A consumer chooses a bundle (z, z, . . . , z) where z satisfies $z Σp_k = w$.
The book (Rubinstein's) states that the demand function x(p,w) can be rationalized if there exists a preference such that x (p,w) is the best bundle in B(p,w). Even if it satisfies Walras'Law and homogeneous of degree zero, we still cannot determine if it is fully rationalizable.
I understand that the bundle needs to be the best bundle in the budget set.
Yet, does it mean that it can be rationalized only preferences are strictly convex and there is at most one solution?
How can we determine that the above statement can be rationalized?