What is the point elasticity when price is 12 rupees for the demand function P = 60 – 3q.
– 0.25
−0.25 option is correct.
Point price elasticity of demand for a linear demand curve is defined as \(E_{p} = \dfrac{dq}{dp} \cdot \dfrac{p}{q}\), evaluated at the given price–quantity combination.
Step 1 — invert the demand curve \(P = 60 - 3q\) to solve for quantity at the stated price: \(12 = 60 - 3q \Rightarrow q = 16\).
Step 2 — compute the slope \(\dfrac{dq}{dp}\). From \(q = \dfrac{60 - P}{3}\), we get \(\dfrac{dq}{dp} = -\dfrac{1}{3}\).
Step 3 — substitute into the elasticity formula: \(E_{p} = -\dfrac{1}{3} \cdot \dfrac{12}{16} = -\dfrac{12}{48} = -0.25\).
Elasticity is negative because the demand curve slopes downward, and the absolute value is less than unity, so demand at this price is inelastic. Options ignoring the sign or the p/q ratio miss either the slope or the point of evaluation.
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