Two consumers, A and B, consume books and wine. Consumer A's initial endowment is (60,10); that is, A has 60 books and 10 bottles of wine. Consumer B's initial endowment is (20,30). They have no other assets, and make no trades with anyone other than each other. For A, a book and a bottle of wine are perfect substitutes; her utility function is UA(Xb,Xw) = Xb +Xw, where Xb is the number of books she consumes, and xw is the number of bottle of wines she consumes. Consumer B's preferences are given by the utility function uB(xb,xw) = xbxw.
(1) Draw an Edgeworth box with B's consumption measured from the upper right- hand corner of the box. On this diagram, mark the initial endowment, and label it e. Use red ink to draw A's indifference curve that passes through her initial endowment. use blue ink to draw B's indifference curve that passes through her initial endowment.
(2) At any Pareto optimal allocation, where both people consume some of each good, it must be that their marginal rates of substitution are equal. Why? What are A and B's marginal rates of substitution? What is the equation of the contract curve? Use black ink to draw the contract curve on the diagram.
(3) In a competitive equilibrium, A will consume some books and wine. But in order for her to do so, what must the ratio of prices be? What is the competitive equilibrium of this exchange economy?