Final answer:
The elasticity of demand varies along a linear demand curve, so different values are obtained when calculating the elasticity as price falls from 5 to 4, and from 9 to 8. By using the demand curve equation P = 2/Q and the formula for elasticity, we can determine these different elasticity values.
Step-by-step explanation:
To derive the elasticity of demand from the demand curve equation P = 2/Q, we have to understand that the price elasticity of demand is defined as the percentage change in quantity demanded divided by the percentage change in price. Firml when the price falls from 5 to 4 and from 9 to 8, we will see different elasticity values since the elasticity of demand is not constant along a linear demand curve.
Let's calculate the elasticity of demand when the price falls from 5 to 4:
We first find the corresponding quantities (Q) from the demand curve for each price (P).
For P = 5, Q = 2/5 = 0.4
For P = 4, Q = 2/4 = 0.5
Then, we use the elasticity formula:
Elasticity = (ΔQ/Q_average)/(ΔP/P_average) where Δ represents the change and P_average and Q_average are the averages of the initial and final prices and quantities, respectively. The change in quantity (ΔQ) is 0.5 - 0.4 = 0.1, and the change in price (ΔP) is 4 - 5 = -1. The averages are Q_average = (0.4 + 0.5)/2 and P_average = (5 + 4)/2.
The same steps are repeated to calculate the elasticity when the price falls from 9 to 8.
Due to the nature of the demand curve, these elasticity values will differ, suggesting that the elasticity of demand changes along the curve. Therefore, we would not expect the answers to be the same for different price ranges.