Business Cycle Dynamics of a New Keynesian Overlapping Generations Model with Progressive Income Taxation

money balances (24), and from the Calvo price staggering model:

кt+ι + (δ - 1)кt = (y/k)yt — (c/k)ct,                 (44a)

c:     Â   ^τ°^τ ' ^{+ τ} "дУ^

Et^λt+1 ^- ^t ^{- βr} —:----E—Et^πt+1

1 — τ '

^-βrτ "gyE_tgt+1

= ^βrτ"gyE_tyt +1 ^{- β}r^{(1 -} τ' ) Etr_t +1^,

(44b)

( β∕π ) Etλ t+1 — λ t — ∆1 Etπ t+1 + ∆2 Etrn t+1 = — ∆3 E_tC t +1,                     (44c)

Etrn t+1 — m t + π t = θ t,                               (44d)

βEtπ t+1 — ∏ t + ⁽¹ — ^{Ф )(1} — ^βφ ) g t = 0,                                (44e)

^φ

^{1 + (1} — ^{(β π))[(1} — Y⁾⁽¹ — ^σ) — ^1] =^{: δ}1 ^,

∆₁ - 1 =: ∆₂,

⁽¹ — ^(β^^π))Y⁽¹ — ^σ) =^{: δ}3∙

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