(c) Now, the store where Robert goes for shopping has changed the prices to p, = 2 and py = 6, however, it also has a new special offer: for any amount of Y that Robert buys, he gets the same amount of X for free. Robert's income is M = 6. Draw Robert's budget line. Write down the equation of this line. Find Robert's utility-maximising bundle. (d)(d.1) Arthur's income is M = 6 and he goes to the same store as Robert. His utility function is U(x, y) = min{r, y}. What is his optimal bundle under the prices of part (c), including the special offer. Provide a graphical argument justifying your answer. (d.2) Simon's income is M = 6 and he goes to the same store as well. His utility function is U(r, y) = 2r + 2y. What is his optimal bundle under the prices of part (c), including the special offer. Provide a graphical argument justifying your answer.

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