Mutt's utility function is U(m, j)  max3m, j and Jeff's utility function is U(m, j)  4m  j.Mutt is initially endowed with 4 units of milk and 2 units of juice and Jeff is initially endowed with 4 units of milk and 6 units of juice.If we draw an Edgeworth box with milk on the horizontal axis and juice on the vertical axis and if we measure goods for Mutt by the distance from the lower left corner of the box, then the set of Pareto optimal allocations includes the

A) left edge and bottom edge of the Edgeworth box.
B) right edge of the Edgeworth box but no other edges.
C) bottom edge of the Edgeworth box but no other edges.
D) left edge of the Edgeworth box but no other edges.
E) right edge and top edge of the Edgeworth box.

Mutt's utility function is max{3m, j}, which means he prefers the maximum of either thrice the amount of milk or the amount of juice. Jeff's utility function is 4m + j, indicating he values both milk and juice, with a higher weight on milk. Given their initial endowments, the set of Pareto optimal allocations would favor scenarios where Mutt could potentially trade some of his juice for more milk, as he values them equally only when the quantity of juice is triple that of milk. However, since the utility functions and endowments suggest that both parties have different preferences with Mutt having a more extreme preference for either good, the Pareto optimal allocations are not straightforwardly determined by their initial endowments alone. The correct answer, focusing on the edges of the Edgeworth box, would be the left edge, as it represents allocations where Mutt has maximized his utility by potentially trading away juice for milk, reaching a point where he cannot improve his utility without making Jeff worse off. This is because on the left edge, Mutt would have all the milk (his preferred good when considering his utility function), and Jeff would have all the juice, aligning with their utility functions' preferences. However, this explanation simplifies the complex dynamics of Pareto optimality and the specific utility functions given, which do not directly translate to the edges of the Edgeworth box without considering the possibility of trade and the specific shape of their indifference curves within the box.