The working agent receives income from effective labor e(s, j)nts,j and capital kts,j as
well as government transfers trt and profits Ωt which are spent on consumption cs, and
next-period capital kts++11,j and money Mts++11,j . He pays taxes on his nominal income
Ptyts,j:
Ptyts,j = Ptrtkts,j + Ptwte(s, j)nts,j .
The government adjust the tax income schedule at the beginning of each period for the
average rate of inflation in the economy which is equal to the non-stochastic steady
state rate π. Therefore, nominal income is divided by the price level, Pt-1π, and the
tax schedule τ (.) is a time-invariant function of (deflated) income with τ0 > 0. Notice
that when we have unanticipated inflation, πt = pp-i > π, the real tax burden increases
as the agent’s real income moves into a higher tax bracket, the so-called “bracket creep“
effect.
The nominal budget constraint of the retired worker is given by
P ( s∙++1 3 sj ʌ ( s +1 3 Ms3 ʌ I P s,3
Pt kt+1 - (1 - δ)kt + Mt+1 - Mt + Ptct
PtySj
Pt-1 ∏
(4)
= PtrtksS3 + Pent + Pttrt + PtΩt - PtTt
s = T + 1, . . . , T + TR, j = 1, . . . , ne,
with the capital stock and money balances at the end of the life at age s = T + T R being
equal to zero, ktT +T R +1,j = MtT +T R +1,j ≡ 0 for all productivity types j ∈ {1, . . . , ne},
because the household does not leave bequests. Furthermore, since retirement at age
T + 1 is mandatory, ntT +1,j = ntT +2,j = . . . = ntT+TR ,j ≡ 0. Pent are nominal pensions
and are distributed lump-sum. They are not taxed. Again, the government adjusts
pensions each period for expected inflation according to Pent = pen Pt-1π, where pen
is constant through time. If inflation is higher then expected, πt > π , the real value of
pensions declines.
The real budget constraint of the s-year old household with productivity type j is given
by
(1 + rt - δ)ks3 + mt, + wte(s,j)ns, + trt + ωt - τt yS⅛πp} - cs,
ks+1,j+ s+1,j
kt+1 +mt+1 =
s= 1,...,T,
(1 + r, - δ ) kSi + m∏j + pnπ + trt + Ω t - τt ( yjt ´ - cS,,
s=T+1,...,T+TR,