The demand function for the Melbourne–Launceston (MEL–LST) route is PAX (000s) = 320 − 0.4 × Fare. Evaluate this at a Fare of AUD 150. Which of the following statements is TRUE?

Question

BlackTom AI · Accepted Answer

Demand is linear: PAX (000s) = 320 − 0.4 × Fare, so at Fare = 150, PAX = 320 − 0.4×150 = 260 (000s).

1. Relevant knowledge points and concepts
- Point price elasticity of demand (ε) is ε = (dQ/dP) × (P/Q). It measures percent change in quantity demanded from a marginal percent change in price. For a linear demand, dQ/dP is the slope (here −0.4). A negative ε follows the law of demand; magnitude |ε| < 1 means inelastic, |ε| > 1 means elastic.

2. Complete reasoning process step by step
- Compute quantity at the given price.
- Apply the point elasticity formula using the slope and the computed P and Q.
- Interpret the magnitude.

3. Calculations with intermediate steps
- Compute Q: 0.4 × 150 = 60; Q = 320 − 60 = 260 (000s).
- Slope dQ/dP = −0.4 (units: thousands of passengers per AUD).
- Compute P/Q = 150 / 260 = 15 / 26 ≈ 0.576923.
- Elasticity ε = (−0.4) × 0.576923 = −0.230769 ≈ −0.23.
- Magnitude |ε| ≈ 0.23 < 1, so demand is inelastic.

4. Why the correct answer is correct
- Option (a) states Q = 260 (000s), ε ≈ −0.23 and that demand is inelastic. These follow directly from the algebra and the point elasticity formula: the slope is −0.4, the computed ε is about −0.2308 in magnitude below one, therefore inelastic.

5. Why the other options are incorrect
- (b) has the same Q and ε but claims demand is elastic; this contradicts |ε| < 1, so it’s wrong.
- (c) gives Q = 320 (000s) and ε ≈ −0.19; Q = 320 would correspond to Fare = 0, not Fare = 150. The ε ≈ −0.19 comes from using the wrong Q, so (c) is incorrect.
- (d) flips the sign to +0.23; elasticity should be negative for a normal downward‑sloping demand curve, so (d) is wrong.

6. Conclusion
The correct statement is option (a): PAX = 260 (000s), ε ≈ −0.23, and demand is inelastic at this fare. This matches the provided answer.

The demand function for the Melbourne–Launceston (MEL–LST) route is PAX (000s) = 320 − 0.4 × Fare. Evaluate this at a Fare of AUD 150. Which of the following statements is TRUE?单项选择题

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