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 ...

Answer Details

Concept. Price elasticity of demand (PED) measures how responsive quantity demanded is to a change in price. It is the percentage change in quantity demanded divided by the percentage change in price.

Given: Price rises from N5.00 (January) to N7.00 (February); quantity bought falls from 20 kg to 16 kg.

(a)(i) Percentage change in quantity bought.

\[ \%\Delta Q = \frac{16 - 20}{20}\times 100 = \frac{-4}{20}\times 100 = -20\% \]

(a)(ii) Percentage change in price.

\[ \%\Delta P = \frac{7 - 5}{5}\times 100 = \frac{2}{5}\times 100 = +40\% \]

(a)(iii) Coefficient of price elasticity of demand.

\[ e = \frac{\%\Delta Q}{\%\Delta P} = \frac{-20}{40} = -0.5 \]

Ignoring the negative sign (which merely reflects the inverse law of demand), the coefficient is 0.5.

(b)(i) Since the coefficient is less than 1, demand is inelastic.

(b)(ii) How we know. The proportionate change in quantity demanded (20%) is smaller than the proportionate change in price (40%). When the percentage change in quantity is less than the percentage change in price, giving a coefficient below 1, demand is price-inelastic: buyers are relatively unresponsive to the price change.

Examination takeaway. Always compare the two percentages: quantity changing by less than price means inelastic (e < 1); by more than price means elastic (e > 1); and the minus sign only signals the normal downward-sloping demand relationship.