Keisha and Sukhbir are the only inhabitants of the city Tropica. The only two goods available for consumption in this city are apples (A) and pizza (P). The utility functions of Keisha and Sukhbir are given by U_K = A_K^1/3 P_K^2/3 and U_S = A_S^1/2 P_S^1/2, respectively. Further, Keisha and Sukhbir already have some apples and pizza slices. Keisha has 30 apples and 20 pizza slices while Sukhbir has 20 apples and 30 pizza slices. There is no money in this economy and individuals barter or trade directly with one another.

a) If they are to trade, please provide an example of a pareto efficient allocation. Draw it on your Edgeworth Box.