It wouldn't really cost them much to keep supply engines that don't have to be developed. Furthermore, though Marmoni is credited with all the engine wok, a lot of it is done at the Fuji Technical Center in Japan. So I really don't see why they wouldn't take advantage of something they already have to keep their name in (or introduce Lexus' into) the sport.
One thing is just supplying Williams with engines, another matter is - what I think is at least the intention of the thread - if Williams becomes a full works-supported team (a relationship they had previously with Honda, Renault and BMW)
, in this case by Toyota. Even despite all the cost-cutting measures this would be a lot more expensive for Toyota - they would financially support the Grove team as much as they currently do for the Cologne team, plus the rest of money comes from sponsors.
In the other case, what you mentioned, if Toyota continues its relationship with Williams in the current way I don't see much reason for Toyota to stay, because Williams as a full privateer with an average budget wouldn't really reach the top and Toyota wouldn't need such kind of advertising. The leaders of Toyota company have already made it clear that in 2009 either wins or departure will take place.
So in either case - I don't see Toyota continuing with Williams if they withdraw from F1 with their own team.
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