On Dictatorship, Economic Development and Stability

The behavior of the individuals is represented by a logarithmic life-cycle utility function,
which is assumed to be additively separable,

ln(ct) + β ln(dt+1) + ln(pt + l) + β ln(pt+1 + l).                    (2)

The left part of (2) is the utility derived from consumption of the single private good
at time t, c_t, and at time t + 1, d_t+1 . β > 0 is the discount factor denoting a relative
impatience. l > 0 is the exogenous natural level of social order associated with a particular
society. The budget constraint is

ct + st = (1 - τt)wt                                      (3)

d_t+1 = (1 - τ_t+1)R_t+1s_t,                              (4)

where savings are denoted s_t, the real wage is w_t and the interest factor is R_t+1 .

The second part of (2) is the utility derived from the public good, the level of social order,
p, defined by :

pt = (1 - qt)τtf (kt),                                       (5)

where τ ∈ (0, 1) is the income tax rate set by the dictator and q_t ∈ (0, 1) is the rate
of predation. The public good⁸ , p, provided by the dictator, represents the protection of
persons and individual property rights on the consumption good against other individuals,
but not against the dictator’s predation.⁹

⁸ Social order cannot be a private good because it is a good with externalities. The absence of violence
is essentially a social phenomenon. If an individual pays to prevent another individual from using violence
against him, both will benefit from the absence of violence. Therefore, both will have an incentive to free
ride on bearing the cost of social order.

⁹ Alternatively, p could be interpreted as the provision of public utilities or infrastructure. What is

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