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Hot-Dog Vendor Economics

A Slate article mentions that the annual price of a hot-dog stand license near the Metropolitan Museum of Art in New York City is $362,201. Licenses are very limited and are bought at auction. The price presumably reflects the economic rent associated with the particular site (the price would be a lot lower in the middle of Central Park). Yet at a fixed cost of $1,000 per day, how can a hot-dog vendor make enough money to cover his variable cost, including the value of his own time?
If, on average, he sells only one hot dog and drink every minute the Met is open, with about 500 average daily opening minutes, that’s 500 servings per day. If he charges $3 for a dog and drink, his revenue of $1,500 leaves him $500 per day to cover variable costs. Seems possible, but I would expect that he’s not making economic profits.
If the city were to issue many more licenses, we would see more vendors, cheaper hot dogs, but, in the end, no higher net returns to the vendors.
(Hat tip: T.W.)