Question

When the price of a commodity declines from Rs. 15 per unit to Rs. 10 per unit, its demand increases from 40 units to 50 units. Calculate elasticity of demand. 
 

Hint:

Arc elasticity: $E_d=\dfrac{\Delta Q/\bar Q}{\Delta P/\bar P}$; take absolute value for magnitude.

Answer 1

Use the arc (mid-point) elasticity formula to avoid base dependence: 
\[ E_d=\dfrac{\%\Delta Q}{\%\Delta P}=\dfrac{\dfrac{Q_2-Q_1}{(Q_1+Q_2)/2}}{\dfrac{P_2-P_1}{(P_1+P_2)/2}}. \] Given $P_1=15$, $P_2=10$, $Q_1=40$, $Q_2=50$. 
 

Step 1: $\Delta Q=50-40=10$, average quantity $\bar Q=\dfrac{40+50}{2}=45 $\Rightarrow$ %\Delta Q=\dfrac{10}{45}=0.2222$. 
 

Step 2: $\Delta P=10-15=-5$, average price $\bar P=\dfrac{15+10}{2}=12.5 $\Rightarrow$ %\Delta P=\dfrac{-5}{12.5}=-0.4$. 
 

Step 3: $E_d=\dfrac{0.2222}{-0.4}=-0.5555\ldots$; demand elasticity in absolute value $|E_d|\approx 0.56$. 
Interpretation: The demand is inelastic (less than 1 in absolute value): a 1% fall in price raises quantity demanded by only about 0.56%. 
Why mid-point? Using averages treats the two observations symmetrically and is standard for discrete changes. 
Graph (verbal): On a demand curve, mark points $(P_1=15, Q_1=40)$ and $(P_2=10, Q_2=50)$; arc elasticity is computed over the chord connecting these points.