Only individuals A and B live on a desert island where no production is possible.A is endowed with 12 units of good X and 18 units of good Y.B is endowed with 6 units of good X and 42 units of good Y.In the Edgeworth box,good X is measured on the horizontal axis.Individual A's utility function is U_A = 3XY so her MU_X = 3Y and her MU_Y = 3X.Individual B's utility function is UB = 10 so his and his MU_Y = 5 .Which of the following allocations are on the contract curve?

Question

Quizplus · Accepted Answer

To determine whether an allocation is on the contract curve, we need to make sure that neither A nor B has any incentive to further reallocate the goods.
For allocation A, A has 12 units of X and 24 units of Y, resulting in an MRS of 2. B has 6 units of X and 36 units of Y, resulting in an MRS of 7. Since A's MRS is less than B's MRS, A has an incentive to trade some of their Y for B's X, moving them towards allocation C. 
For allocation B, A has 10 units of X and 28 units of Y, resulting in an MRS of 14/3. B has 8 units of X and 32 units of Y, resulting in an MRS of 10/3. Since A's MRS is greater than B's MRS, B has an incentive to trade some of their Y for A's X, moving them towards allocation C.
For allocation C, A and B both have 9 units of X and 30 units of Y, resulting in equal MRSs of 3. Neither A nor B has any incentive to further reallocate the goods, so allocation C is on the contract curve.

Only Individuals a and B Live on a Desert Island