What would be the value of the Marginal Rate of Substitution (MRS) when Good-X increases by 5 with the decrease of Good-Y by 15?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → -3
Note: The given answer is as per the official NTA Answer Key. However, there seems to be a mistake in the options. The marginal rate of substitution is only the magnitude (size) of ΔY / ΔX, so here it is 3, which is not among the options. Option (3), −3, is the slope ΔY / ΔX with its minus sign, as explained below.
Given:
Increase in Good-X, ΔX = +5
Decrease in Good-Y, ΔY = −15
The Good-Y given up for each extra unit of Good-X, on the same indifference curve, is the marginal rate of substitution (MRS). It is the value of ΔY / ΔX without the minus sign:
\( \displaystyle \frac{\Delta Y}{\Delta X} = \frac{-15}{5} = -3 \), the slope of the indifference curve
\( \displaystyle \text{MRS} = \left| \frac{\Delta Y}{\Delta X} \right| = \left| -3 \right| = 3 \)
MRS = 3: the consumer gives up 3 units of Good-Y for each extra unit of Good-X.
NCERT (2026-27): “2.1.2 Ordinal Utility Analysis … It is clear that when a consumer gets one more banana, he has to forego some mangoes, so that her total utility level remains the same and she remains on the same indifference curve. Therefore, indifference curve slopes downward. The amount of mangoes that the consumer has to forego, in order to get an additional banana, her total utility level being the same, is called marginal rate of substitution (MRS). In other words, MRS is simply the rate at which the consumer will substitute bananas for mangoes, so that her total utility remains constant. So, MRS = |ΔY / ΔX| … MRS = |ΔY / ΔX| means that MRS equals only the magnitude of the expression ΔY / ΔX. If ΔY / ΔX = −3 / 1 it means MRS=3.” |