Question 24 of 26intermediate🔧 ApplyNumerical3 marks

Suppose the price elasticity of demand for a good is −0.2-0.2. If there is a 5% increase in the price of the good, by what percentage will the demand for the good go down?

Correct Answer

Given: Price elasticity of demand (eDe_D) = -0.2 Percentage change in price = 5% (increase)

Formula: Price elasticity of demand is defined as:

eD=percentage change in demandpercentage change in pricee_D = \frac{\text{percentage change in demand}}{\text{percentage change in price}}

Calculation: Substituting the values in the formula:

−0.2=percentage change in demand5%-0.2 = \frac{\text{percentage change in demand}}{5\%}

Percentage change in demand = −0.2×5%=−1%-0.2 \times 5\% = -1\%

Conclusion: The demand for the good will go down by 1%. Since the absolute value of elasticity (0.2) is less than 1, the demand is inelastic, meaning the percentage change in demand is less than the percentage change in price.

Exercise: EXERCISES | Q: 24
For More Understanding

Explanation

This question tests the application of the price elasticity formula. The textbook defines price elasticity of demand as the percentage change in demand divided by the percentage change in price. By rearranging this formula, we can find the percentage change in demand by multiplying elasticity by the percentage change in price. The negative sign indicates that demand moves in the opposite direction of price change - when price increases, demand decreases.

Solution Steps

  1. Step 1: Identify the formula: e_D = (percentage change in demand) ÷ (percentage change in price)

  2. Step 2: Substitute the given values: -0.2 = (percentage change in demand) ÷ 5%

  3. Step 3: Rearrange to find percentage change in demand: percentage change in demand = -0.2×50.2 \times 5%

  4. Step 4: Calculate: percentage change in demand = -1%

  5. Step 5: Interpret the result: Demand decreases by 1% (the negative sign indicates a decrease)

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