On Dictatorship, Economic Development and Stability

As a result, the condition for an insurrection is the difference between the two. This
difference must be negative:

I_t+1 = ln[(1 - τ_t+1)] + ln[(1 - q_t+1)τ_t+1Ak_t^α₊₁ + l] - ln l < 0.             (9)

Obviously, for the dictator the constraint I must be positive or null.

2.3 Equilibrium

The equilibrium on the goods market at time t is given by the accounting identity in per
capita terms,

yt = f(kt) = gt + ct + dt + st +pt,                         (10)

where yt is output, ct consumption, st savings and pt resources devoted to the maintenance
of social order at time t.

The total stock of capital is built from the savings of the young generation:

kt+1 = st.                                          (11)

2.3.1 Problem of the dictator

The objective of the dynastic dictator is to maximize his utility with respect to con-
sumption, gt , from time 0 to ∞. This requires that he must stay in power through the
entire period. In other words, the problem is to find an equilibrium path that guarantees
the permanence of dictatorship and a maximum present value of utility for the dictator.
Since the dictator has no savings¹⁰ , he must choose a suitable tax rate to have an optimal
¹⁰ The dictator does not need save as he has the power to prey on national resources in the future. In
an open economy framework, he could open saving accounts in foreign countries, as it often happens to

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