Question 3 "High-Life" is an apartment complex offering pre-sale units before con- struction. Each apartment unit is custom-built. Buyers can choose the apartment size (in sq. meters), denoted by r, and the height from the ground floor (in metres), denoted by y. The apartment size, however, needs to be at least 6, sq. meters and at most dy sq. metres. The apartment height is restricted by the building code to be at most & metres high. Let p, be the price of r, per sq. meter, and py be the price of y, per meter. No underground apartment units are built. Joanne is considering buying an apartment in this complex. She only cares about the apartment level: the higher, the better. Joanne's budget is My. Assume that MJ 2 P261; that is, Joanne has enough budget to purchase at least the smallest apartment unit on the ground floor. Another potential buyer, George, cares about both the apartment level as well as the apartment size. George's budget is Mo. Assume that Mo 2 pron; that is, George has enough budget to purchase at least the smallest apartment unit on the ground floor. Suppose George's utility function is V = r"y where a, 8 > 0. Use the above information to answer the followings: (a) (2 marks) Write down OR draw Joanne's choice set. [Hint: Joanne's choice set is all the possible (r, y) that Joanne can choose from the developer.] (b) (2 marks) Given the choice set in part (a), write down OR draw Joanne's "feasible" budget set. [Hint: Her "feasible" budget set must be a subset of her choice set.] (c) (2 marks) Propose ONE utility function that represents Joanne's preferences. (d) (5 marks) Draw TWO indifference curves of Joanne in the x-y plane. Draw an arrow pointing towards the direction of higher utility. (e) Joanne's weak preferences can be defined as (TA: YA) ~ (TB. yB) if and only if yA 2 yB Using this information, derive an analogous definition of: (i) (5 marks) her strict preferences () in terms of TA, Tg, yA, and yB. (ii) (5 marks) indifference preferences (rv) in terms of FA, Is, yA, and yB- (f) (5 marks) Suppose Joanne is a utility maximiser. Find her Marshallian demand function for r and her Marshallian demand function for y. Explain and show your work. (g) (2 marks) Propose an alternative utility function that represents George's preference. (h) (5 marks) Suppose George is a utility maximiser, use the tangency condition and the budget equation to derive George's Marshallian demand of r and y. Explain and show your work. (i) (5 marks) Are there any circumstances under which the answer derived in part (h) does not yield the George's optimal bundle? Explain. (j) (2 marks) Suppose you know the parameters a, B, 6, 61, 62, Pz. Py: My, and Mc. and you also know that both Joanne and George are utility maximizers. Can you tell who is happier with their chosen apartments? Explain