consider a consumer with preferences represented by a utility function

u(x1,x2) = x1 + x2, where > 0 is a parameter. Fix prices p = (p1,p2) > 0 and income m > 0.

1. (a)[2] Illustrate the consumer's indifference curve through the bundle (0, 1).
2. (b)[2] Show that the consumer's preferences are convex.
3. (c)[2] Write down the consumer's utility maximisation problem.
4. (d)[2] Argue that the consumer's budget constraint holds as an equality at any optimal

consumption bundle (x1*, x2*).

1. (e)[2] When is x2 = 0 optimal for the consumer?