Numerical Problems of Price Elasticity of Demand

Price of a commodity rises from ₹5 to ₹6. As a result, its demand falls from 100 units to 80 units. Find out the price elasticity of demand by percentage method.

Solution:
Given           P = 5; Q = 100
                     P₁ = 6; Q_l = 80
                    ΔP = 6 - 5 = 1
                    ΔQ = 100 - 80 = 20
                    \[e_p=\frac{\Delta Q}{\Delta\mathrm{P}}\times\frac{\mathrm{P}}{\mathrm{Q}}\]
                   \[=\frac{20}{1}\times\frac{5}{100}=1.\]
Ans: Price elasticity of demand is equal to unity.

A consumer purchases 20 units of a commodity when its price was ₹4 per unit. He purchased 30 units of it when its price fell to ₹3 per unit. What is the price elasticity of demand for the commodity?

Solution:
Given            P = 4; Q = 20
                     P₁ = 3; Q_l = 30
                     ΔP = 4 - 3 =1
                     ΔQ = 30 - 20 = 10 
                     \[e_p=\frac{\Delta Q}{\Delta\mathrm{P}}\times\frac{\mathrm{P}}{\mathrm{Q}}\]
                     \[=\frac{10}{1}\times\frac{4}{20}=2\]
Ans: Price elasticity of demand is equal to 2.

A household increases the demand for a commodity from 40 units to 50 units when its price falls by 10 per cent. What is the price elasticity of demand? Is it elastic or inelastic?

Solution: Percentage change in quantity
                 \[=\frac{Q_1-Q}{Q}\times100\]
                 \[=\frac{50-40}{40}\times100=\frac{10}{40}\times100=25\]
             \[e_p=\frac{\text{Percentage change in quantity}}{\text{Percentage change in price}}\]
                  \[=\frac{25}{10}=2.5\]
Ans: Price elasticity of demand is 2.5. The demand is elastic because price elasticity of demand exceeds unity.

When price of a good is ₹15 per unit, the consumer buys 12 units of the good. When price rises to ₹18 per unit, the consumer continues to buy 12 units. Calculate price elasticity of demand.

Solution: 
Here, ΔP = 18 - 15 = ₹3, ΔQ = 12 - 12 = 0,
P = 15, Q = 12 
             \[e_p=\frac{\Delta Q}{\Delta P}\times\frac{\mathrm{P}}{\mathrm{Q}}=\frac{0}{3}\times\frac{15}{12}=0\]

300 units of a commodity are demanded when its price is ₹20 per unit. If price falls by 10 per cent, its quantity demanded rises by 60 units. Calculate its price elasticity.

Solution:
\[\text{Price falls by}=20\times\frac{10}{100}=\bar{\mathrm{₹}}2\therefore\Delta\mathrm{P}=2\]
P = 20; Q = 300
ΔQ = 60
\[e_{p}=\frac{\Delta Q}{\Delta P}\cdot\frac{P}{Q}=\frac{60}{2}\times\frac{20}{300}=2\]

The price elasticity of demand is 2. If price changes by 5 per cent. What will be the percentage change is quantity?

Solution:
                 \[e_p=\frac{\%\text{Change in quantity demanded}}{\%\text{Change in price}}\]
                  \[2=\frac{\%\text{Change in quantity demanded}}{5}\]
Hence, % change in quantity demanded = 2 x 5 = 10.

The price elasticity of demand is 0.5. The % change in quantity is 6. What is % change in price?

Solution:
                 \[e_p=\frac{\%\text{Change in quantity demanded}}{\%\text{Change in price}}\]
                  \[\Rightarrow\quad0.5=\frac{6}{\%\text{Change in price}}\]
\[% \mathrm{Change~in~price}=\frac{6}{0.5}=\frac{6}{5/10} =6\times\frac{10}{5}=12\]