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, for example, cobb douglas)

(b) Write another one(alternative utility function)

(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.