It nevertheless remains useful to develop the detailed index formally. If your interest in the subject is not very strong, you are advised to skip the remainder of this chapter. The reader who studies this section will notice that we do not achieve very much. Some of the formulas look complex, but on close inspection only say the obvious.
Formal development
We assume a ‘basic insurance’ setup for social security. The unemployed get a benefit of B. At higher earning levels they may have additional insurance, and be paid on top of B. But this is of no concern for our issue. Also, who is on benefit but gets a job offer, accepts this, on the penalty of losing the benefit anyhow. This means that nominal transfer payments are NTRF = B U. We also take b = NTRF / LE = B u (redefining the symbol b - no longer the IS curve). Similarly q = Q / LE.
Let g = NG / LE be average nominal government expenditure per worker, with g = gn + gp + gs. We will assume Ricardian equivalence, so that government budget deficits are regarded as part of taxes, so that there effectively is no deficit. [84] Hence TAX = NG + NTRF.
Then the average wage tax rate AWTR
TAX / WT = (TAX/LE) / (WT/LE) = (g + b) / W.
For the special interests we distinguish two kinds of situations.
· When average income itself is the special interest, then gs can also be regarded as net income, part of gn, and then this case is equivalent to gs = 0. Note that we could include gn in Net[W] mathematically anyhow (but don’t do this for clarity).