Consider an economy with two people, Donald and Hillary, and two goods, x and y. Donald is endowed with x¯ units of good x and has none of good y. Hillary is endowed with y¯ units of good y and has no units of good x. Their preferences over these two goods are identical and represented by the Cobb-Douglas utility functions:
UD = x(D)^1/3*y(D)^1/3
UH = x(H)^1/3*y(H)^1/3
Derive the Utility Possibility Frontier in this economy.