In the market for backpacks, 100 backpacks are sold at $40 each. Then a fall in wages results in sales of 500 backpacks at a price of $20 each. Using the midpoint method, what is the absolute value of the elasticity of demand for backpacks?
A) 0.125
B) 0.5
C) 2
D) 8

Question

Quizplus · Accepted Answer

We can calculate the elasticity of demand using the midpoint method formula:

Elasticity of Demand = [(Q2 - Q1) / ((Q2 + Q1)/2)] / [(P2 - P1) / ((P2 + P1)/2)]

where Q1 = 100, Q2 = 500, P1 = $40, and P2 = $20.

Plugging in the values, we get:

Elasticity of Demand = [(500 - 100) / ((500 + 100)/2)] / [($20 - $40) / (($20 + $40)/2)]

Elasticity of Demand = [400 / 300] / [-20 / 30]

Elasticity of Demand = 1.33 / -0.67

Elasticity of Demand = -2 (absolute value)

Therefore, the absolute value of the elasticity of demand for backpacks is 2. This means that the demand for backpacks is relatively elastic, as the quantity demanded changes more than proportionally to the change in price.

In the Market for Backpacks, 100 Backpacks Are Sold at $40