Let's walk through the step-by-step solution to compute the Price Elasticity Demand (\(E_d)). --- Step 1 Understand the given data Variable | Value|------------|---------| | Initial (\(P1\)) | \$50 | | New Price (\(P_2\)) | \$ | | Initial Quantity Demanded (\(Q_1\)) | 120,000 units | | New Quantity Demanded (\(Q_2\)) | 108,000 units | --- ## Step 2: Calculate the change in price (\(\Delta P\)) \[ \Delta P = P_2 - P_1 = 55 - 50 = \$5 \] ## Step 3: Calculate the change in quantity demanded (\(\Delta Q\)) \[ \Delta Q = Q_2 - Q_1 = 108,000 - 120,000 = -12,000 \text{ units} \] (Note: The negative sign indicates a decrease in quantity demanded.) --- ## Step 4: Calculate the average price (\(\frac{P_1 + P_2}{2}\)) and average quantity (\(\frac{Q_1 + Q_2}{2}\)) \[ \text{Average Price} = \frac{50 + 55}{2} = \frac{105}{2} = \$52.50 \] \[ \text{Average Quantity} = \frac{120,000 + 108,000}{2} = \frac{228,000}{2} = 114,000 \text{ units} \] --- ## Step 5: Calculate the elasticity \(E_d\) The elasticity formula is: \[ E_d = \left( \frac{\Delta Q}{\Delta P} \right) \times \left( \frac{P_{avg}}{Q_{avg}} \right) \] Substituting the values: \[ E_d = \left( \frac{-12,000}{5} \right) \times \left( \frac{52.50}{114,000} \right) \] Calculate each part: \[ \frac{-12,000}{5} = -2,400 \] \[ \frac{52.50}{114,000} \approx .0004605 \] Now multiply: \[ E_d = -2,400 \times .0004605 \approx -1.105 \] --- ## **Final Answer:** \[ \boxed{ E_d \approx -1.105 } \] ### Interpretation: - The absolute value of the price elasticity of demand is approximately **1.105**. - Since \( |E_d| > 1 \), demand is **elastic**; consumers are relatively sensitive to price changes. A 1% increase in price results in approximately a 1.105% decrease in quantity demanded. --- ## Summary: - **Price Elasticity of Demand** during 2023-24 = **approximately 1.105 (elastic demand)**.

# Step-by-Step Calculation of Price Elasticity of Demand We will calculate the Price Elasticity of Demand (\(E_d\)) for a premium cotton shirt based on the provided data. ## Step 1: Understand the Given Data | Variable | Value | |--------------------------------|----------------| | Initial Price (\(P_1\)) | \$50 | | New Price (\(P_2\)) | \$55 | | Initial Quantity Demanded (\(Q_1\)) | 120,000 units | | New Quantity Demanded (\(Q_2\)) | 108,000 units | ## Step 2: Calculate the Change in Price (\(\Delta P\)) \[ \Delta P = P_2 - P_1 = 55 - 50 = \$5 \] ## Step 3: Calculate the Change in Quantity Demanded (\(\Delta Q\)) \[ \Delta Q = Q_2 - Q_1 = 108,000 - 120,000 = -12,000 \text{ units} \] (Note: The negative sign indicates a decrease in quantity demanded.) ## Step 4: Calculate the Average Price and Average Quantity ### Average Price \[ P_{avg} = \frac{P_1 + P_2}{2} = \frac{50 + 55}{2} = \$52.50 \] ### Average Quantity \[ Q_{avg} = \frac{Q_1 + Q_2}{2} = \frac{120,000 + 108,000}{2} = 114,000 \text{ units} \] ## Step 5: Calculate the Elasticity \(E_d\) The formula for elasticity is: \[ E_d = \left( \frac{\Delta Q}{\Delta P} \right) \times \left( \frac{P_{avg}}{Q_{avg}} \right) \] ### Substitute the Values \[ E_d = \left( \frac{-12,000}{5} \right) \times \left( \frac{52.50}{114,000} \right) \] ### Calculate Each Part 1. **Change in Quantity per Change in Price:** \[ \frac{-12,000}{5} = -2,400 \] 2. **Price to Quantity Ratio:** \[ \frac{52.50}{114,000} \approx 0.0004605 \] ### Combine to Find \(E_d\) \[ E_d = -2,400 \times 0.0004605 \approx -1.105 \] ## Final Answer \[ \boxed{E_d \approx -1.105} \] ### Interpretation - The absolute value of the price elasticity of demand is approximately **1.105**. - Since \( |E_d| > 1 \), demand is **elastic**; consumers are sensitive to price changes. A 1% increase in price results in approximately a 1.105% decrease in quantity demanded. ## Summary - **Price Elasticity of Demand** during 2023-24 = **approximately 1.105 (elastic demand)**.

# Price Elasticity of Demand (Definition) ## Definition Price Elasticity of Demand (\(E_d\)) measures how the quantity demanded of a good responds to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. ## Formula The formula for calculating \(E_d\) is: \[ E_d = \left( \frac{\Delta Q}{\Delta P} \right) \times \left( \frac{P_{avg}}{Q_{avg}} \right) \] Where: - \(\Delta Q\) = Change in quantity demanded - \(\Delta P\) = Change in price - \(P_{avg}\) = Average price - \(Q_{avg}\) = Average quantity demanded ## Interpretation - **Elastic Demand**: \( |E_d| > 1 \) (Consumers are sensitive to price changes) - **Inelastic Demand**: \( |E_d| < 1 \) (Consumers are less sensitive to price changes) - **Unitary Elastic Demand**: \( |E_d| = 1 \) (Percentage change in quantity demanded equals percentage change in price) ### Importance Understanding price elasticity helps businesses and policymakers make informed decisions regarding pricing strategies, product availability, and revenue predictions.

# Average Price and Average Quantity ## Definitions ### Average Price The **Average Price** is the midpoint between the initial price and the new price of a product. It provides a representative price level that can be used for calculations related to elasticity and demand. #### Formula The formula for calculating the Average Price (\(P_{avg}\)) is: \[ P_{avg} = \frac{P_1 + P_2}{2} \] Where: - \(P_1\) = Initial Price - \(P_2\) = New Price ### Average Quantity The **Average Quantity** is the midpoint between the initial quantity demanded and the new quantity demanded. This value is useful in elasticity calculations to reflect changes in demand over a range of prices. #### Formula The formula for calculating the Average Quantity (\(Q_{avg}\)) is: \[ Q_{avg} = \frac{Q_1 + Q_2}{2} \] Where: - \(Q_1\) = Initial Quantity Demanded - \(Q_2\) = New Quantity Demanded ## Importance Both Average Price and Average Quantity are critical for calculating the Price Elasticity of Demand (\(E_d\)), which helps businesses understand consumer sensitivity to price changes. This understanding aids in effective pricing strategies and revenue management decisions.