duration Ta, uncertain promotion to the higher-income boss position thereafter, and retirement
after Tb years in office if promoted respectively. Worker i makes the choice to become an
activist if the expected income along the bureaucratic career path exceeds the income as an
ordinary worker, given his personal ability:15
Ta Ta +Tb Ta +Tb Ta +Tb
(1)
∫(W-ωi)e-rtdt +π∫Re-rtdt + (1-π)∫We-rtdt ≥ ∫We-rtdt
0 Ta Ta 0
Inequality (1) yields the cutoff level of disutility ω* that determines activist participation:
-rTb
(2) ω = ∏R - W )-^~.
erTa - 1
The supply of activists - the number of workers for whom ω i < ω^ holds under a given
contract - is then the left tail of the distribution of the disutility from the activist service:
(3) Nas =Z(ω*).
Since the activists constitute typically only a relatively small proportion of the total
population, Na << 1, Z can be approximated with a linear function so that (3) becomes, Nas =
ζω↑ where ζ is a constant. In addition, let us measure time in units of the term of activist
service, Ta, so that Ta ≡ 1.16 Then the supply of activists is expressed as:
15 Post-retirement income flows are not included in the expression, since they are identical for all
agents by assumption.
16 This approach is justified by the fact that the activist service is typically institutionalized (for
example, as a probationary period for a new party member or the length of military service for a
recruit) and its duration is fixed at least in the short run. By contrast, the tenures are seldom regulated
explicitly and its actual length fluctuates as a result of policy changes or political perturbations. Note
that a change in the term of activist service ceteris paribus translates, by rescaling the time axis, into an
increase in the rate of future discounting and a decrease in the length of boss tenure in an equal
proportion.
15