For the following scenario, select all answers that are correct.

Consider demand for digital SLR cameras in some market. When the price of digital SLR cameras was $2000, consumers bought 4000 units. Instead, when the price fell to $1200, consumers bought 5000 units.

Important note: if you arrive at an answer for the price elasticity of demand that is a negative number, you should ignore the minus sign and choose the corresponding answer that is a positive number.

Question

For the following scenario, select all answers that are correct.

Consider demand for digital SLR cameras in some market. When the price of digital SLR cameras was $2000, consumers bought 4000 units. Instead, when the price fell to $1200, consumers bought 5000 units.

Important note: if you arrive at an answer for the price elasticity of demand that is a negative number, you should ignore the minus sign and choose the corresponding answer that is a positive number.

BlackTom AI · Accepted Answer

Midpoint (arc) elasticity of demand uses the average percentage changes: Elasticity = (ΔQ / average Q) ÷ (ΔP / average P). It measures responsiveness of quantity demanded to price changes, and when computed as an absolute value we ignore the negative sign.

1) Relevant knowledge points and concepts
- Midpoint (arc) elasticity formula to avoid asymmetry between directions of change.
- If |elasticity| < 1 demand is inelastic (quantity responds less than proportionally); if > 1 it is elastic.
- Total expenditure (total revenue) = Price × Quantity. For a price decrease: if demand is inelastic, TR falls; if elastic, TR rises.

2) Step-by-step reasoning and calculations
- Given: P1 = $2000, Q1 = 4000; P2 = $1200, Q2 = 5000.
- ΔQ = Q2 − Q1 = 5000 − 4000 = 1000.
- Average Q = (Q1 + Q2) / 2 = (4000 + 5000) / 2 = 4500.
- Percentage change in Q (midpoint) = ΔQ / average Q = 1000 / 4500 = 0.222222... (22.222...%).
- ΔP = P2 − P1 = 1200 − 2000 = −800.
- Average P = (P1 + P2) / 2 = (2000 + 1200) / 2 = 1600.
- Percentage change in P (midpoint) = ΔP / average P = −800 / 1600 = −0.5 (−50%).
- Midpoint elasticity (absolute value) = |(0.222222...) / (−0.5)| = 0.444444... ≈ 0.44 (rounded to 2 decimals).

3) Intermediate results shown above; final elasticity = 0.44.

4) Why the correct answers are correct
- Elasticity = 0.44 (absolute value) matches the first correct choice. Because |elasticity| < 1, demand is inelastic here.
- Total expenditure: TR1 = 2000 × 4000 = $8,000,000; TR2 = 1200 × 5000 = $6,000,000. TR decreased when price fell, which is exactly what occurs when demand is inelastic.

5) Why other options are incorrect
- 0.625 is not obtained from the midpoint formula with these numbers; it is an incorrect calculation.
- "The demand for SLR cameras is elastic" is incorrect because the computed |elasticity| = 0.44 < 1, so demand is inelastic.

6) Conclusion
Both "Using the midpoint method, the price elasticity of demand is 0.44 (rounded to 2 decimal places)" and "Total expenditure (or total revenue) in the SLR camera market decreased with the price fall" are correct, matching the provided answers.

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