DSE 2012 Solutions?

[sarawagisruti]

Kindly forward me the link to the 2012 DSE paper detailed solutions, if available.

I have a doubt in Question 45 of the paper..

f(x, y) = x + y + xy where x, y E R++. For c E R++, let
us define,

L = {f(x, y) E R++ |f(x, y) <= c}
U = {f(x, y) E R++ |f(x, y) >= c}
I = {f(x, y) E R++ |f(x, y) = c}

Which of the above sets are convex?
(a) L
(b) U
(c) I
(d) All of them

[economist]

See the function is concave as the hessian matrix is negative definite. Concavity implies quasiconcavity , so upper level set is convex. Upper level set is defined as U in the question so answer is b.

[sarawagisruti]

Thankyou :)