Shoes are priced at $75 per pair.

A vendor sells 20 pairs per day.

The vendor explores selling at $100 per pair.

At that price, the vendor sells 15 pairs over the day.

What is the elasticity of shoe sales to price.

Question

Shoes are priced at $75 per pair.

A vendor sells 20 pairs per day.

The vendor explores selling at $100 per pair.

At that price, the vendor sells 15 pairs over the day.

What is the elasticity of shoe sales to price.

BlackTom AI · Accepted Answer

We start by restating the information and framing the elasticity calculation clearly.
The initial price is 75 dollars and initial quantity is 20 pairs. The price rises to 100 dollars (a change of +25), and quantity drops to 15 pairs (a change of -5).
Elasticity of demand is defined as the percentage change in quantity demanded divided by the percentage change in price:
Elasticity = (%ΔQ) / (%ΔP).
Compute the percentage changes using the base values given:
%ΔP = ΔP / P_initial = 25 / 75 = 1/3 ≈ 0.3333.
%ΔQ = ΔQ / Q_initial = (-5) / 20 = -1/4 = -0.25.
Now form the ratio: Elasticity = (-0.25) / (0.3333) ≈ -0.75.
With that groundwork, evaluate each option by translating the fractions involved into the percentage-change form.
Option 1: -(25) / (5) equals -5. This option is a simple ratio of 25 to 5 and does not reflect the percentage-change formula at all; it ignores the base values 75 and 20, so it’s not correct as an elasticity expression.
Option 2: -(25/75) / (5/20) translates to -(ΔP / P_initial) divided by (ΔQ / Q_initial) rather than (ΔQ / Q_initial) divided by (ΔP / P_initial). This yields -(1/3) / (1/4) = -4/3 ≈ -1.333. While it uses the same pieces, it computes the reciprocal of the proper elasticity, so it does not match the standard elasticity definition.
Option 3: -(5/20) / (25/75) equals (-0.25) / (0.3333) ≈ -0.75. This exactly matches the standard elasticity calculation using ΔQ/Q_initial over ΔP/P_initial, so it is the correct form for elasticity given the data, even though the sign and magnitude must be interpreted in the context of the calculation method.
Option 4: -(5) / (25) equals -0.2. This is simply -5/25, a straightforward ratio that ignores the percentage-change framework entirely, so it cannot be the elasticity value derived from the data.
In summary, each option encodes a different way of combining the changes in price and quantity, but only option 3 aligns with the conventional elasticity formula using the specified bases for percentage changes. The other options either misplace the numerator and denominator, invert the ratio, or rely on raw changes without converting to percentages.

ERMCPS5350_003_2025_3 - INTRO TO QUANTITATIVE RISK MANAGEMENT 11. Quiz for Class 11

Shoes are priced at $75 per pair. A vendor sells 20 pairs per day. The vendor explores selling at $100 per pair. At that price, the vendor sells 15 pairs over the day. What is the elasticity of shoe sales to price.

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