or
0 = £b - τPAY G] yιt + 1+r £b - τP+AIYG] y1t+1
+ μ 1+7 )2 £b - τ P+2YG ] y1t+2......
and therefore
∞i
τ =X I 1 + g ʌ τPAYG
i=0 (j + rJ t+i
i.e. the sustainable tax equals the present value of the PAYG-tax calculated
by the growth corrected real rate of interest. Note that this presumes that the
initial debt level is zero.
38
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