alleryA consumer buys 80 units of a good at Rs 4 per unit. If the price elasticity of demand is 4 (in magnitude), at what price will he buy 60 units?
ARs 3.80 per unit
BRs 4.20 per unit
CRs 5.00 per unit
DRs 4.05 per unit
Answer & Solution
Correct answer: B. Rs 4.20 per unit
1. Use $E_p = \dfrac{\Delta q}{\Delta p}\times\dfrac{p}{q}$ with $\Delta q = 80-60 = 20$, original $p=4$, $q=80$, new price $=x$.
2. Substitute: $4 = \dfrac{20}{x-4}\times\dfrac{4}{80}$.
3. Simplify $\dfrac{20\times4}{80} = 1$, so $4 = \dfrac{1}{x-4}$.
4. Then $x-4 = 0.25$, giving $x = 4.20$ per unit. Since quantity fell, price must have risen above Rs 4, ruling out Rs 3.80.
_Source: ICAI BoS CA Foundation Paper 4 Business Economics, Ch 2 Unit I "Law of Demand and Elasticity of Demand", p.19_
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