It remains to be shown for 7 < 1 that g⅛ε → 1 for ε → ∞. For ε → ∞,
eiε → ∞ for at least one investor. By equation (43), eiε → ∞ if πε— 1+si → 0.
Since πε — 1 + si > 0 Vi, ε and s⅛ < Sj Vj, j = h,πε — 1 + si → 0 for ε → ∞
must hold for i = h only. Hence ehε → ∞ and, therefore, by equation (44),
ghε → 1 for ε → ∞. It follows from πε — 1 + s⅛ → 0 for ε → ∞ and πε > 0
that Sfl must not exceed 1. ■
46