If φo is sufficiently large, reflecting a small dispersion of the ideological preferences
of outsiders, we may have φo > φi+φαiψh2. In that case it follows from (A.10) that
the individual outsider is politically more influential than the individual insider,
as noted in section 2.4. However, in the benchmark case where φo = φi = φ,
(A.10) simplifies to equation (2.20) in the text, representing the situation where
lobby members have greater political power.
Appendix 2. The political equilibrium
This appendix explains the derivation of the political equilibrium presented
in section 3.1 and reports some comparative-static results which are used in the
proofs of the propositions stated in Appendix 3.
Using (2.20), (2.21) plus the facts that Ui = Ug = u (W + rk) + g (G) and
G = α, we construct the Lagrangian £ corresponding to the maximisation problem
specified at the start of section 3.1,
$ = ɪ + αipi £u (W + rk) + g (α) - UB]
2
+ (1 - αi ) po
[(≡) u (W + rŋ ÷(⅛)
u (w (r + τ) + rk} + g (α) — UB
+λ [τ (1- α) k (r + τ) - αW]+η [W - w (r + τ)] ,
where η is the Kuhn-Tucker multiplier associated with the recruitment constraint
W ≥ w. Exploiting (2.13), (2.14) and the fact that (1 — α) k = k in symmetric
capital market equilibrium, we find the first-order conditions for maximisation
with respect to W, α and τ to be
d$/dW = 0 =⇒ [αipi + (α — αi) po] ug — αλ + η = 0, (A.11)
d$/da = 0 =⇒ [αipi + (1 — αi) po] g0 + Po (ug — up) — λ (τk + W)
k
n n (1 — α) k0
[kαiug (pi — po) + kαpo Ugfg — u'p) + λτ (1 — α) k0 + ηk] = 0,
(A.12)
∂$/дт = 0 =⇒ λ (1 — α)(k + τk0) + ηk — (1 — α) kpou'p
33