1. Now, the store where Robert goes for shopping has changed the prices topx= 2andpy= 6, however, it also has a new special oer: for any amount ofYthat Robert buys, he gets the same amount ofXfor free. Robert's income isM= 6. Draw Robert's budget line. Write down the equation of this line. Find Robert's utility-maximising bundle. (5 marks)

(d)(d.1) Arthur's income isM= 6and he goes to the same store as Robert. His utility function isU(x, y) = min{x, y}. What is his optimal bundle under the prices of part (c), including the special oer. Provide a graphical argument justifying your answer. (3 marks)

(d.2) Simon's income isM= 6and he goes to the same store as well. His utility function isU(x, y) = 2x+ 2y. What is his optimal bundle under the prices of part (c), including the special oer. Provide a graphical argument justifying your answer. (2 marks)