A consumer has a direct utility function of the form

Good 1 is a discrete: i.e. the only consumption levels of good 1 are x1 = 0

and x1 = 1. For convenience, assume that u(0) = 0 and p2 = 1

(a) What kind of preferences does this consumer have?

(b) For determine the Marshallian demand functions of the consumer.

(c) Why the assumption that p2 = 1 necessary in this problem?