On Dictatorship, Economic Development and Stability

and stability of steady states for all types of dictatorship and examine their implications on
economic development. The dynamic system of dictatorship without insurrection threat
is as follows:

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

qt+1 = 1

1   /"' ( ^σ-1 )(1 -a )

α σ τ_tk_t

^Tt +¹                                                               α ( σ-1)

/            ∖ 1 ,             ι 1 + α ( σ— 1)        /э ,             . . σ

^{(1 + ρ} )^{σ (1 - τ}t )   ^σ     1+β⁽¹ - ^α ) A

Equation (20) equalizes savings and investment. Equation (21) indicates that the dynam-
ics of the predation rate, q, is constant and equal to one. Finally, equation (22) gives the
expected income tax rate as a function of the current income tax rate and the current
capital stock. It is computed by eliminating the Lagrange multiplier λ from (16)-(18),
and plugging (20) in (18).

3.1 Steady state

Proposition 1 Any form of dictatorship characterized by the dynamic system (20)-(22)
admits a unique interior steady state.

Proof:

• There exists a unique interior steady state characterized by:

20

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