How is price elasticity of supply computed by arc method?

The arc elasticity of supply measures the responsiveness of quantity supplied to a change in price over a range (arc) of values. It is computed using the midpoint (arc) formula:

$$E_s=\frac{\%\text{ change in quantity supplied}}{\%\text{ change in price}}=\frac{\Delta Q/\overline{Q}}{\Delta P/\overline{P}}$$

Where:

• $\Delta Q=Q_2-Q_1$ (change in quantity supplied),
• $\overline{Q}=\frac{Q_1+Q_2}{2}$ (average quantity),
• $\Delta P=P_2-P_1$ (change in price),
• $\overline{P}=\frac{P_1+P_2}{2}$ (average price).

The formula simplifies to:

$$E_s=\frac{(Q_2-Q_1)}{(P_2-P_1)}\times \frac{\overline{P}}{\overline{Q}}$$

This method avoids asymmetry in elasticity calculations when moving from $P_1$ to $P_2$ or vice versa.