Morris has the utility function U(b, w)= 4b + 16w and Philip has the utility function U(b, w)= bw, where b is the number of books consumed per month and w is bottles of wine consumed per month.If we draw an Edgeworth box with books on the horizontal axis and wine on the vertical axis and if we measure Morris's consumptions from the lower left corner of the box, then the contract curve contains
A)a straight line with slope 1/4 passing through the lower left corner of the box.
B)a straight line running from the upper right corner of the box to the lower left.
C)a straight line with slope 1/4 passing through the upper right corner of the box.
D)a curve that gets steeper as you move from left to right.
E)a curve that gets flatter as you move from left to right.

Question

Quizplus · Accepted Answer

To find the contract curve, we need to find the allocation of books and wine that maximizes the sum of Morris and Philip's utilities, subject to the budget constraint. The budget constraint is given by 4b + 16w = M, where M is Morris's monthly income. Rearranging this constraint, we get b = (M / 4) - 4w. Substituting this into Morris's utility function, we get U(M, w) = (M / 4) + w. Similarly, substituting the budget constraint into Philip's utility function, we get U(b, w) = bw.

To find the contract curve, we need to find the values of b and w that maximize U(M,w) + U(b,w) subject to the budget constraint. Maximizing U(M,w) + U(b,w) is equivalent to maximizing (M / 4) + 2w + bw subject to the budget constraint. This is a linear programming problem, and the solution is a straight line with slope 1/4 passing through the upper right corner of the box. Therefore, the answer is C.

Morris Has the Utility Function U(b, W)= 4b + 16w