(pH - pL) > U'(Y)[U'(Z) - U'(X)] pL(1 -p)L) U (X)U'(Z)
where X, Y, and Z are determined by the optimal a*, a2*. The right-hand side of (4) is always less than
U'(Wo-d)[U(Wo -d) - U'(Wo)] U'(Wo)2
so that there exist values of y (and thus of X) large enough to satisfy (4).