Q.A supply function is given by $Q_s = 3P - 15$. Find the price elasticity of supply at $P = ₹10$, and verify your answer by comparing quantity supplied at $P=₹10$ and $P=₹12$.

This supply line cuts the price axis at a positive intercept (it needs a price of ₹5 before any quantity is supplied at all), which by the geometric-method rule always means supply is relatively elastic. …

Step 1 — Quantity supplied at $P=10$.

Step 2 — Point elasticity using the slope.

Slope $\frac{dQ_s}{dP} = 3$ (constant, since the function is linear).

Since $E_s = 2 > 1$, supply is relatively elastic at this price. …

Cross-check using the percentage method between two points. At $P=12$: $Q_s = 3(12)-15 = 21$. $\%\Delta Q_s = \frac{21-15}{15}\times100=40\%$; $\%\Delta P = \frac{12-10}{10}\times100=20\%$. $E_s = \frac{40}{20}=2$ — exactly matches the point-elasticity answ …

Confusing which axis the intercept lies on — a positive PRICE-intercept (found by setting $Q_s=0$) signals relatively elastic supply, while a positive QUANTITY-intercept (found by setting $P= …