A town's fireworks show: is it efficient, who is Mr. X, and can a private firm supply it?

What kind of good the show is. A fireworks display in the sky has the two features of a public good:

• Non-rival: one resident's watching takes nothing away from anyone else's view.
• Non-excludable: once the rockets go up, they can be seen from rooftops and streets all over the town, so it is extremely hard to keep anyone from enjoying them.

Is the show efficient? A public good is worth providing when its total benefit to the community is at least its total cost, the test of cost-benefit analysis. Since the show is non-rival, every resident enjoys the whole of it, so its total value is the sum of what each resident puts on it: N × ₹1,500 for a town of N residents. The cost is ₹9,00,000.

The show is efficient when N × 1,500 ≥ 9,00,000, that is, when N ≥ 9,00,000 ÷ 1,500 = 600 residents. The question does not give the number of residents, so the answer turns on it:

• At least 600 residents: efficient. For example, with 1,000 residents the total value is 1,000 × 1,500 = ₹15,00,000, which exceeds the cost by ₹6,00,000. (With exactly 600, value just equals cost, ₹9,00,000, and the town is no better or worse off.)
• Fewer than 600 residents: not efficient. With 400 residents the total value is 400 × 1,500 = ₹6,00,000, ₹3,00,000 short of the cost.

Even a small town usually has well over 600 residents, so the show is very likely efficient, but strictly the answer depends on N. Put another way, if the cost is shared equally, each resident's share is ₹9,00,000 ÷ N, which is at most ₹1,500 exactly when N is at least 600; with 1,000 residents each would pay ₹900 for an experience worth ₹1,500.

What we call Mr. X. Mr. X is a free rider: a person who enjoys the benefit of a good while avoiding paying for it. He will see the show whether or not he contributes, so contributing gains him nothing. Every resident is in the same position, so each is tempted to wait for the others to pay. The free-rider problem arises from the positive externality: what one resident pays for benefits everyone else. Under a voluntary scheme the money raised may therefore fall short of ₹9,00,000 and the show may not be held, even though it is worth more to the town than it costs.

Can a private firm supply the show? Not by selling it to the viewers. A firm can earn only if it can make people pay, and it cannot stop anyone who has not paid from watching the sky. Like Mr. X, most residents would watch without buying a ticket, so the firm could not cover the ₹9,00,000 cost. A public good left to the market is supplied in an inefficient quantity, here probably not at all, which is why such goods are usually provided by the government. The show can still be held:

• Compulsory payment. If every resident is required to pay a set share, the free-rider problem is solved. The town body could raise the cost through a levy or its taxes and pay a fireworks company to put on the show; a private firm can then supply it under contract.
• Voluntary or sponsored funding. A voluntary collection is not ruled out: if enough residents contribute, the ₹9,00,000 can still be raised, though free riders like Mr. X make the total uncertain. A local business or group that gains from the crowd or the publicity could also choose to pay for the show and hire a firm to stage it. Neither route is sure, because the firm still cannot charge those who watch.
• Exclusion, where it becomes possible. A good that cannot be sold to non-payers today can be supplied by the market once a way of excluding non-payers is found, as happened with lighthouses. Selling seats at the Exhibition grounds does not achieve this here, because the show is visible from outside the ground.

Answer. The show is efficient if the town has at least 600 residents (total value N × ₹1,500 at least the ₹9,00,000 cost), which even a small town is likely to have. Mr. X is a free rider. A private firm cannot cover the cost by charging viewers, because no one can be kept from seeing it. The show can still be held if someone else meets the cost: voluntary contributions or a sponsor may do so, but free riding makes them unreliable, so the surest route is compulsory payment through the town body, which may then hire a private firm to put it on.