$1.80, give or take a buck

The other morning, I heard it mentioned (again, not for the first time) that for each dollar given in unemployment benefits, there is an economic boost of $1.80, due to some enigmatic multiplier.  I've always figured that some numerical shenanigans similar to the Missing Dollar puzzle were involved in this claim, but I am not an economist. However I've purchased a burger or two, so I can at least talk about that.

(Let me say in advance that none of this is intended as an editorial of the merits of such government programs; any opinion of how much or in what manner the government should provide for those that don't provide for themselves is irrelevant.)

For the sake of argument, let's say that a dollar that Bill earns and would otherwise receive is instead given to Ted. The hypothesis says that when Ted spends that dollar at BurgerWorld, the economy sees growth of $1.80. Here's my question: Would this dollar also grow the economy by $1.80 if Bill went to BurgerWorld?

If so, then there is no net difference, is there? The economic growth created by Bill's burger is now created by Ted's burger, but the result is the same; tranferring the dollar didn't create anything. If not, then the process of transferring the dollar somehow makes it worth more. This seems ... magical. Either way, the claim that the transfer results in a multiplier seems ludicrous.

Now, I know what you may be thinking. "Oh, but the point is, if you give a dollar to Ted, both Bill and Ted will buy a burger, instead of just the one burger that Bill buys; this means that two dollars are spent and the economy grows!" (The unstated basis of this argument is that it's OK to sacrifice future growth to obtain current growth.) However, this presumes that Bill doesn't adjust his spending to compensate for the missing dollar. And, that's still only $1.00 at most that would not have been spent otherwise; where's the other 80 cents?