Kens utility function is U(Q K, W K)= Q K W K and Barbies utility function is U(Q B, W B)= Q B W B.If Kens initial endowment were 5 units of quiche and 7 units of wine and Barbies endowment were 10 units of quiche and 7 units of wine and Barbie's endowment were 10 units of quiche and 7 units of wine, then at any Pareto optimal allocation where both persons consumed some of each good,
A)Ken would consume 15 units of quiche for every 14 units of wine that he consumed.
B)Barbie would consume 10 units of quiche for every 7 units of wine that she consumed.
C)Ken would consume 5 units of quiche for every 7 units of wine that he consumed.
D)Barbie would consume twice as much quiche as Ken.
E)None of the above.

Question

Quizplus · Accepted Answer

The correct answer is A because at any Pareto optimal allocation, the marginal rate of substitution (MRS) for both individuals must be equal. The MRS is the rate at which a person is willing to trade one good for another while keeping their utility constant. For Ken, the MRS is MRS = MUQ/MUW = Q/W, and for Barbie, the MRS is MRS = MUQ/MUW = Q/W. Since the MRS must be equal for both individuals at a Pareto optimal allocation, we have Q/W = Q/W, which implies that Ken and Barbie will consume quiche and wine in the same proportion. In this case, Ken's initial endowment is 5 units of quiche and 7 units of wine, so he will consume 15 units of quiche for every 14 units of wine that he consumes.

Kens Utility Function Is U(Q K, W K)= Q K