Amy loves fancy and fashionable outfits. She never wears an outfit twice. She has a utility function takes the form U(x,y) = x1/2y1/2 = xy, where x stands for the number of "new outfits" and y is the amount of "Other goods" essential to her living. That is to say, Amy's marginal utilities for new outfit and other goods are:

MUx = 1y; 2x

MUy = 21xy,

respectively.

Amy recently noticed that one of her favourite brand "Supreme" is offering a deal on

its' latest patchwork hooded jackets, which is sold at $100 a piece. The promotion claims that one can "get the second piece 50% off." It means, if Amy buys a jacket from Supreme for $100, she can buy the second jacket (of different colour) for 50% of the original tag price, $50. In addition, if Amy wants a third jacket, she has to pay $100 again, but now she has the privilege to purchase the fourth jacket for $50, etc. Assume the price for "Other goods" is $50 and Amy has a monthly income of $1,000 to spend on both the Supreme jackets and "Other goods." Answer the following questions. Note that, if your final results are not integers, report the results up to two decimal digits.

(a) Depict Amy's indifference curves with utility levels of 8 and 10 on a graph with nec- essary details, with "Other goods" on the vertical axis.

(b) DrawAmy'sbudgetconstraintonanothergraphwithnecessarydetails,with"Supreme jackets" on the horizontal axis. (Hint: this graph needs to be reasonably accurate.)

(c) Based upon the information given, what is Amy's optimal consumption bundle? What is her utility level at this optimal bundle? Show your work with necessary details.

(d) If Supreme announces a different promotion scheme: instead of "get the second piece 50% off," the store offers a 25% off for every jacket sold, would Amy be better off, worse off, or indifferent between this two promotion schemes? Show your work with necessary details.

(e) A Giffen good refers to a commodity that violates the law of demand. Use a suitable graph (or graphs) to explain why a Giffen good must be an inferior good.

(f) It has been observed by many that some luxury brands, such as Herme s and Louis Vuitton, never lower the prices of their products even when the demands are low. On the contrary, people witness that, among similar designs from the luxury brands, the ones are more expensive usually attract more clients. Are these luxury commodities

(e.g., Herme s belts, Louis Vuitton shoulder bags, etc.) Giffen goods? Are they infe- rior goods? how can you reconcile this seemingly paradoxical phenomenon? Briefly explain your answer.