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.

DetJ = - (1 - q)

11~k⁽¹^-^q⁾¹^—^σ⁺^α

∖ (1 + ρ ) ^γ