(a) Define price elasticity. (b) If at N 8.00 per tuber, twenty tubers were demanded and when the price fell to N 6. 00 per tuber, thirty tubers were demand...

Answer Details

(a) Price elasticity of demand measures how responsive the quantity demanded of a good is to a change in its price. It is the ratio of the percentage change in quantity demanded to the percentage change in price:

\[ E_d = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}} \]

If a small price change causes a large change in quantity, demand is elastic (\(E_d>1\)); if quantity barely responds, demand is inelastic (\(E_d<1\)).

(b) Identify the values. Original price and quantity: \(P_1 = N8.00\), \(Q_1 = 20\) tubers. New price and quantity: \(P_2 = N6.00\), \(Q_2 = 30\) tubers. So \(\Delta Q = 30-20 = 10\) and \(\Delta P = 6-8 = -2\).

Percentage change in quantity demanded:

\[ \frac{\Delta Q}{Q_1}\times 100 = \frac{10}{20}\times 100 = 50\% \]

Percentage change in price:

\[ \frac{\Delta P}{P_1}\times 100 = \frac{-2}{8}\times 100 = -25\% \]

Therefore:

\[ E_d = \left|\frac{50\%}{-25\%}\right| = 2 \]

The elasticity of demand is 2. Since \(E_d = 2 > 1\), demand for the tubers is elastic: quantity demanded responds more than proportionately to the price change. The value is normally reported as a positive number even though price and quantity move in opposite directions, because the negative sign only reflects the downward-sloping demand curve.