On Dictatorship, Economic Development and Stability

lβ (1 -α )
(1+β )(1 -q)2

A (1 -q) 1-σ+^{α+ 2} g ^—1
(1+ ρ )   ^- Υ

A (1 - g) 1-σ ^{+ α+ 2} ( ( + + α )k α (^{1 σ} + )
^{a (1 q})           l⁽ 1 σ ^{+ α}) ^-      A(1 — q)

Ω H--_i---------

α (1+ ρ )^- Υ

where,

Υ = (αq)^1-σ [lβ(1 - α)]^{- 1}-^σ (⁽¹ -^( 1 -^α)]α - l(1 - q)^α´

_- (1 _- g) _^—1( σ____l ) ^{l (1+β} )^α

^{(1 q})     ⁽ (1 — σ) 1 — q ) A [lβ(1 — )]^α

₁__l (1+β )^α

A [lβ(1 — a)]^α (1 — q)^{2 __}

The trace of J is:

A (1 _- ɑ) 1^-σ^+α+2 ( ( _i—l _α ʌ k^α - ^{l ( 1—σ + α} ) ʌ

-^{l    q} )            lkɪ-σ ' ^α -       A (1 -g)

^{ω l}                    :-----r—ï------------------

α (1 + ρ )^1—σ Υ

(42)

and the determinant of J is:

DetJ = -

^μ lβ(1 - α) ∖ Aa(1 - g) 1—-^+αk^α-¹
∖ ^{1+ β} J ∖   (1+ ρ ) 1^—- Υ

(43)

Then, we rearrange the determinant and the trace by removing the ^k0s and express them

in terms of q and k to analyze them more easily.

43