Where does all the NGDP come from?

We have nominal gross domestic product, the sum of all prices paid in the domestic economy, the blue line. That sum includes money used multiple times in the period, I call that the velocity.  My definition is close enough to the M1 and M2 velocities, also plotted. (The M2 is scaled by 10).

When they compute NGDP, they just add up the balances in the accounts and income statements. Then they estimate the velocity because they know the total amount of money outstanding and they know the relative change in balances.

But the increase in NGDP ultimately comes from the Fed digitizer, and has to be unencumbered. I  ignore the amount borrowed by Congress, under the assumption they they pay fair market rates, and the market equalizes returns. This is likely valid over a long  period, like eight years. Lent money does not do the trick in the steady state.  I ignore the reserve requirement, as that is included in the NGDP numbers. The only relevant multiplier is the velocity over the measuring period. 

So the rise in NGDP comes from Ben's digitizer, multiplied by the proper velocity We know Ben's digitizer produced 80 billion/yr in subsidies, or free money for Congress. Letting time be 8 years, then we have 640 billion worth of seigniorage, paid to Congress.  So we can see that the 680 billion times the M2 velocity gives some 1.2 tillion, and by the M1 velocity gives something like 4 trillion. The actual change is 2 trillion or so. Some mix of M1 and M2 likely make the numbers come out.

But the real GDP supposedly equalizes prices over transaction rates.  They actually weight the prices according the the frequency of purchase by the consumer. Thus the velocities computed from the NGDP accounts, are not matched to consumer spending. But as long as inflation is constant, the ratio of NGDP to RGDP should not matter, is the assumption. How true is this?

True until the wage inflation pushes the middle class taxpayer into the higher brackets.  Then,  Congress has a problem.