Stakeholder Activism, Managerial Entrenchment, and the Congruence of Interests between Shareholders and Stakeholders

as an equality:

xb_r (π) =

[Γ — ∆θ(p + τ)] πa — λτ∆θ(1 — π(1 — a))
(1 — π)(1 — λ)τ

(3)

Let ∆θ = θR— θI. By inspection of (3), b_r (π) < 1 if and only if Γ < Γ₁(π) ≡ ∆θ(p+τ(1+λ))+
(∆θτ(1—π)∕πα) and b_r(π) > 0 if and only if Γ > Γ_o(π) ≡ (p+τ)∆θ+(∆θλτ(1—n(1—a)))∕πa.
Notice that since λ ∈ (0,1), Γ_o (π) < Γ₁(π). ■

Proof of proposition 1 Let H₁ = ∆θ(p+τ(1 — λ)) and H₂ = ∆θ(1 — a)(p+τ(1 — λ)) +aΓ
where ∆θ = θR — θI. If managerial entrenchment is to be countered, shareholder value writes
as

Vsh(Xr(π)) = ( ^θI + ^nA* ) (Hi — πH).
∆θ(1 — π)

The first order condition for shareholder value maximization is given by

π²∆θH2 — 2π∆θH — (θɪH — ΘrHi) _
∆θ(1 — π)²              = 0'

Solving for π* we obtain

— *
^π1,2

1±

Θr a(Γ — ∆θ(p + τ (1 — λ)))
∆θ(aΓ + ∆θ(1 — a)(p + τ (1 — λ)))

if Γ < ∆θ(p + τ(1 — λ)), the discriminant is negative and V_S⁰_H (π) > 0, for all π ∈ (0, 1).

In this case shareholders always want to set π as close to 1 as possible. Conversely, if

Γ > ∆θ(p + τ(1 — λ)), the optimal level of corporate governance quality is given by

π^* = 1 —

Θr a(Γ — ∆θ(p + τ (1 — λ)))
∆θ(aΓ + ∆θ(1 — a)(p + τ (1 — λ)))

Notice that π* is decreasing both in a and Γ. ■

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