Alex and Brenda have the following utility functions oyer cake and diamonds: UA(CA,D\"'} = (C'HD') UtCB\") = (6\")(03) Total cake and diamond endowments in the economy are wc = 20 and WE, = 10. The contractcurye for this economy is the set of allocations that satisfy 13*\"1 = it\". It is a diagonal line going from corner to corner of the Edgeworth Box. A 1il'ii'alrasian auctioneer will call out prices pc and p3 and will equate supply and demand in the market of each good until allocations reach an equilibrium. Part 1. You are a central authority who desires the equilibrium allocations to be as "fair" as possible. that is, you want C" = ti"Er = 10 and D" = D'5 = 5, so that Alex and Brenda each end up with halfthe total endowments of both goods. 'i'ou know this point lies on the contract-curye because D\" = if", and you know the Second Welfare Theorem states that any point of the contract-curye can be reached as an equilibrium with the appropriate initial endowments. You can't control the initial cake endowments, they are w? = 15, w? = 5. But you -can- control initial diamond endowments w and w {and you know w must equal 10 wg\" because wg = 10}. "four task is to find the w needed for your desired C\