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Page 2 > of 2 ZOOM + k Suppose Minerva (M) and Rubeus Hagrid (R) are hanging out at the local public pool. The summer is coming to a close, so the concession stand is handing out the remaining Ice Mice (I) and Honeydukes (H) in stock. Minerva ultimately ends up with 50 Ice Mice and 20 Honeydukes, while Rubeus (sorry, Hagrid) received 50 Ice Mice and 80 Honeydukes. Let Ir be the quantity of Ice Mice individual x has, and Hr be the quantity of Honeydukes individual x has, where x is Minerva or Rubeus. Minerva's utility function is: UM(IM, HM) = AIR + 2HR Rubeus' utility function is: UR(IR, HR) = 412 + 2HR Part a) Find Minerva and Rubeus' marginal rates of substitution (MRS) at this initial allocation. Part b) Would Minerva and Rubeus have any incentive to trade at this initial allocation? Why? Sketch an Edgeworth box, with the quantity of Ice Mice on the horizontal axis. Show the initial allocation and Minerva and Rubeus' indifference curves through this allocation. It should reflect whether or not they want to trade. If there is room to trade, label the area with allocations that they would be willing to trade to. Part c) Suppose Minerva and Rubeus decide to trade. To help with their trading, their friend Albus establishes a price system, where the price of Ice Mice is Pr = 4, and the price of Honeydukes is PH = 1. Find both Minerva and Rubeus' utility maximizing bundles, given these prices.Page