Appendix A: Proof of Lemma 1
First, we consider an increase in Wq to ∣>Wi, holding the required expected
return R* constant; b > 1. Then η changes to aη; a> 0. Define eɪ := (e — e)
for the initial endowment Wq and define eb := (e—e) for the initial endowment
bW^o. Then we need to show that
E[f(e1)] > E[f(eb)]
— —aη
or
aE[f(e1)] >E[f(eb)]. (22)
From equation (15) it follows that V ε,
— E[f (eb)] + f (ebS') = aη θε = a( — E[f (ei)] + f (ele))- (23)
As the mean absolute deviation between payoffs across states has to grow
with Wq , the monotonicity of f implies that also the mean absolute deviation
I E[f (e)] — f (e)] I has to grow. Hence a > 1. Now assume, by contradiction,
that inequality (22) is not true. Then equation (23) implies
f (ebε) ≥ af (elεy, V ε. (24)
As a > 1 and f > 0, this implies
f (ebε) > f (elεy, V ε.
36
More intriguing information
1. Partner Selection Criteria in Strategic Alliances When to Ally with Weak Partners2. Technological progress, organizational change and the size of the Human Resources Department
3. Effects of a Sport Education Intervention on Students’ Motivational Responses in Physical Education
4. The name is absent
5. The resources and strategies that 10-11 year old boys use to construct masculinities in the school setting
6. The name is absent
7. Opciones de política económica en el Perú 2011-2015
8. The name is absent
9. The name is absent
10. Modeling industrial location decisions in U.S. counties