I am suprised that an employer would allow the price to be considered after the booking. Personally, if I was the employer I would pick a price and agre on it before (route, dates, class, carrier, etc). You can book a full fare in Y and show that price because technically anything less than that is at a discount. But honestly, it seems like you or the employer can easily get ripped off in this deal, just my opinion.
I know where everyone'e intentions are and they sound great, but it could be dangerous dealing with the price so no one gets ripped.