Suppose the price of product X is reduced from $16.00 to $12.00 and, as a result, the quantity of X demanded increases from 300 to 450.Using the midpoint method, the price elasticity of demand for X in the given price range is:
A)1.40
B)1.00
C)0.40
D)0.29

Question

Quizplus · Accepted Answer

Using the midpoint method formula for calculating price elasticity of demand:

%ΔQd = [(Q2-Q1)/((Q2+Q1)/2)] * 100

%ΔP = [(P2-P1)/((P2+P1)/2)] * 100

Price elasticity of demand = %ΔQd / %ΔP

Substituting the given values:

%ΔQd = [(450-300)/((450+300)/2)] * 100 = 50%

%ΔP = [(12-16)/((12+16)/2)] * 100 = -25%

Price elasticity of demand = 50% / (-25%) = -2

Since the price elasticity of demand is a negative value, we can take its absolute value to get the magnitude of the elasticity. Therefore, the price elasticity of demand for X in the given price range is:

|Price elasticity of demand| = |-2| = 2

However, the question asks for the elasticity using the midpoint method, which takes the average of the initial and final prices and quantities to calculate the percentage changes. Therefore, we need to calculate the midpoint for both price and quantity:

Quantity midpoint = (300 + 450) / 2 = 375

Price midpoint = ($16.00 + $12.00) / 2 = $14.00

%ΔQd = [(450-300)/375] * 100 = 40%

%ΔP = [(12-16)/14] * 100 = -28.57%

Price elasticity of demand = 40% / (-28.57%) = -1.4

Again, taking the absolute value:

|Price elasticity of demand| = |-1.4| = 1.4

Therefore, the price elasticity of demand using the midpoint method is 1.4, which corresponds to choice A.

Suppose the Price of Product X Is Reduced from $16