Definition: “Uniform prices” means P = Pb = Pgs = Pgb = Pgn = Pq. If this happens then one price index P suffices.
Theorem B1: In a pragmatic Madisonian real welfare state with Ricardian equivalence and uniform prices, (i)
RIR = (B + g) / ((1 + Z) W) (base year)
and
B = W ((1 + Z) RIR - NG/WT) (henceforth)
(ii) If RIR is constant, then: (1) A constant quote for government layouts (or progression factor
= 1) only allows for some variation in B/W by variation in the average tax rate difference Z. (2) If Z is constant, then B is fully indexed on W.
Proof: