On Dictatorship, Economic Development and Stability



2.3.2 First-order Kuhn-Tucker conditions

The first-order Kuhn-Tucker conditions are computed by forming and maximizing the

following Lagrangean with respect to τt, qt and kt+1:

max L =
τt, qt, kt


X ( qtτtAk? )1 σ -

t(1 - σ)(1 + P)t

XXX (T⅛{kt+1 -+(1 -τt)(1 -α)Ak} +

XX jɪ: {ln[(1 - Tt +1)] + ln[(1 - qt+1)TtAk^ + l] - ln l}

∑ (T+>{qt - 1}

The first-order Kuhn-Tucker conditions are :

∂ L

τt^~
∂τ
t


(qtτtAkα)1 σ - λtτt {
μ
t-1(1 + P) τt I -——
1 - τt

1+β(1 - α) A -
.    (1 - qt ) Akα ¾

(1 - qt)τtAkα +1 f

(16)


qt7r = ( qtτtAkt )1 +

∂qt

+ qlμl-1(1+ρ ) ½ (1 - q,AA k+1 ¾ - qtit=o           (17)


∂ L

dkt +1


= α (qtτt+1 a)1 σkt+1 )   - λt(1 + P) +


+ λt+1 11 + βα(1 - α)(1 - τt+1)Akt+x1! -


(18)


(1 - qt+1)τt+1 aAkt+1 ¾

(1 - qt +1 ) τt +1 Akt+1 + l ʃ


=0


18




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