Understanding Price Elasticity of Demand

Price elasticity of demand ($E_d$) measures the responsiveness of the quantity demanded of a good to a change in its price. The percentage method calculates this elasticity using the percentage change in quantity demanded divided by the percentage change in price.

The formula for price elasticity of demand using the percentage method is:

$$E_d = \left| \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}} \right|$$

Let's break down the given information and calculate the components needed for the formula.

Calculating Percentage Change in Price

• Initial Price (P): Rs. 20 per unit
• New Price (P1): Rs. 15 per unit
• Change in Price ($\Delta$P): P1 - P = Rs. 15 - Rs. 20 = -Rs. 5

Now, we calculate the percentage change in price:

$$\text{Percentage Change in Price} = \left( \frac{\Delta P}{P} \right) \times 100$$ $$\text{Percentage Change in Price} = \left( \frac{-5}{20} \right) \times 100$$ $$\text{Percentage Change in Price} = (-0.25) \times 100$$ $$\text{Percentage Change in Price} = -25\%$$

The price falls by 25 percent.

Identifying Percentage Change in Quantity Demanded

The question directly states that when the price falls, the demand rises by 25 percent.

• Percentage Change in Quantity Demanded ($\%\Delta Q_d$): +25% (It's positive because demand rises).

Calculating Price Elasticity of Demand

Now we can substitute the percentage changes into the elasticity formula:

$$E_d = \left| \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}} \right|$$ $$E_d = \left| \frac{+25\%}{-25\%} \right|$$ $$E_d = |-1|$$ $$E_d = 1$$

Result

The price elasticity of demand is 1. This means that a 1 percent change in price leads to a 1 percent change in the quantity demanded. In this specific case, a 25% fall in price led to a 25% rise in demand.

The calculated price elasticity of demand is 1.0.