a restaurant is calculated as the number of meals at a restaurant that John is willing to give up every month for an extra opportunity to watch movies in a theater.
For instance, with Basket A, John has meals at a restaurant eighteen times. On moving from Basket A to B, John has meals at a restaurant only eleven times. He gives up seven meals at a restaurant for watching an extra movie in a theater. This means that MRS is seven.
In general, consider the indifference curve IC depicting relative preferences for goods X and Y.
MRS for these goods, X and Y, is the quotient of change in the quantity of Good Y and Good X while moving from one point to another on the indifference curve. This is the same as the slope of the indifference curve.
5.9 Calculating Marginal Rate of Substitution
The marginal rate of substitution, or MRS, is the rate at which a consumer is ready to give up one product in exchange for another while maintaining the same satisfaction.
Formula
MRS for two goods, X and Y, is denoted as MRS of X for Y. It is the quotient of change in the quantity of Good Y and the quantity of Good X while maintaining the same level of satisfaction.
MRSXY = – (ΔY/ ΔX)
Where,
MRSXY is MRS of X for Y
ΔY is the change in the quantity of Good Y
ΔX is the change in the quantity of Good X
MRS as the slope of the indifference curve
MRS represents the slope of an indifference curve at a particular point. An indifference curve is not a straight line but a curve, as the slope varies at different points. To find MRS at a particular point, a tangent line can be drawn. The slope of the tangent line represents the slope of the indifference curve at that combination of goods X and Y.