Question 4 {20 marks). Robert's utility function is U[I,y) =2+y. In every graph for this question. set 3; in the vertical axis and :r: in the horizontal axis. {3) Obtain the marginal rate of substitution MRS. Obtain the equation of the indifferenCe curve; for E = 2 and F = 4 {solving for y as a function of :17}. Draw these indifference curves. identifying the intersections with each of the axes. {5 marks) (b) Suppose pH = 2 and Robert's income is M = 6. In a new graph. show the total. income and substitution effects {on the demand of I} of a drop in the price of :r from pI = 4 to pI = 2. {5 marks} {(2) Now. the store where Robert goes for shopping has changed the prices to p, = 2 and p" = fl. 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 = ti. Draw Robert's budget line. 1Write down the equation of this line. Find Robert's utility-maximising bundle. {5 marks] (d}[d.1} Arthur's income is M = and he goes to the same store as Robert. His utility function is U (I, y) = min{:t,y}. What is his optimal bundle under the prices of part {c}, including the special offer. Provide a graphical argument justifying your answer. (3 marks} {d2} Simon '5 income is M' = 6 and he goes to the same store as well. His utility' function is Ulm. y) = 23: + 2y. What is his optimal bundle under the prices of part (c). including the special offer. Provide a graphical argument justifying your answer. (2 marks}