Suppose a consumer has a utility function: u( x1 , x2) = min {x1, 2x2},
i.) Prove that the set of bundles ( x1, x2) = min {x1, 2x2} ≥ 10 is a convex set.
ii.) Prove that, for any bundles (x1, x2) and (y1, y2), the utility function satisfies:
u( x1/2 + y1/2 , x2/2 +y2/2 ) ≥ min { u(x1, x2) , u(y1 , y2)}