Bill and Ted both like goods X and Y, but their preferences for these goods are not the same.
Bill's preferences can be represented by the utility function
equation U(x,y)=x^2y
Ted's preferences, by contrast, are represented by the utility function
equation U(x,y)=xy^3
Bill and Ted have the endowments:
Bill (6,13)
Ted (44,12)
Starting from this allocation, the Lord High Social Planning Dictator has decreed that Bill and Ted must trade with one another to attain the new allocation:
Bill (35,7)
Ted (15,18)
What are the optimal amounts of X and Y consumed by Bill and Ted when each maximizes his utility subject to the value of his endowment and the relative price of X (Px /PY =p)
Options:
a) Bill's optimal quantity of X < 30; Bill's optimal quantity of Y > 10
Ted's optimal quantity of X > 20, Ted's optimal quantity of Y > 10
b)Bill's optimal quantity of X > 30; Bill's optimal quantity of Y < 10
Ted's optimal quantity of X > 20, Ted's optimal quantity of Y > 10
c) Bill's optimal quantity of X < 30; Bill's optimal quantity of Y > 10
Ted's optimal quantity of X > 20, Ted's optimal quantity of Y < 10
d) Bill's optimal quantity of X > 30, Bill's optimal quantity of Y > 10;
Ted's optimal quantity of X > 20, Ted's optimal quantity of Y > 10
e)Bill's optimal quantity of X < 30; Bill's optimal quantity of Y < 10
Ted's optimal quantity of X > 20, Ted's optimal quantity of Y > 10
And is the relative price an equilibrium price?