Austerity measures have they ever saved an economy?

Where does the money wasted on government inefficiency go? For example, if the government spends $600 on a hammer, and the hammer-maker gets his $20 for it, what happens to that other $580? Isn't there some fat there that can be trimmed?

I guess it could've been phrased better as it costing the government $600 to give the contractor $20 for a hammer. I'm under the impression that there is a cost to running the government, itself, and that it can be terribly inefficient in how much it costs it to spend money to buy things. I don't know how bad it is, and I doubt it really costs $600 for a hammer, but I don't think that all of the "spending" (or costs) of the government contributes to private income.

I'm in over my head... So then its not really spending... but if you gotta move $600 around to spend $20, then surely there's some inefficiencies there that could be trimmed down, no?I wouldn't want to have to pull $20 out of the ATM every time I wanted to buy a $0.25 pack of gum.