Alice has convex preferences over consumption bundles containing goods x and y. Where (x, y) is the consumption bundle, Alice's preferences are as follows: (5, 2) ∼ (4, 2) ? (3, 2) ∼ (3, 5) ∼ (3, 6)

(a) Write a utility function that can represent Alice's preferences. (Hint: Try one of the 'types' of utility functions we have seen in lecture)

(b) Write another one.

(c) Are Alice's preferences strictly convex? Explain.

(d) Derive Alice's demand functions for x and y, where the budget set is m ≥ pxx + pyy.