微观问题求解

Let u be a continuous utility function representing a locally non-satiated preference
relation. Denote by x and h the associated Walrasian and Hicksian demand
correspondences, respectively, and by v and e the indirect utility and expenditure
functions, respectively. Prove the following statements when p ≫ 0.
a) x(p, e(p, u)) ⊂ h(p, u).
b) h(p, u) ⊂ x(p, e(p, u)).
c) h(p, v(p,w)) ⊂ x(p,w).
d) x(p,w) ⊂ h(p, v(p,w)).
e) w = e(p, v(p,w)).
f) u = v(p, e(p, u)).