Lett be the 7th digit of your Student ID. Consider the utility function u(r, g) = 1 t+2 -In(1+x) + 1 t+2 zln(1 + y) (a) [10 MARKS] Compute the Hessian matrix D²u(x, y). Is u concave or convex? (b) [4 MARKS] Give the formal definition of a convex set. (c) [8 MARKS] Using your conclusion to (a), show that I+(1) = {(x, y) = R²: u(x, y) ≥ 1} is a convex set. (d) [8 MARKS] Compute the 2nd order Taylor polynomial of u(x, y) at (0,0).