Question in microeconomics

2. [20] Consider an Edgeworth box economy where preferences and endowments are given by u'(x],r;) = 4 (x])$ +x), el = (15,5) u?(x], 13) = 2 (27) 1 + 13, e? = (5, 15). (a) [6] Find all the interior Pareto optimal allocations, using r, as the pa- rameter (that is, express the PO allocations in terms of r?). (b) [6] Find all the boundary Pareto optimal allocations (c) [4] State the definition of a contract curve. (d) [4] Does a Walrasian equilibrium allocation always have to be on the contract curve? How about an equilibrium with transfers? Explain your