We found seats in Business Class departing Los Angeles LAX on Thursday, September 20, returning from Beijing PEK on Thursday, September 27. Flights connect in Shanghai PVG.
Other dates are available for fall travel starting in September.
Since this is priced nearly $1000 less than the competition, we recommend you book quickly and avoid making non-refundable bookings related to this flight. If this happens to be a mistake, the airline may choose not to honor it. Though, this price doesn't seem extraordinarily ridiculous and I would assume that it will be honored.
Need a hotel in Shanghai? Here's what's available for the above dates on Hotelwatchdog.