To calculate the own-price elasticity of demand (PED) when the price changes, we use the formula:

$\text{PED} = \frac{\%\text{ Change in Quantity Demanded}}{\%\text{ Change in Price}}$

Given the demand equation: $Q = 1000 - 20P$

Step 1: Find the Initial Quantity Demanded ($Q_1$) and New Quantity Demanded ($Q_2$)

1. Initial Price $P_1 = 30$: $Q_1 = 1000 - 20 \times 30 = 1000 - 600 = 400$

2. New Price $P_2 = 25$: $Q_2 = 1000 - 20 \times 25 = 1000 - 500 = 500$

Step 2: Calculate the Change in Quantity Demanded and Change in Price

1. Change in Quantity Demanded ($\Delta Q$): $\Delta Q = Q_2 - Q_1 = 500 - 400 = 100$

2. Change in Price ($\Delta P$): $\Delta P = P_2 - P_1 = 25 - 30 = -5$

Step 3: Calculate the Percentage Changes

1. Percentage Change in Quantity Demanded: $\%\text{ Change in Quantity Demanded} = \frac{\Delta Q}{Q_1} \times 100 = \frac{100}{400} \times 100 = 25\%$

2. Percentage Change in Price: $\%\text{ Change in Price} = \frac{\Delta P}{P_1} \times 100 = \frac{-5}{30} \times 100 \approx -16.67\%$

Step 4: Calculate the Own-Price Elasticity of Demand

$\text{PED} = \frac{25\%}{-16.67\%} \approx -1.5$

Rounding this to two decimal places: $\text{PED} \approx -1.50$

The own-price elasticity of demand when the price declines from $30 to $25 is approximately -1.50.

Interpretation

Since the absolute value of the elasticity is greater than 1, the demand for this brand of sandals is elastic in this price range, meaning that the percentage change in quantity demanded is greater than the percentage change in price.

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Relative Questions:

1. What happens to total revenue when the price is decreased for an elastic demand?
2. How does this elasticity change if the price drops further, say from $25 to $20?
3. What are the factors that generally affect the elasticity of demand for a product?
4. How would a perfectly inelastic demand curve look compared to this one?
5. How would you interpret the elasticity if the value was less than 1?

Tip:

Elasticity helps businesses understand how sensitive their consumers are to changes in price, which can be crucial for pricing strategies.