A commodity's market supply curve is given by the equation Qs = 5P (a straight line passing through the origin

Worked Examples · Example 3

Q. A commodity's market supply curve is given by the equation Qs = 5P (a straight line passing through the origin). Show, by computing the price elasticity of supply at two different price levels — ₹4 and ₹8 — that elasticity of supply equals 1 at every point on such a curve.

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Step 1 — Elasticity at P = ₹4. From $Q_s = 5P$ , at $P=4$ : $Q_s = 5\times4 = 20$ . Since the slope $b=5$ is constant:

E_s = b \times \frac{P}{Q} = 5 \times \frac{4}{20} = \frac{20}{20} = 1

Step 2 — Elasticity at P = ₹8. At $P=8$ : $Q_s = 5\times8 = 40$ .

$E_s = 5 \times \frac{8}{40} = \frac{40}{40} = 1$ …

Q.A commodity's market supply curve is given by the equation Qs = 5P (a straight line passing through the origin). Show, by computing the price elasticity of supply at two different price levels — ₹4 and ₹8 — that elasticity of supply equals 1 at every point on such a curve.