Dan and Marilyn consume two goods, x and y.They have identical Cobb-Douglas utility functions.Initially Dan owns 10 units of x and 10 units of y.Initially Marilyn owns 40 units of x and 20 units of y.They make exchanges to reach a Pareto optimal allocation which is better for both than the no-trade allocation.Which of the following is not necessarily true about the allocation they trade to?
A)Marilyn consumes 5 units of x for every 3 units of y that she consumes.
B)The locus of Pareto optimal allocations is a diagonal straight line in the Edgeworth box.
C)Dan's consumption of x is greater than his consumption of y.
D)Dan consumes more than 10 units of x.
E)Marilyn consumes at least 40 units of x.

Question

Quizplus · Accepted Answer

In a Pareto optimal allocation with Cobb-Douglas utility functions, the consumption bundles depend on the marginal rates of substitution being equalized between the two parties, not on their initial endowments. Marilyn consuming at least 40 units of x is not guaranteed because trade could lead to her ending up with less than her initial endowment of x in exchange for a more preferred bundle of goods.

Dan and Marilyn Consume Two Goods, X and Y