On Dictatorship, Economic Development and Stability

(1 -τ)( σ+a (1 -σ ))
aσ

)’

—q

—ql τ

(τ( σ+α-ασ )
—

^{+ 1})∙

As for the first additive term of the trace, Ω, it can be rewritten as follows:

σ Λ _ l(1+β)^α (1—q)^α-2
1—σ y¹      A[lβ(1—a)]^α

₁     l (1+β )^α (1—q)^α-2

¹       A [ lβ (1—a )] α

(45)

The big term that is common to the nominator and the denominator can be identified,

by replacing 1 — q by its steady state expression, as (1 — τ)/(1 — q).

After simplifications, Ω becomes:

— ^{[ τ}(^{1 —} <^{)] + α}<

—q + τ

As a result, we obtain the final expression for the trace J:

trJ =

— [1 — q(2 — α + a )1 — <7(1 — α )

—q + τ

(46)

The final part of this proof consists in comparing ∖trJ∣ and ∣1 + DetJ∣, i.e.,

ισ [1—q(2—a+α )] —9(1—a)

—q+τ

I and I                 I.

l l —q+τ ¹

• If q ∈

2 —¹
______σ

2 a» (1—σ )

, 1 , then either ɪ [1 — q(2

— α + ^a )1 < 0 or