Given the figures below :
Price of commodity A in January = N5.00
Price of commodity A in February = N7.00
Quantity of A bought in January = 20 kg
Quantity of A bought in February = 16 kg (a) Calculate:
(i) Percentage change in quantity bought (% )
(ii) Percentage change in price of A (% )
(iii) Coefficient of price elasticity of demand (e)
(b) From your answer:
(i) is the demand elastic or inelastic?
(ii) How do you know this?
Explanation
| Month | Price | Quantity Demanded |
| January | N5 | 20k |
| Febuary | N7 | 16k |
(a) (i) Percentage change in quantity demanded:
\(\frac{4}{20} \times \frac{100}{1}\) = 20%
Note 20kg - 16kg = 4kg
(ii) Percentage change in price of A:
\(\frac{2}{5}\) x 100 = 40%
(iii) Co-efficient of price elasticity
ED = Percentage change in quantity demanded
Percentage change in Price
\(\frac{20%}{40%}\) = \(\frac{1}{2}\) or 0.5
ED = 0.5 Atternatively use Calculus.
ED = \(\frac{dq}{dp} \times \frac{p}{q}\)
dQ = 20 - 16 = 4
dp = 7 - 5 =2
\(\frac{4}{20} \times \frac{ 5}{2}\)
\(\frac{20}{40} = \frac{1}{2}\) or 0.5