What is the calculable effect of counterfeiting on an economy?
I'm adding this as a separate answer because it's quite independent of my other answer.

We've agreed that if there are X dollars existing and you counterfeit Y dollars, then you've stolen Y/(X+Y) of the value of those X dollars.  

This assumes you do your counterfeiting all at once, and without warning. 

If instead you do your counterfeiting slowly over time, or if it can be anticipated, then there's an additional effect:  people try to rid themselves of money holdings in order to avoid being stolen from.  (That is, they try to trade dollars for goods before the dollars lose value.)

This is costly to the moneyholders, with no offsetting benefit to anyone.  One way to see that it's costly to moneyholders is that they now own less money, which makes their lives less convenient.  A different way to see that it's costly to the moneyholders is that the rush to trade money for goods bids up prices, which lowers the value of money.  (These are not two different costs; they are two different ways to think about the same cost.)

So in this case, you have stolen more than Y/(X+Y) of the value of originally existing money, but kept somewhat less (because by the time you get to spend your dollars, they're worth less than dollars were worth at the outset).  The difference between what you steal and what you keep simply dissipates.