Let a consumer has the following utility function on R 2 +: u(x) = max{x1, x2}, where > > 0.

(a) (2 marks) Is the preference relation u representing monotone? Prove your argument.

(b) (6 marks) Derive the demand for good 1 and good 2 of the consumer as functions of price p = (p1, p2) and income w, where p1 > 0, p2 > 0, w > 0. Show your work.