t = 0
3. [30 MARKS] Let t be the 7th digit of your Student ID. Consider the utility function
u(x,y)
=
1
t +2
1
-In(1 + x) +
-In(1+ y)
t +2
(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 г+(1) u(x, y) ≥ 1} is a convex set.
=
{(x, y) = R2:
(d) [8 MARKS] Compute the 2nd order Taylor polynomial of u(x, y) at (0,0).