Calculate the price elasticity of demand for a change in price from $100 to $140

Price

Quantity

$100

100

$140

20

Question

Calculate the price elasticity of demand for a change in price from $100 to $140

Price

Quantity

$100

100

$140

20

BlackTom AI · Accepted Answer

Let's start by identifying the given data and what we need to compute. The price changes from $100 to $140, and the quantity demanded changes from 100 units to 20 units. We will use the arc (midpoint) formula for price elasticity of demand to avoid issues with the direction of the change.

Step 1: Compute the percentage change in quantity demanded using the midpoint (average) quantity.
- Initial Q = 100, Final Q = 20, Midpoint Q = (100 + 20) / 2 = 60
- Change in Q = 20 − 100 = −80
- Percent change in Q = (ΔQ) / (Midpoint Q) = (−80) / 60 = −4/3 ≈ −1.333...

Step 2: Compute the percentage change in price using the midpoint (average) price.
- Initial P = $100, Final P = $140, Midpoint P = (100 + 140) / 2 = 120
- Change in P = 140 − 100 = 40
- Percent change in P = (ΔP) / (Midpoint P) = 40 / 120 = 1/3 ≈ 0.333...

Step 3: Form the elasticity ratio.
- PED using arc/midpoint method = (Percent change in Q) / (Percent change in P) = (−1.333...) / (0.333...) = −4

Step 4: Interpret the result.
- The magnitude is 4, and the negative sign indicates that quantity demanded moves inversely with price, as expected for a standard downward-sloping demand curve.

If one were to use a simple (non-midpoint) approach, the numbers would align with the same conclusion here, but the midpoint method provides a symmetric measure between the two price points and is typically preferred for discrete changes.

In summary, the price elasticity of demand for the move from $100 to $140 with quantity dropping from 100 to 20 is −4.0, indicating a highly elastic demand over this range.

BECO011 Week 2 Practice quiz

Calculate the price elasticity of demand for a change in price from $100 to $140 Price Quantity $100 100 $140 20

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