Answer the following question.
Explain the meaning of the marginal rate of substitution. Why does it diminish as one good is substituted for the other? Explain.
Solution
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. This rate tends to decline when the consumer consumes more of one 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,
`("Change in consumption of Good" 2)/("Change in consumption of Good" 1) = (Δ"y")/(Δ"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,
`(10 - 6)/(2 -1) = (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,
`(6 -3)/(3 -2) = (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,
`(3 -1)/(4 -3) = (2)/(1) = 2`
Hence, we can see that the Marginal Rate of Substitution (MRS) is declining as and when the consumer consumes an additional unit of Good 1 and we can say that MRS is diminishing in nature.
