On a regional route, the base market is QD = 500 − 2 × Fare and QS = −100 + 3 × Fare (base equilibrium: P* = AUD 120, Q* = 260,000 seats). A fuel price spike then shifts supply leftward to QS = −160 + 3 × Fare, with demand unchanged. Which of the following statements is TRUE?

Question

BlackTom AI · Accepted Answer

Set quantity demanded equal to quantity supplied using the new supply: 500 − 2P = −160 + 3P.

1. Relevant concepts
- Market equilibrium occurs where QD = QS.
- A leftward (upward) shift of the supply curve raises price and lowers equilibrium quantity (other things equal).
- The algebraic demand and supply functions give quantities in the same units (here thousands of seats; base equilibrium P = 120 gives Q = 260 → 260,000 seats).

2. Step-by-step reasoning and algebra
- Start with equality: 500 − 2P = −160 + 3P.
- Move terms: 500 + 160 = 3P + 2P → 660 = 5P.
- Solve for price: P = 660 / 5 = 132 (AUD).

3. Calculation of equilibrium quantity (showing intermediate steps)
- Substitute P = 132 into demand (or supply): Q = 500 − 2×132 = 500 − 264 = 236.
- Interpreting units: 236 corresponds to 236,000 seats (consistent with base Q* = 260 → 260,000 seats).

4. Why this answer is correct
- The supply shift from QS = −100 + 3P to QS = −160 + 3P reduced supply at every price by 60 units, forcing the market price up to clear excess demand. The algebra gives the new equilibrium P = AUD 132 and Q = 236 (thousand) seats, i.e. a price increase and a quantity decrease relative to the base (120, 260,000).

5. Why the other options are incorrect
- Option a (P = 108, Q = 284,000) contradicts the effect of a leftward supply shift — it implies price falls and quantity rises, the opposite of expectation and inconsistent with the equations.
- Option b (P = 132, Q unchanged at 260,000) is inconsistent because a supply shift with unchanged demand must change quantity as well as price; plugging P = 132 into demand gives Q = 236, not 260.
- Option c (P unchanged at 120, Q = 236,000) cannot hold because at P = 120 the shifted supply and demand are not equal (demand 260 ≠ supply −160+3×120 = 260? actually supply would be −160+360=200), so price must adjust.

6. Conclusion
The correct equilibrium after the supply shift is P* = AUD 132 and Q* = 236,000 seats, confirming option d.

On a regional route, the base market is QD = 500 − 2 × Fare and QS = −100 + 3 × Fare (base equilibrium: P* = AUD 120, Q* = 260,000 seats). A fuel price spike then shifts supply leftward to QS = −160 + 3 × Fare, with demand unchanged. Which of the following statements is TRUE?单项选择题

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