Price Elasticity of Demand Calculator

How to Calculate Price Elasticity of Demand

Price elasticity of demand is a measure of the relationship between a change in the quantity demanded of a particular good and a change in its price. Understanding this concept is crucial for businesses and economists to analyze consumer behavior and make informed pricing decisions.

Price Elasticity of Demand Formula

The formula for calculating price elasticity of demand is:

$$\text{Price Elasticity of Demand} = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}}$$

Where:

• Percentage Change in Quantity Demanded = \\(\frac{Q_2 - Q_1}{Q_1} \times 100\\)
• Percentage Change in Price = \\(\frac{P_2 - P_1}{P_1} \times 100\\)
• \\(Q_1\\) and \\(P_1\\) are the initial quantity and price
• \\(Q_2\\) and \\(P_2\\) are the final quantity and price

Calculation Steps

1. Determine the initial price (P₁) and quantity (Q₁).
2. Determine the final price (P₂) and quantity (Q₂).
3. Calculate the percentage change in quantity demanded.
4. Calculate the percentage change in price.
5. Divide the percentage change in quantity by the percentage change in price.
6. Take the absolute value of the result.

Example Calculation

Let's calculate the price elasticity of demand for a product with the following data:

• Initial Price (P₁): $10
• Final Price (P₂): $12
• Initial Quantity (Q₁): 100 units
• Final Quantity (Q₂): 80 units

Step 1: Calculate percentage change in quantity demanded

$$\text{Percentage Change in Quantity} = \frac{80 - 100}{100} \times 100 = -20\%$$

Step 2: Calculate percentage change in price

$$\text{Percentage Change in Price} = \frac{12 - 10}{10} \times 100 = 20\%$$

Step 3: Calculate price elasticity of demand

$$\text{Price Elasticity of Demand} = \frac{-20\%}{20\%} = -1$$

Step 4: Take the absolute value

$$|\text{Price Elasticity of Demand}| = |-1| = 1$$

Therefore, the price elasticity of demand for this product is 1, indicating unit elasticity.

Visual Representation

This diagram illustrates the change in demand due to a price change. The blue line represents the demand curve, and the red points show the initial and final price-quantity combinations. The slope of this line visually represents the price elasticity of demand.