Alex and Brenda have the following utility functions over cake and diamonds: UA(CA.DA) = (CAXDA) US$3.03) = (CBXDB) Total cake and diamond endowments in the economy are we = 20 and w; = 10. . . . . 1 The contract-cu rye for this economy is the set of allocations that satisfy DA = E CA. It is a diagonal line going from corner to corner of the Edgeworth Box. A Walrasian auctioneer will call out prices pc and p0 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\"1 = 6*3 = 10 and D\" = D*3 = 5, so that Alex and Brenda each end up with half the total endowments of both goods. You know this point lies on the contract-curve because D\" = $0\