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Exercises · Q26

Q.Suppose there was a 4% decrease in the price of a good, and as a result, the expenditure on the good increased by 2%. What can you say about the elasticity of demand?

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A 4% price decrease causing a 2% increase in total expenditure implies that demand is elastic (|E| > 1), because the quantity demanded rose by more than 4% — enough to more than offset the price drop.

The key here is to connect price elasticity of demand with total expenditure — a classic relationship in microeconomics. When price falls, expenditure can go up, down, or stay the same depending on how responsive quantity demanded is. If demand is elastic (|E| > 1), a price cut leads to a proportionally larger rise in quantity, so total expenditure rises. If demand is inelastic (|E| < 1), the quantity rise is smaller, and expenditure falls. If unitary elastic, expenditure stays unchanged.

We are told: price falls by 4%, and expenditure rises by 2%. That tells us the quantity effect dominated the price effect. Let’s formalise this.

Total expenditure E=P×QE = P \times Q.

Percentage change in E≈%ΔP+%ΔQE \approx \%\Delta P + \%\Delta Q (for small changes).

Price elasticity of demand Ed=%ΔQ%ΔPE_d = \frac{\%\Delta Q}{\%\Delta P}.

Given %ΔP=−4%\%\Delta P = -4\% and %ΔE=+2%\%\Delta E = +2\%, we can find %ΔQ\%\Delta Q:

%ΔE=%ΔP+%ΔQ\%\Delta E = \%\Delta P + \%\Delta Q

2%=(−4%)+%ΔQ2\% = (-4\%) + \%\Delta Q

%ΔQ=6%\%\Delta Q = 6\%

So quantity demanded increased by 6% when price fell by 4%. Now compute elasticity:

Ed=%ΔQ%ΔP=6%−4%=−1.5E_d = \frac{\%\Delta Q}{\%\Delta P} = \frac{6\%}{-4\%} = -1.5

The absolute value is ∣Ed∣=1.5|E_d| = 1.5, which is greater than 1. Hence demand is elastic. …

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