The log-linearized budget equations for generation s = T + TR are:
cτ+τ R ,j ^ T+τ Rj — (1 — τ0 ) yτ+τ R ,j yτ+τ Rj — trtrt — ΩΩ t
= (1 - δ) kτ+τRj ^T+τRj + mτ+τRj mτ+τRj
( τ 0yτ+τ Rj + pens + mτ+τ Rj ) π t,
j = 1, . . . , ne.
(30)
From the factor market equilibrium conditions (15) and (16) we obtain:
w t + αNt = αKt + g t + Zt,
rt + (α — 1)Nt — (α — 1)Ki't + gt + zt.
(31)
From aggregate profits Ωt = (1 — gt)ZtNt αKα, we derive
— (1 — α ) Nt = αKt + (1 — ь ) g t + Zt.
(32)
The aggregate consistency conditions (23c), (23b), and (23d), imply
ne τ+τR
KK = X X
j =1 s=2
ne τ
NN = XX
j =1 s=1
μ(j) ks,ksj
t + t R k kt ,
μ( j) ns,j^ sj
n b ,
T + TR t ,
ne τ+τR
Σ∖ μ μ(j) sjjsjj
(33)
T-+ T + T Rm j m t ■
j =1 s=2
Finally, the log-linearized budget constraint of the government (21) is given by:
ne τ+τR
X X T+T R τ 0ys,j y s, — trtrt = (1 — θ ) m7m t
j =1 s=1
ne T+T R μ ( j ) T R
ʌ
θm θ t,
— Σ τ , τRτ0ys,j + (θ — 1)m + (m — m) — TMTRpens πt
T + TR T + TR
j=1 s=1
(34)
where m = m — P”= 1 (μ(j)/(T + TR))m1 ,j.
Next we derive the set of equations (26b). We begin with the log-linearized budget
equations of generation s = 1. From (5) we derive:
k 2,jμ 2+1 + θm 2 j m 2+1 + ( τ 0y1 ,j + m1 ,j ) ∏ t = (1 — τ0 ) y1 ,j ∙y 1,j + trtrt + ΩΩ t — c1 ,j c t1 ,j,
j = 1, . . . , ne.
29