Using the demand schedule table (Price $5→Quantity 60, $10→50, $15→40, $20→30, $25→20, $30→10), calculate the price elasticity of demand when price changes from (i) $5 to $10 and (ii) $25 to $30.

What you are calculating here

Price elasticity of demand (PED) measures how responsive quantity demanded is to a change in price. Because the question gives two price points each time, the midpoint (arc elasticity) formula is the standard choice so your percentage changes do not depend on which direction you calculate.

Use the midpoint (arc) elasticity formula

$$PED=\frac{\frac{\Delta Q}{\bar Q}}{\frac{\Delta P}{\bar P}}$$ where $\Delta Q = Q_2-Q_1$, $\bar Q=\frac{Q_1+Q_2}{2}$, $\Delta P=P_2-P_1$, and $\bar P=\frac{P_1+P_2}{2}$.

(i) Price changes from $5 to $10

From the table: $P_1=5,\ Q_1=60$ and $P_2=10,\ Q_2=50$.

Compute changes and midpoints:

• $\Delta Q = 50-60=-10$, and $\bar Q=\frac{60+50}{2}=55$
• $\Delta P = 10-5=5$, and $\bar P=\frac{5+10}{2}=7.5$

Now plug in: $$PED=\frac{-10/55}{5/7.5}=\frac{-0.1818}{0.6667}\approx -0.27$$ Magnitude $|PED|\approx 0.27<1$, so demand is inelastic over this range.

(ii) Price changes from $25 to $30

From the table: $P_1=25,\ Q_1=20$ and $P_2=30,\ Q_2=10$.

Compute changes and midpoints:

• $\Delta Q = 10-20=-10$, and $\bar Q=\frac{20+10}{2}=15$
• $\Delta P = 30-25=5$, and $\bar P=\frac{25+30}{2}=27.5$

Now plug in: $$PED=\frac{-10/15}{5/27.5}=\frac{-0.6667}{0.1818}\approx -3.67$$ Magnitude $|PED|\approx 3.67>1$, so demand is elastic over this range.

Quick interpretation tip

PED is usually negative for a normal downward-sloping demand curve. When comparing responsiveness, economists often compare the magnitude $|PED|$ to 1.