An additional stationarity constraint to their problem results from the necessity to balance the
inflow of promoted activists and retiring bosses:
(8) πNa = Nb-.
Tb
To simplify further analysis, let us combine the two constraints, by plugging (8) into (4) and
rearranging the terms:
(9) Na =[*N, ∆R (1 - e - rTb )/T„ ∣∙,
where ∆R = R - W is the boss premium. Hereafter, the combined constraint (9) is referred to
as the feasible supply of activists.
The representative boss’s problem is then:
Tb
(10) max ∫ f (Na)e-rtdt
Tb 0
subject to (9).
The bosses’ objective function (7) can be characterized by the lines of equal levels of
residual life-time rents in the (Tb, Na) plane - isorents. The optimal solution to the problem
(10) - an equilibrium in the regime’s political labor market - is attained at the point of
tangency of an isorent and the feasible supply curve in the (Tb, Na) plane that corresponds to
constraint (9). Replacing the left-hand side of (7) with an arbitrary constant, integrating the
expression, taking logs, and rearranging term obtains an algebraic expression for the isorent:
rC
(11) N = f -11—-
a-
V1 - e
17
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