Q.A straight-line supply curve, when extended backward, cuts the price axis at ₹4 (where quantity supplied would be zero), and passes through the point where price is ₹10 and quantity supplied is 60 units. Find the price elasticity of supply at this point using the point (geometric) method.

When a straight-line supply curve cuts the positive price axis rather than passing through the origin, its elasticity at every point exceeds 1.

Step 1 — Equation of the supply line. The line passes through $(P=4, Q=0)$ and $(P=10, Q=60)$. Its slope is:

So the supply function is $Q_s = 10(P-4) = 10P - 40$ (check: at $P=4$, $Q_s = 0$; at $P=10$, $Q_s = 60$ ✓).

Step 2 — Apply the point-elasticity formula. For a linear supply function $Q_s = a+bP$, elasticity at any point equals $b \times P/Q$:

Step 3 — Confirm using the axis-intercept rule. Since the line's price-axis intercept (₹4) is positive and the line does NOT pass through the origin, elasticity of supply must exceed 1 at every point on it — this matches the calculated value of 1.67.

Cross-check via the arc method, using another pair of points on the SAME line: at $P=8$, $Q_s = 10(8)-40 = 40$; at $P=10$, $Q_s=60$. Average $P=9$, average $Q=50$.

This is close to, and — like the point-elasticity value of 1.67 — comfortably above 1, confirming relatively elastic supply; the two values differ slightly because point elasticity varies continuously along any straight-line supply curve that does not pass through the origin, always staying above 1 as the axis-intercept rule predicts.

Assuming every straight-line supply curve has the SAME elasticity at every point — this is true ONLY for a line passing through the origin; a line with a positive price-axis intercept has elasticity that varies continuously along its length, though it always remains above 1.