Q.A supply function is given by $Q_s = 2P + 10$. Find the price elasticity of supply at $P = ₹15$, and verify your answer using the quantity-axis intercept.

This supply line cuts the quantity axis at a positive intercept (some quantity is still supplied even at a price of zero), which by the geometric-method rule always means supply is relatively inelastic. …

Step 1 — Quantity supplied at $P=15$.

Step 2 — Point elasticity using the slope.

Slope $\frac{dQ_s}{dP} = 2$ (constant).

Since $E_s = 0.75 < 1$, supply is relatively inelastic at this price. …

Cross-check using the percentage method between two points. At $P=20$: $Q_s = 2(20)+10 = 50$. $\%\Delta Q_s = \frac{50-40}{40}\times100=25\%$; $%\Delta P = \frac{20-15}{15}\times100\appro …

Assuming a positive quantity-intercept means the good is 'always available free of cost' — it is simply a mathematical feature of the line describing relatively inelastic supply over the region actually obs …