Final answer:
Using the Midpoint Method to calculate the price elasticity for pencils shows that a price increase from €0.10 to €0.20 results in a decrease in quantity demanded from 1000 to 500 units, yielding an elasticity of 1. This confirms that the demand for pencils is unit price elastic.
Step-by-step explanation:
When discussing an increase in the price of pencils from €0.10 to €0.20 resulting in a decrease in the quantity demanded from 1000 pencils to 500 pencils, using the Midpoint Method is essential to calculate the Price Elasticity of Demand.
The Midpoint Method uses the average percent change in both the price and the quantity demanded to determine elasticity. The formula for the Midpoint Method is defined as:
Elasticity = (Percentage Change in Quantity Demanded) / (Percentage Change in Price)
To calculate the percentage changes, the change in each variable is divided by the average of the old and new values, multiplied by 100. For price: ((0.20 - 0.10) / ((0.20 + 0.10) / 2)) * 100 = 66.7%. For quantity: ((500 - 1000) / ((500 + 1000) / 2)) * (-100) = -66.7%. Therefore, Elasticity = |-66.7%| / 66.7% = 1.
This means the demand for pencils is indeed unit price elastic, where a one percent price change results in a one percent change in quantity demanded.
The complete question is:Using the midpoint method to calculate elasticity, if an increase in the price of pencils from €0.10 to €0.20 reduces the quantity demanded from 1000 pencils to 500 pencils, then the demand for pencils is unit price elastic.