Why are theater tickets so expensive in New York?

A simple question of economics.

New York theater productions are (thought to be) the best in the world

These cost a lot to put on.

Not all make a profit

Actors and actresses at this level are expensive

Its New York, one of the most expensive cities in the world in which to do business

And so on

And finally if people go to the theater less the tickets will fall in price until the seats are full again

Or another way, people will pay this much so they will charge as much as they can and keep the theater full. This maximises potential profits.