1. Consider an economy with two goods x and y, and 2 individuals A and B with preferences represented by the utility functions:

U A (x_A , y_A ) = x _A y _A

UB (x_B , y_B )= x_B y_B

where xi and yi represent the consumption of goods x and y by each individual i = A, B. The initial endowment of the goods is that A has 12 units of x and 2 units of y while B has 8 units of x and 18 units of good y.

(i) Show how the two goods must be allocated among the two individuals at any Pareto efficient allocation in this economy. Draw the corresponding contract curve in the Edgeworth box. Make sure to label everything clearly.

(ii) Assume A gets to choose a new allocation to maximize utility subject to the constraint that B's utility is no lower than at the endowment point. Solve formally for the Pareto efficient allocation.