No. Prices are not arbitrary; they're determined by market forces. I don't really agree with the idea that the minimum wage should be intended to support an adult (I think our welfare systems should be reformed to eliminate cliffs), but if you set it to the average price of a bunch of stuff in a region it's gonna be an actual number.

You can change the set of stuff, but it's much harder to cheat if you actually have to say what a living wage should be spent on.