Hello,

There is one important case where tangency is sufficient,and that is the case of convex preferences. The perfect point of convex selection should be any point which convinces the condition of the tangencies.

There are three tangential conditions in this case, but only two optimal points are required, but the tangential conditions are not sufficient. However, projection is another point. If the curves of mediocrity are strictly convex, each budget line has only one classic substitute.

Thank you.