Political Rents, Promotion Incentives, and Support for a Non-Democratic Regime

^dNrf '(Na (Tb ))(1 - e ’ r^Tb )+ f (Na (Tb )) re ' T = 0

Substituting the expression for dNa/dTb from (12) and rearranging terms obtains:

Na (Tb )f '(N, (Tb )) =    2ГТ,

f (N, (T, ))      e -1 - ГТ,

that determines the optimal tenure and, implicitly, the optimal probability of promotion.
Representation (16) of the first-order condition separates conveniently the effect of the boss
tenure (on the right-hand side) from the productivity of activists services (left-hand side).

To analyze the comparative statics of the equilibrium in the political labor market, let
us consider the two sides of (16) as the functions of Na, denoting the left-hand side expression
X(Na) and the right-hand side Y(Na) = Y(T,(Na)). The inverse feasible supply function, T,(Na),
can be obtained from (12). The solution to (16) is therefore the point of intersection of the two
curves X(Na) and Y(Na). Under this approach, the position of X(Na) depends exclusively on
the properties of a given f(Na), while the position of Y(Na) is affected by the same parameters
as the supply of activists. It can be shown that Y(N_a) has the following properties: Y(N_a)>0,
Y'(N_a)>0, Y(0) = 0, it has a vertical asymptote at N_max = KNbrr∆∆R , and its slope is
proportional to the inverse of Nmax.²¹ An immediate implication is that the equilibrium number
of activists is affected by exogenous changes in bosses rents and wages in the same way as

the supply of activists and increases in the number of bosses:

²¹ Proof of this statement can be obtained from the author.

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