Consider the utility function (x, y) = xy, which describes the enjoyment Emi gets from consuming tacos (x) and sandwiches (y) over a period of 1 week. a) Does Emi like both tacos and sandwiches? Does she like variety? b) Let Emi have budget I=$24, and let prices be P.=$2, Py=$4. Find Emi's optimal basket of goods x and y. Is this an interior or a corner solution? c) Suppose that, in order to boost salles, the sandwich vendor introduces a discount card. Each week, every sandwich a consumer buys after the first 3 will be on a 50% off sale. (Purchase records are not transferred from week to week.) Draw the new budget constraint and express it algebraically d) Will the change from part c have an effect on Emi's purchase? Check how much of each good Emi will want to buy now. 2. Emi's friend Xindi also likes tacos, but she doesn't like sandwiches. Instead, she always consumes exactly two tacos (good x) with one glass of horchata (y), and she doesn't enjoy either good without the other. Suppose prices are the same as initially in problem 1, so that horchata is twice as expensive as tacos (P=$2, Py=$4), and Xindi has the same budget as Emi: 1=$24 a) How can we write Xindi's utility function? b) What basket of goods does Xindi purchase? c) If the horchata vendor implements the same sale as at part c of the previous question, how will this affect Xindi's purchase? d) What if instead all horchata goes on sale (even the first 3 glasses)? 3. Emi and Xindi have another friend, Alia, who only likes tacos. She only buys tacos from two local restaurants: Roberto's (x) and Alberto's (y). But let's face it, Roberto's is the best, and she likes their tacos 1.5 times as much, regardless of how many she is currently consuming of each. (In other words, we would have to offer Alia at least 3 Alberto's tacos in order for her to give up 2 Roberto's tacos.) a) Suppose that I=$24, and initially Px = 4 and py = 2 (these are reversed from problems 1 and 2). Draw Alia's budget line, and the indifference curve that goes through her optimal basket. What combination of goods will she buy? b) What if Roberto's decreases its price by 50% (for all units)? C) Can you tell what would happen if Roberto's decreased price, but only for tacos above the first 3? (You don't have to do the math, just use the graph) d) Now go back to the initial prices, and suppose Alia's parents send her a gift certificate to Roberto's of $8 each week. (this certificate can't be used to buy tacos from Alberto's). Draw the new budget line and determine what combination of tacos Alia will now consume each week