The diagram below illustrates supply and demand in the market for tickets to Jay Chou's live concert in Melbourne, March 2025. Supply is price inelastic at the quantity of 10,000 (i.e., the full capacity of Rod Laver Arena). The equilibrium price is $100 per ticket.If a ceiling of $50 per ticket is introduced, the number of tickets sold will be ___________. Furthermore, if the government charges $10 tax on every ticket, total tax revenue raised will be ___________.

Question

BlackTom AI · Accepted Answer

Supply is perfectly price‑inelastic (a vertical supply) at 10,000 tickets, so the market cannot supply more than 10,000 regardless of price. At the given equilibrium the price is $100 and quantity 10,000.

Step‑by‑step reasoning:
1) Price ceiling of $50 is below the equilibrium price ($50 < $100) so the ceiling is binding: it would create excess demand (quantity demanded > quantity supplied) at $50. However, because supply is perfectly inelastic at 10,000 (the arena’s capacity), the maximum quantity that can be sold remains 10,000. The market cannot increase supply above the capacity, so the number of tickets actually sold equals the supply capacity: exactly 10,000. (This is the standard result: quantity sold under a binding ceiling = quantity supplied; here quantity supplied is fixed at 10,000.)

2) Tax revenue from a per‑ticket tax = (tax per unit) × (number of units sold). With a $10 tax and the supplied quantity unchanged at 10,000, total tax revenue = $10 × 10,000 = $100,000. Showed intermediate steps: 10 × 10,000 = 100,000.

Why the correct answer is correct:
- The vertical supply curve fixes quantity at 10,000 irrespective of price controls or taxes, so quantity sold under a $50 ceiling is exactly 10,000.
- Since quantity is unchanged, taxing $10 per ticket yields $10 × 10,000 = $100,000 in revenue.

Why the other choices are incorrect:
- “Less than 10,000” is wrong because supply cannot shrink below capacity in this setup (the vertical supply is at 10,000).
- “Unknown/depends on elasticities” is wrong because supply elasticity is given (perfectly inelastic), so the outcome is determinate.
- “More than 10,000” is impossible because of the capacity constraint.

Conclusion: the correct choice is a. Exactly 10,000; exactly $100,000.

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