These three derivatives can be jointly interpreted as a positive effect of expected rent - the
product of the boss premium and the probability of promotion - on the equilibrium number of
activists.
2.4. Production technology
Further analysis requires specification of the activists’ production function, f(Na). I
argued earlier in this paper that activists serve primarily as labor supervisors. Activists-
supervisors, whose function is to elicit a higher level of effort from fellow workers, can be
considered as a sort of labor-augmenting technology. Then the rent-production function can
be represented as:
(19) f(Na) = F{K, (1+aNa) L},
where K is capital, L is labor, a is a productivity parameter. F(K,L) is the production function
of the economy such that: FK >0, FL >0, FKK <0, FLL <0, FKL >0.
Under these conditions, the left-hand side of (16) becomes:
(20) X(Na) = aNa FL L/F.
Obviously, X(Na) >0, X(0) =0. In addition, X'(0)>0, and X(Na) reaches the maximum at a
certain point, which may or may not lie within the range of admissible values of Na, to the left
of min(1, y∣κNbr∆R ). To verify the latter properties, let us are differentiate X(Na) with respect
to the number of activists:
(21)
dX
dNa
= aL- [(Fl + aLN Fll F — aLNa (Fl )2 ]= a'
F2 L a LL a L F 2
(
Fl + aLNa Fll
I
1F1 j
f J
20