In Europe, there’s (typically) large government financing of theatres, in the US on the other hand, financing of The Arts is left up to philanthropists. Ergo, most theatres are NOT FOR PROFIT organizations. (Sorry, really annoys me the terminology that’s become commonplace in calling them (even in the California law) non-profit).
Basically, if you are an NFP, you can make all the profit you want, you just can’t disperse it to shareholders. You CAN give it as bonuses to employees, which has happened to me on more than one occasion.
Anyway—as an NFP, donations to you are tax deductible, which makes you more lucrative to companies and individuals to contribute to.
Most theatres tend to be about 50% self supporting, with the other 50% coming from donations. That means, if they could sell the same number of tickets, and charged twice as much, they’d be breaking even. But if you double ticket prices, you lose more than half the audience, etc.
It’s better, from a theatre’s standpoint, to convince the 1–5% of supporters to contribute large amounts of money charitably, than it is to attempt to break even on ticket sales alone.
Now, the way for-profit theatre generally works is that you have producers who buy shows, and produce them. Some flop, some make insane amounts of money, some break even. Shows have closed on opening night to cut the losses.