3) (4pts) Optimal choice: example #

Emi and Xindi have another friend, Alia, who only likes tacos. She only buys tacos from two local restaurants: Alberto's (x) and Roberto'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) Write Alia's utility function and draw some of her indifference curves.

b) What basket of goods does Alia purchase?

c) what if tacos go on sales for 1$?

d) Continuing from these prices, suppose that, in order to boost salles, the Roberto introduces a discount card. Each week, every taco 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. Will this change have an effect on Alia's purchase? Check how much of each good Alia will want to buy now.

e)Find and writedown formally Alia's demand functions x(Px, Py, I) and y*(Px, Py, I) including for the threshold case. Can you find a compact way of expressing her indirect utility function?

Holding I=$24, Py=$4:

f)draw the price consumption curve for x;

g) draw the demand curve for x