μ βα(1 — α)A ∖ 1 -α
\(1 + β )(1 + ρ ) /
(23)
1—
It is straightforward to compute (k,τ) by solving the system (20)-(22) at the steady
state.
Hence, the dictator’s steady state consumption:
- A α ∖ . 1 ( βα (1 — α ) ∖ 1-α
g =q V — 1+P) A 1-α ((1 + β)(1 + ρ))
• The steady state is ”degenerate” if and only if σ > 1, k = 0 and τ = 1.
(k, τ) = (0, 1) is a solution to the system (20)-(22) if and only if the exponent of k
in equation (22) is positive, i.e., if σ > 1.¥
The ”degenerate” steady state will not be studied since it has no interest. The interior
steady state describes how the dictator’s time preference, ρ, affects the long run output
of the economy. If the dictator strongly prefers to consume in the present instead of
smoothing his consumption streams, the income tax rate, τk, will be high and will hamper
capital accumulation. Such a political economic argument may be a cause of poverty
traps in developing countries (see Kanczuk (1998) and Azariadis (2001)). In contrast,
if the dictator cares about his future consumption or, equivalently, about the long-term
development of the country he rules, then he will choose a lower tax rate, τk.
21
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