(4)
Nas =πκ(R-W)(1-e-rTb),
where κ = ζ /( e- - 1).
It is can be easily verified that the supply of activists increases in the expected rents
(boss rent17 and tenure, and the probability of promotion) and decreases in the value of the
next best alternative for a worker (workers’ wage):
(5)
∂Nas
∂R
∂Ns ∂Ns ∂Ns
> 0, —- > 0, —- > 0, —- < 0.
∂Tb ∂π ∂W
2.3. The bosses’ problem
At the core of the representative boss’s choice problem is the tradeoff between
additional rents provided by the activists and the limitation of tenure that the provision of
incentives for the activists implies. The bosses, entering the contract with the activists, seek to
maximize their residual life-time rents:
_ Tb
(7) R = ∫ f (Na ) e - rtdt
0
To achieve this goal, they choose the probability of promotion, π, and the length of tenure, Tb,
taking into account the workers’ response expressed in the form of the supply of activists (4).
17 Boss rent, R, as introduced in Section 2.1, is a function of the number of activists. However, an
individual worker has no information on the outcomes of the current and future recruitment campaigns
at the time he or she is making the decision to become an activist. Therefore, R in the expression for
the supply of activist should be interpreted as an exogenously determined expectation of rent, which
does not generally satisfy R = f(Na). This identity should hold in the long-run equilibrium, but since
the regimes of the type discussed here are relatively short-lived, the long-run equilibrium may never
be reached.
16
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