Using the midpoint method, the elasticity of demand for headsets is about _____.
Answer (2)
Using the midpoint method, the price elasticity of demand for headsets is calculated to be approximately 14.16. This indicates that the demand is highly elastic, meaning small price changes can result in significant changes in quantity demanded. Understanding this elasticity helps businesses make informed pricing decisions.
;
Calculate the average quantity: 2 494 + 359 = 426.5 .
Calculate the average price: 2 5750 + 5880 = 5815 .
Calculate percentage changes: Quantity 426.5 − 135 × 100 = − 31.653% , Price 5815 130 × 100 = 2.236% .
Determine price elasticity of demand: 2.236 − 31.653 = 14.16 .
14.16
Explanation
Understanding the Problem We are asked to calculate the price elasticity of demand using the midpoint method, given the original and new quantities and prices for headsets. The midpoint method helps us to compute percentage changes relative to the average of the initial and final values, providing a more accurate elasticity measure.
Calculating Average Quantity and Price First, we need to calculate the average quantity and average price. The average quantity is calculated as: 2 Original Quantity + New Quantity = 2 494 + 359 = 2 853 = 426.5 The average price is calculated as: 2 Original Price + New Price = 2 5750 + 5880 = 2 11630 = 5815
Calculating Change in Quantity and Price Next, we calculate the change in quantity and the change in price. The change in quantity is: New Quantity − Original Quantity = 359 − 494 = − 135 The change in price is: New Price − Original Price = 5880 − 5750 = 130
Calculating Percentage Changes Now, we calculate the percentage change in quantity and the percentage change in price. The percentage change in quantity is: Average Quantity Change in Quantity × 100 = 426.5 − 135 × 100 = − 31.653% The percentage change in price is: Average Price Change in Price × 100 = 5815 130 × 100 = 2.236% Note that the values provided in the table for percentage change in quantity (-28.97%) and average quantity (431.5) are slightly different from our calculated values. We will use the calculated values for accuracy.
Calculating Price Elasticity of Demand Finally, we calculate the price elasticity of demand by dividing the percentage change in quantity by the percentage change in price and taking the absolute value: Price Elasticity of Demand = Percentage Change in Price Percentage Change in Quantity = 2.236 − 31.653 = ∣ − 14.159∣ = 14.159 Rounding to two decimal places, the price elasticity of demand is approximately 14.16.
Final Answer Therefore, using the midpoint method, the price elasticity of demand for headsets is about 14.16.
Examples
Understanding price elasticity of demand is crucial for businesses. For example, if a company knows that the demand for its product is highly elastic (greater than 1), it understands that a small increase in price will lead to a large decrease in quantity demanded. This knowledge can help the company make informed decisions about pricing strategies, promotions, and product development. Conversely, if demand is inelastic (less than 1), the company knows that it can increase prices without significantly impacting the quantity demanded, which can help maximize revenue.
