Question

If the daily consumer income rises from Rs. 300 to Rs. 350, his purchase of a good X increases from 25 units per day to 40 units; find the income elasticity of demand for X.
$
  {\text{A}}{\text{. 2}} \\
  {\text{B}}{\text{. 1}} \\
  {\text{C}}{\text{. 3}} \\
  {\text{D}}{\text{. 4}} \\
 $

Answer 1

Hint:
 The income elasticity is the ratio of the percentage change in the demand of the product by the consumer to the percentage change in the income of the consumer. In general, it is the responsiveness of the quantity demanded a good to a change in consumer income.

In this question, we need to determine the change in the income of the consumer and the percentage change in the demand of the product X and, at last, substitute the determined values in the formula ${\text{E = }}\dfrac{{{\text{% change in quantity}}}}{{{\text{% change in income}}}}$.

Complete step by step solution:
Substitute Rs. 300 and Rs. 350 as the old income and the net income respectively in the formula ${\text{Percentage change in income = }}\dfrac{{{\text{New income - old income}}}}{{{\text{old income}}}}$ to determine the percentage change in income of the consumer.
$
  {\text{Percentage change in income = }}\dfrac{{{\text{New income - old income}}}}{{{\text{old income}}}} \\
   = \dfrac{{350 - 300}}{{300}} \\
   = \dfrac{{50}}{{300}} \\
   = \dfrac{1}{6} \\
   = \dfrac{{100}}{6}\% \\
 $
Again, substitute 25 units per day and 40 units per day as the old purchase and the new purchase quantities respectively in the formula ${\text{Percenatge change in quanity = }}\dfrac{{{\text{New quanity - Old quantity}}}}{{{\text{Old quantity}}}}$ to determine the percentage change in the quantity of the product demanded by the consumer.
$
  {\text{Percenatge change in quanity = }}\dfrac{{{\text{New quanity - Old quantity}}}}{{{\text{Old quantity}}}} \\
   = \dfrac{{40 - 25}}{{25}} \\
   = \dfrac{{15}}{{25}} \\
   = \dfrac{3}{5} \\
   = \dfrac{{300}}{5}\% \\
   = 60\% \\
 $

Now, to calculate the income elasticity of demand for the product X, substitute $\dfrac{{100}}{6}\% $ for the percentage change in income and $60\% $ for the percentage change in the demand of the product X in the formula ${\text{E = }}\dfrac{{{\text{% change in quantity}}}}{{{\text{% change in income}}}}$, we get:
 $
  {\text{E = }}\dfrac{{{\text{% change in quantity}}}}{{{\text{% change in income}}}} \\
   = \dfrac{{\left( {\dfrac{3}{5}} \right)}}{{\left( {\dfrac{1}{6}} \right)}} \\
   = \dfrac{{18}}{5} \\
   = 3.6 \\
   \approx 4 \\
 $
Hence, the income elasticity of demand for X is 4.
Option D is correct.

Note:
It should be noted here that the percentage change is the ratio of the difference in the quantity to the original quantity and not the new quantity. Old quantity is used because with reference to that quantity percentage is determined.