What's the use of dating a megabillionaire if he can't throw some bucks your way? Google CEO Eric Schmidt, who's been seeing video producer Kate Bohner since last fall, hasn't come through with funding for her documentary production firm, so she's out of a job.

Bohner, a former journalist and TV personality who was once briefly married to author Michael Lewis, took up with the married Schmidt last year while she was living and working in south Florida. Since then, Schmidt "paid her an ungodly amount of money" to relocate her business, Kate Bohner Productions, to Los Angeles; she set up shop on Pacific Avenue in Venice, Calif. He's been spending the occasional weekend with her, flying down from the Bay Area on Thursday and leaving Saturday, staying at the Beverly Hills Hotel. (Schmidt saw her twice in October and at least once in November.)

But besides paying for the move and buying Bohner a new set of diamond earrings on every trip, Schmidt, whose net worth has been estimated at $6 billion, hasn't been forthcoming with cash. He attended a meeting at Bohner's firm to get pitched on funding a new $1 million documentary show. It sounds like he didn't bite, because Bohner's said to be losing her job.

Will Schmidt set Bohner up with a job at Google, as he did with a previous girlfriend, PR exec Marcy Simon? Bohner has told people she's already been working for Google — for free. She's been writing executive summaries about Google's push into the cell-phone market, work she estimates she could have billed at $250,000.

So why is Schmidt being so cheap? It's possible he's nervous about bad publicity that could come from leaving a money trail. He's said to have an arrangement with his wife Wendy, but she may not appreciate having the name of Schmidt's girlfriend make the headlines. So why doesn't he buddy up with some other media mogul and get them to fund Bohner's company on the sly? Ah, there's the rub: Schmidt has been so aggressively unlikeable in his dealings with other media CEOs that he doesn't have any chits to cash in.