For the rest of this question consider a two goods economy where Kim and Jung can trade Ferraris (good x) and VR headsets (good y) with each other. Kim and Jung both enjoy driving Ferraris and having more VR headsets (so more friends can play the same game). They start at the same (high) level of income. Kim has an initial endowment of (x^o_x, y^o_x) = (10,30) and Jung has an initial endowment of (x^o_j, y^o_j) = (30,10) 

a) Illustrate the initial endowment in an Edgeworth box. Clearly label the axes and explain the dimensions of the box. Show the indifference curve each of them is on at the endowment point.

b) Consider an allocation where Kim gets (XkYx) = (40,40) and Jung gets the remaining Ferraris and VR headsets. Show where this point is in the Edgeworth box. Is this allocation Pareto efficient? Is it equitable? How likely is this to arise in practice?

c) Assume that Kim has preferences Ux (xx,y) = 3xx + yx and Jung has prefer- ences U,(x, y) = x, +3y). Will Kim and Jung trade? Calculate the general equilibrium allocation for Kim and Jung. Compute the utility at the endowment point and at the general equilibrium allocation. Is the new allocation on the con- tract curve?

d) Assume that a social planner could redistribute initial wealth (the amounts of x and y that Kim and Jung have). Can they reallocate resources so that Kim and Jung reach the allocation (XxYx) = (20,20) and (x, y) = (20,20) as a general equilibrium (.e. post-trade) allocation? Can the social planner redistribute re- sources to make the allocation where Jung owns all the resources in the econ- omy a general equilibrium allocation?