For the question below, use these symbols correspondingly:

Preference relation: ?

Strictly preferred to: ?

Indifference: ~

Is a subset of: ? i.e. A ? B means A is a subset of B

Please bold things like R (real numbers), R+means positive real numbers, vice versa.

5. [This question gives you some practice with a. type of preference called \"Cobb- Douglas preferences\" which shows up in many applied economic models because they are easy to do calculus with] Let X = Riv let u : X > R be given by u(:1:) := $312173, and let i: be the preference relation 011 X given by utility representation u. Show that: (a) The function u is not concave. [Hint: Take a second partial derivative with respect to one of the coordinates] (b) The preference relation E; is convex. [Hint: You may use the fact that the function f : X > R given by f(:1;) = (Li/213;]? is concave. If you feel like doing some math, try to Show that f is concave, but you don"t need to do this]