Question

If a consumer daily 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?
A) $2$
B) $1$
C) $3$
D) $4$

Answer 1

Hint:
We will use the direct formula to calculate the elasticity of demand of the required goods. The change in income quantity and change in demand is already given to us so we will use the direct values in the formula to calculate the required entity.

Complete step by step solution:
It is given that for a customer his daily income rises from Rs. $300$ to Rs. $350$, his purchase of a good X increases from $25$ units per day to $40$ units.
Let us assume that the demand is denoted by letter $Q$ .
Similarly, we will denote the income by letter $M$.
Let us assume that ${Q_1} = 25$ and ${Q_2} = 40$ .
Therefore, the change in demand is given by:
$\Delta Q = {Q_2} - {Q_1} \Rightarrow \Delta Q = 15$
Similarly let us assume that ${M_1} = 300$ and ${M_2} = 350$ .
Therefore, the change in the income is given by:
$\Delta M = {M_2} - {M_1} \Rightarrow \Delta M = 50$
Now the elasticity of income is given by following formula:
$\varsigma = \dfrac{{\Delta Q}}{{\Delta M}} \times \dfrac{{{M_2} + {M_1}}}{{{Q_2} + {Q_1}}}$
Substituting the above values in the formula we get the following:
$\varsigma = \dfrac{{15}}{{50}} \times \dfrac{{650}}{{65}}$
Simplifying we get,
$\varsigma = 3$

Hence, the correct option is C.

Note:
Note that once you understand all the concepts given in the data the problem is very much easy to solve as it is just a substitution problem. It is also important to use the formula correctly and put all the quantities in the appropriate places. The formula contains some straightforward calculations so it is not a very complicated problem even if the numbers are big.