How do i know if a set of bundles forms a convex set?

Question

this problem says that the set is the set of bundles that Edward weakly prefers to the bundle (20, 6). does this set of bundles form a convex set?

The two curves given were: (xA, xB) and (25,4) have the equation: xA = 100/xB

and (xA, xB) and (20,6) have the equation: xA= 120/xB

so how do i know if the set of bundles weakly preferred to (20,6) forms a convex set?

please help!!

Answer 1

In a convex set, the shortest path between any 2 points (even for points on the boundary) passes through points all of which belong to the set. In the examples you've mentioned, the curves are Hyperbolic in nature. Any 2 points on the curve (Hyperbola) passes through points that are external to the set; hence not convex.

Answer 2

plot y = 100/x (for x>0),

fill in the area above the curve, and

ask yourself whether it is convex.