Mutt's utility function is U(m, j)= max{3m, j} and Jeff's utility function is U(m, j)= 3m + j.Mutt is initially endowed with 6 units of milk and 2 units of juice and Jeff is initially endowed with 2 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)bottom edge of the Edgeworth box but no other edges.
B)left edge of the Edgeworth box but no other edges.
C)right edge of the Edgeworth box but no other edges.
D)left edge and bottom edge of the Edgeworth box.
E)right edge and top edge of the Edgeworth box.

Question

Quizplus · Accepted Answer

To determine the set of Pareto optimal allocations, we need to find all possible allocations where neither Mutt nor Jeff can be made better off without making the other worse off. This occurs at the point where their indifference curves are tangent.

Mutt's utility function has a maximum of 6 when he has all milk and 0 juice, and a maximum of 2 when he has all juice and 0 milk. Jeff's utility function has a maximum of 18 when he has all milk and 0 juice, and a maximum of 6 when he has all juice and 0 milk.

So, the set of Pareto optimal allocations lies between the points (6,0) and (0,6), which form the bottom left and top right corners of the Edgeworth box. The Pareto optimal allocations lie along the contract curve, which is the line connecting the tangency points of Mutt's and Jeff's indifference curves.

The tangency points occur at the corners of the Edgeworth box where their indifference curves intersect. These points are (4,4) and (2,2). Therefore, the set of Pareto optimal allocations includes the left edge and the bottom edge of the Edgeworth box, where the allocations are (6,2), (5,3), (4,4), (3,5), and (2,6).

Mutt's Utility Function Is U(m, J)= Max{3m, J} and Jeff's