I think some people here are missing the point of first class. I doubt too many of domestic first class seats are actually sold at first class prices (though certainly any airline employees can correct me). The reason first class fares are so high is to ensure that airlines have high availability for frequent fliers (FFs).
Think like an airline. Frequent fliers are typically business travelers who not only fly alot, they typically pay extremely high coach fares because they can't reserve in advance, and need flexible reservations. This means that keeping a frequent flier flying your airline can easily be worth tens of thousands of dollars a year in revenue. So putting your FF's in first class as often as possible is how you earn their loyalty. You would rather put an FF paying $500 for coach in first than an infrequent flier paying $600, because the FF is going to come back again and again and again, all at your top coach fares. So you jack first class fares up to 4 times coach (or more) to "discourage" the infrequent traveler from taking your first class inventory from your best customers, or at least ensuring you make a whopping profit on it if they do.
My employer will only pay for coach tickets, but since I fly a great deal (25,000 miles since July) I am upgraded to first class for free most of the time. How? On the west coast I typically fly Alaska and they upgrade me since I'm an MVP (soon to be MPV Gold). They have a little system that is similar to the other airlines I think illustrates how First Class inventory is managed to maximize FF loyalty and hence profitability.
More than 2 days before flight - First class fares are about 4-6 times higher than coach, or a free upgrade from coach if you are an Alaska MVP Gold (meaning you fly at least 35,000 miles per year on their mostly short hops).
1-2 days before flight - First class fare is still 4X-6X, but if you are an MVP (15,000 miles per year), they'll upgrade you for free.
Day of travel - Aha, first class hasn't sold out, and all the FFs have been upgraded. Now the airline will try to get something for the first class seats before it's too late. Anyone can upgrade for $50 per segment, so for example there is no reason to buy a first class fare at the counter before your flight, just buy coach and pay the $50..
Of course I'm over simplifying, there are many wrinkles to this, you can also use miles to upgrade or coupons given to you if you use the Alaska credit card, but it all comes back to rewarding loyalty, if you have lots of miles they'll open first class for you.
So next time you walk through the first class cabin, don't think you are in the company of a group of "millionares or billionaires". In reality they are a sad bunch of mostly middle class schlubs, in jobs requiring them to fly constantly, away from their families, eating strange food in strange cities while sleeping in strange beds. Their plush seats are courtesy of an airline that is the one familar and friendly place on their exhausting and lonely trips, with a staff that will work very hard to ensure the FF's always feel welcome and comfortable. That's one reason why cabin crew try to greet first class passsengers by name, but in many cases I'm sure it also because they've seen same poor soul on their flight every week for the last year