question archive Suppose that the demand curve for tickets to see a football team play a game is given by [Math Processing Error]Q=80,000−40P and the marginal cost is zero
Suppose that the demand curve for tickets to see a football team play a game is given by [Math Processing Error]Q=80,000−40P and the marginal cost is zero
Subject:MarketingPrice:2.88 Bought3
Suppose that the demand curve for tickets to see a football team play a game is given by [Math Processing Error]Q=80,000−40P and the marginal cost is zero. The team's stadium can host [Math Processing Error]75,000 fans.
i) How many tickets would the team sell if it behaved competitively? And what is the price of the ticket?
ii) How many tickets would it sell, and what price would it charge if it behaved like a monopoly?
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a.
Competitive equilibrium is where P=MC
Here MC=0, then P=0
[Math Processing Error]Q=80000−40PP=2000−0.025QP=MC2000−0.025Q=0Q=80000
But, the stadium can host only 75000. Hence,
[Math Processing Error]P=2000−0.025(75000)=2000−1875=125
Hence the price should only be $125.
b.
If the seller is monopolist his Marginal revenue (MR) should be equal to Marginal Cost (MC).
[Math Processing Error]P=2000−0.025QMR=2000−0.05QMR=MC2000−0.05Q=0Q=40000P=2000−0.025(40000)=1000
Hence the monopolist will charge 1000 and sell only 40000 tickets, although the capacity is higher. Because the higher sale will reduce the profit of monopolist.
