question_answer

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

Answer:

Suppose a consumer consumes two goods X and Y. He wants one more unit of X in exchange for some amount of Y. It is explained in the following numerical example:
Combination of good X and Y	Marginal rate of substitution (MRS)
8X + 20Y	-
9X + 16Y	4Y : 1X
10X + 12Y	3Y : 1X
Since marginal utility of good X goes on falling with every increase in units of X, therefore, consumer will be willing to sacrifice lesser quantity of good Y for obtaining additional units of X.
Initially for getting an additional unit of X, consumer is willing to sacrifice (\[20-l6\]) = 4 units of Y. So MRS is 4Y: IX. When one more unit of X in acquired then (\[16-13\]) = 3 units of Y are sacrificed. MRS has fallen to 3Y: IX. The reason is, as more and more units of X are consumed, marginal utility from each successive unit of X goes on falling this makes the consumer to sacrifice less and less units of Y to get additional unit of X.
Hence, we can say that marginal rate of substitution is always diminishing.