Hermione wants to purchase some Gryffindor scarfs (S) and robes (R). The price of a scarf (Ps) is 1 golden Galleon (g), and the price of a robe (PR) is 2 g. She has an income (M) of 9 g. Her utility function is U(S, R)= S/3 R2/3 [Calculus Help: The derivative of U with respect to S is 3 = (), and the derivative of U with respect to R is = () .] au as a. [13 Points] How many scarfs and robes would she optimally choose to purchase? Let's call Hermione's budget line "LA", and her Optional Consumption Bundle (OCB) - Bundle "A". b. [13 Points] The price of robes suddenly falls to 1g, how many scarfs and robes can she actually buy? Let's call Hermione's new budget line "LB", and her new Optional Consumption Bundle (OCB) - Bundle "B". c. [3 Points] Given the new robe price, let's adjust Hermione's income so that she can exactly afford her old consumption bundle from Part (a), what would her adjusted income be? d. [10 Points] With the adjusted income you found in Part (c) and the new robe price, how many scarfs and robes would she purchase? Let's call Hermione's income-adjusted budget line "Lc", and her Optional Consumption Bundle under the adjusted income - Bundle "C". e. [21 Points] Please draw a graph with S on the x-axis, and R on the y-axis. In your graph, draw the three budget lines LA, LB, and Lc, you found in Parts (a), (b), and (d). Please label the numerical values of their intersections with both axises. Then, label precisely in your graph (showing their coordinates), the Optimal Consumption Bundles A, B, and C, which you calculated above. Please also use arrowed lines between OCBs to indicate the "income effect," the "substitution effect," and the "total effect." 29