Question

A consumer buys 18 units of a good at a price of Rs.9 per unit. The price elasticity of demand for the good is -1. How many units the consumer will buy at a price of Rs.10 per unit? Calculate.

Answer 1

Here the price elasticity of demand (PED) is an economic measure of the change in the quantity demanded of a product related to its change in price. Price of elasticity basically measures the responsiveness of demand after the change in price. In general, people desire less things if those things become more expensive. The demand is price elastic if the price change leads to a bigger % change in demand, then the PED will be therefore greater than 1.

Complete step-by-step solution:
Given that the initial price per unit = Rs.9
No. of units bought by the consumer when Rs.9 per unit = 18
Now the new price per unit = Rs.10
Let the no. of units bought by the consumer when Rs.10 per unit = $x$
% Change in the price is :
$\Rightarrow \dfrac{{9 - 10}}{9} \times 100 = - 11.1\%$
$\therefore$The % change in price is -11.1%
Given that the price elasticity of demand is = -1.
The price of elasticity of demand is given by the negative of the ratio of ( % change in demand) to the ratio of (% change in price.)
Here the % change in demand quantity is given by:
$\Rightarrow \dfrac{{18 - x}}{{18}} \times 100\%$
The price of elasticity of demand is given by:
$\Rightarrow - \dfrac{{\left( {\dfrac{{18 - x}}{{18}}} \right) \times 100\% }}{{ - 11.1\% }}$
The above expression is equated to the given price of elasticity which is -1 :
$\Rightarrow - \dfrac{{\left( {\dfrac{{18 - x}}{{18}}} \right) \times 100\% }}{{ - 11.1\% }} = - 1$
$\Rightarrow - \left( {\dfrac{{18 - x}}{{18}}} \right) \times 100 = - 1( - 11.1)$
$\Rightarrow - (18 - x) \times 100 = 18(11.1)$
$\Rightarrow - (18 - x) \times 100 = 199.8$
Solving for $x$:
$\Rightarrow - 18 + x = 1.998$
$\Rightarrow x = 1.998 + 18$
$\Rightarrow x = 19.998$
$\Rightarrow x \simeq 20$
$\therefore$The no. of units bought by the consumer when Rs.10 per unit = 20

The consumer will buy 20 units at a price of Rs.10 per unit.

Note: Here we discussed that the demand is price elastic if the price change leads to a bigger % change in demand, then the PED > 1. But here in the question given that the PED is negative, that means it is price inelastic where the change in price leads to a smaller % change in demand, hence the PED < 1.