Show that, if the choice set C consists of the bundles W,X,Y,Z (i.e., C = {W,X,Y,Z}), and the preference relation is complete and transitive, there exists a bundle [set of bundles] that is [are] maximal in C with respect to ≿. That is, if a bundle belongs to the “set of maximal bundles”, there is no other bundle in the choice set that is strictly preferred
to it.
Add the bundle Y , and compare it with the maximal bundle (set of bundles) you found when there were only bundles W and X. Use the fact that % is complete and transitive. Think carefully why it is enough to compare Y with the maximal bundle (set of bundles) found in the previous step. Determine the “new” maximal bundle (set of maximal bundles).
Add bundle D and repeat the step 2.
to it.
If you can, please provide a mathematical argument making use of the following steps.
Start with bundles W and X and make use of the fact that ≿ is complete. Determine the maximal bundle [set of bundles] from this two bundles.Add the bundle Y , and compare it with the maximal bundle (set of bundles) you found when there were only bundles W and X. Use the fact that % is complete and transitive. Think carefully why it is enough to compare Y with the maximal bundle (set of bundles) found in the previous step. Determine the “new” maximal bundle (set of maximal bundles).
Add bundle D and repeat the step 2.