Q.A straight-line demand curve meets the price axis at ₹12 (where quantity demanded is zero) and meets the quantity axis at 60 units (where price is zero). Find the price elasticity of demand at the point on this line where price is ₹8, using the point (geometric) method.

On a straight-line demand curve, elasticity at any point can be read off directly from the lengths of the line above and below that point. …

Step 1 — Equation of the demand line. The line runs from $A$ (price-axis intercept, $P=12,\ Q=0$) to $B$ (quantity-axis intercept, $P=0,\ Q=60$). Its equation is:

(check: at $P=12$, $Q=60-60=0$; at $P=0$, $Q=60$.)

Step 2 — Locate the point R at P = 8.

So $R = (P=8,\ Q=20)$. …

Cross-check using the slope formula for point elasticity:

From $Q = 60-5P$, $\dfrac{dQ}{dP} = -5$. At $P=8,\ Q=20$: …

Measuring the segments from the wrong end (swapping lower and upper) inverts the ratio and gives the reciprocal of the correct elasticity; always identify which end of the line is the price-axis inte …