On Dictatorship, Economic Development and Stability

trJ = α + ¹+^ρ - (¹ ~ ^α)(^σ - ¹)
ασ

The determinant of J is:

DetJ = 1 + ρ > 1

Rearranging the terms of the trace of J yields:

trJ=2+ρ+¹ μ (^{ι - α} )^{(1+p - α} ) )
σα

Since the term in brackets is positive, it is straightforward to conclude that |1 + DetJ | <

|trJ |. As a result, the steady state is a saddle point for any σ and ρ.

B Proof of proposition 4

By eliminating the Lagrange multipliers from the equations (16)-(18), we obtain the
following system:

kt+1 = i + β^{(1 - τ}t^{)(1 - α})Ak^α                           (35)

^τt+1 = ^{1 -} Tl        ʌ Λb,a                                         ⁽³⁶⁾

(1 - qt+1)Ak_t+1

[    _ ^{[(1 +} ρ^{)(1 + β)]-τ}tk^{α(1 -} qt^)-                  /O₇X

^qt+1 = --------1—≡----_α ------ (3⁷⁾

^{α 1 -σ} qt ^{σ τ}t+1 kt+1^{1 σ}

40

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