If demand function for a product is Qd 30 - 4P ... - JAMB Economics 2023 Question

Given \( Q_d = 30 - 4P \) and the initial values \( Q_d = 14 \) and \( P = 4 \), we can find \( \Delta Q_d \) and \( \Delta P \):

\[ \Delta Q_d = Q_d(\text{final}) - Q_d(\text{initial}) = (30 - 4 \times 5) - (30 - 4 \times 4) = 10 - 14 = -4 \]

\[ \Delta P = P(\text{final}) - P(\text{initial}) = 5 - 4 = 1 \]

Now, calculate \( \%\Delta Q_d \) and \( \%\Delta P \):

\[ \% \Delta Q_d = \frac{\Delta Q_d}{Q_d(\text{initial})} \times 100 = \frac{-4}{14} \times 100 \]

\[ \% \Delta P = \frac{\Delta P}{P(\text{initial})} \times 100 = \frac{1}{4} \times 100 \]

Now substitute these into the formula for price elasticity of demand (Ed):

\[ Ed = \frac{\%\Delta Q_d}{\%\Delta P} \]

Q = 14, P = 4

Qd = 30 - 4p

∆q/∆p = - 4

Ed = \(\frac{∆q}{∆p}\times\frac{p}{q}\)

= - 4 x 4/14

= Ed = -1.14

Note: The result is negative since demand is typically inversely related to price, but when stating the result, the negative sign is often dropped. So, if the result is -1.14, you can state it as approximately 1.14.