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Exercises · Q25

Q.Suppose the price elasticity of demand for a good is −0.2-0.2. How will the expenditure on the good be affected if there is a 10% increase in the price of the good?

Manipur CohsemTextbookSubjective· 3mImportance★★★★★
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When demand is inelastic (∣Ed∣<1|E_d| < 1), price and total expenditure move in the same direction. A 10% price rise with elasticity −0.2-0.2 causes quantity to fall by only 2%, so total expenditure increases.

Price elasticity of demand measures the responsiveness of quantity demanded to a change in price. It tells us by what percentage quantity demanded changes when price changes by one percent. The formula is:

Ed=Percentage change in quantity demandedPercentage change in priceE_d = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}

An elasticity of −0.2-0.2 means demand is inelastic—the absolute value is less than 1. When demand is inelastic, consumers are relatively unresponsive to price changes. They continue buying almost the same quantity even when price rises, perhaps because the good is a necessity or has few substitutes.

The key insight is how this affects total expenditure (or total revenue from the seller's perspective). Total expenditure is simply price times quantity: Expenditure=P×Q\text{Expenditure} = P \times Q.

When price rises by 10% and elasticity is −0.2-0.2, we can calculate the percentage change in quantity demanded:

Percentage change in Q=Ed×Percentage change in P=(−0.2)×10%=−2%\text{Percentage change in } Q = E_d \times \text{Percentage change in } P = (-0.2) \times 10\% = -2\%

So quantity demanded falls by only 2%.

Now let's trace what happens to expenditure. Initially, suppose P=P0P = P_0 and Q=Q0Q = Q_0, so expenditure is P0Q0P_0 Q_0.

After the changes:

  • New price: P1=1.10P0P_1 = 1.10 P_0 (a 10% increase)
  • New quantity: Q1=0.98Q0Q_1 = 0.98 Q_0 (a 2% decrease)

New expenditure becomes:

Expenditurenew=P1×Q1=(1.10P0)(0.98Q0)=1.078P0Q0\text{Expenditure}_{\text{new}} = P_1 \times Q_1 = (1.10 P_0)(0.98 Q_0) = 1.078 P_0 Q_0

The expenditure has increased by a factor of 1.078, which is a 7.8% increase. …

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