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The Austrian vignette (motorway sticker) costs about €8 for a 10 day pass. I suspect pretty much any (sensible)route will also take you through some reasonably expensive tolled tunnels.
However, the real question is why you would drive to Livigno if you fly to Memmingen? or conversely, why would you fly to Memmingen if you want to get to Livigno?
Unless, I am mistaken, it is a very long, ackward and probably expensive drive and you be bypassing many superb ski resorts along the way in Austria and Switzerland.
If I were you, I would rethink my plans (unless already locked into bookings you can't change) and try for something more convenient, e.g. flights to Bergamo or Milan or else forget about Livigno and head somewhere in Austria.
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