Problem 4. Alberto and Bethany are in an Edgeworth Box economy with 100 units of X and 100 units of Y to divide among themselves. Alberto's preferences can be described by a utility function U(XA,YA) In(2xA+YA) Bethany's utility function is U(XB,YB) = XB+ YB (For yourselves, sketch the contract curve. Note this is similar to Notes #12 & 13 except only one of the two agents has Cobb-Douglas preferences, while for the other the two goods are perfect substitutes.) Suppose Alberto's initial endowment is 50 units of x and zero units of y. a) Is that initial endowment Pareto efficient? b) Sketch the contract curve and the core. Now suppose that Alberto's initial endowment is 50 units of y and zero x. c) Is this alternative endowment Pareto efficient? d) Sketch the contract curve and the core. Now suppose that Alberto's utility function is U(XA,YA) = √XAYA e) Alberto's endowment is as in parts c-d. Suppose trade is restricted to a single offer: Alberto can make ONE trade offer to Bethany (for example, to exchange 10 units of x for 5 units of y). She either accepts or rejects the offer, and no further trade is possible. How many units of x does Alberto offer? f) Same setup as in part e), except Alberto starts with 40 units of x and 10 units of y, and Bethany gets to make a single take-it-or-leave-it offer. How many units of y does Bethany end up with?

Fig: 1