Question

Explain with the help of a numerical example, the meaning of diminishing marginal rate of substitution.

Answer 1

Diminishing marginal rate of substitution implies that the rate at which a consumer is willing to substitute one good for each additional unit of the other good tends to decline when the consumer consumes more of that good. For example,suppose we have the consumption bundles of a consumer as given in the following schedule.

Units of Good 1	Units of Good 2
1	10
2	6
3	3
4	1

We also know that MRS is calculated as,
$\frac{\text{Change in consumption of Good 1}}{\text{Change in consumption of Good 2}}=\frac{2\Delta y}{1\Delta x}$
Now, in the given schedule,
To increase the consumption of Good 1 by 1 unit, the consumer has to sacrifice 4 units (10-6) of Good 2.
So, the Marginal Rate of Substitution when the consumer increases the consumption of Good 1 from 1 to 2 units is, $\frac{10-6}{2-1}=\frac{4}{1}=4$
Now, similarly, when the consumer increases the consumption of Good 1 by one more unit, the consumer has to sacrifice 3 units (6-3) of Good 2.
So, the Marginal Rate of Substitution when the consumer increases the consumption of Good 1 from 2 to 3 units is, $\frac{6-3}{3-2}=\frac{3}{1}=3$
After this, when consumer increases the consumption of Good 1 by one more unit, the consumer has to sacrifice 2 units (3-1) of Good 2.
Thus, the Marginal Rate of Substitution when the consumer increases the consumption of Good 1 from 3 to 4 units is, $\frac{3-1}{4-3}=\frac{2}{1}=2$
Hence, we can see that the Marginal Rate of Substitution (MRS) is declining as and when the consumer consumes additional unit of Good 1 and we can say that MRS is diminishing in nature.