The preferences are complete, transitive, continuous, strictly monotone and strictly convex
The textbook says it is because (1) Budget Set is compact so that a solution exists; (2) B is convex and the utility function representing this preference is strictly quasi-concave
What if I have no information on budget set, that is, I don't know what properties B might have. Can all arguements above still hold?
Can I use the strict increasing utility function to prove the solution is unique? Since a preference with all these assumptions ensures a continuous, strictly increasing and strictly quasi-concave utility function. Then by contradiction, there can not be two or more maximization point of utility function.