1. Consider an economy with two goodsxandy, and 2 individualsAandBwith

preferences represented by the utility functions:

U_A(x_A,y_A)=sqrt(x_Ay_A)

U_B(x_B,y_B)=sqrt(x_By_B)

wherex_iandy_irepresent the consumption of goodsxandyby each individuali=A, B. The initial endowment of the goods is thatAhas 2 units ofxand 8 units ofywhileBhas 8 units ofxand 2 units of goody.

(a) Show formally 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. (2 points)

(b) AssumeBgets to choose a new allocation to maximize her utility subject to the constraint thatA's utility is no lower than at the endowment point. Find the corresponding Pareto efficient allocation. What is the magnitude of the increase inB's utility when moving from the endowment point to this Pareto efficient allocation? Provide a graphical illustration. (3 points)