Consider a consumer with preferences represented by a utility function u(x1,x2) = ax1 + x2, where a > 0 is a parameter . Fix prices p = (p1,p2) > 0 and income m > 0

a) illustrate the consumer's indifference curve through the bundle (0,1)

b) show that the consumer's preferences are convex

c) Write down the consumer's utility maximization problem

d) Argue that the consumer's budget constraint holds an equality at any optimal consumption bundle (x1*,x2*)

e) When is x2* = 0 optimal for the consumer?

f0 Derive the consumer's demand function