When the price of a sweater was $40, the store sold 150 sweaters per month. When it raised the price to $50 each, it sold 120 sweaters per month. Using the midpoint method, the price elasticity of demand for sweaters is _______.

Question

BlackTom AI · Accepted Answer

The problem asks to compute the price elasticity of demand using the midpoint method for the change in price from $40 to $50 and quantity from 150 to 120.
First, identify the changes: ΔQ = Q2 − Q1 = 120 − 150 = −30 and ΔP = P2 − P1 = 50 − 40 = 10.
Next, compute the midpoints (average values): Q_avg = (Q1 + Q2)/2 = (150 + 120)/2 = 135 and P_avg = (P1 + P2)/2 = (40 + 50)/2 = 45.
Now apply the midpoint formula for elasticity: Elasticity = (ΔQ/ΔP) × (P_avg/Q_avg).
Plug in the numbers: ΔQ/ΔP = −30/10 = −3, and P_avg/Q_avg = 45/135 = 1/3.
Multiplying these together gives Elasticity = (−3) × (1/3) = −1.0.
This indicates the elasticity magnitude is 1.0, meaning the percentage change in quantity demanded is equal in magnitude to the percentage change in price, in the opposite direction.
Note: The provided answer option, 1.0, matches the magnitude of the elasticity but the sign is negative in the standard interpretation of a downward-sloping demand curve. The question’s options are not shown here, but the computed midpoint elasticity magnitude is 1.0.

ECON 1023 (002) Midterm 1

When the price of a sweater was $40, the store sold 150 sweaters per month. When it raised the price to $50 each, it sold 120 sweaters per month. Using the midpoint method, the price elasticity of demand for sweaters is _______.

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