Ken's utility function is U(Q_K, W_K)= Q_KW_K and Barbie's utility function is U(Q_B, W_B)= Q_BW_B.If Ken's initial endowment were 4 units of quiche and 10 units of wine and Barbie's endowment were 8 units of quiche and 10 units of wine, then at any Pareto optimal allocation where both persons consume some of each good, A)Ken would consume 4 units of quiche for every 10 units of wine. B)Ken would consume 12 units of quiche for every 20 units of wine that he consumes. C)Barbie would consume 8 units of quiche for every 10 units of wine that she consumes. D)Barbie would consume twice as much quiche as Ken. E)None of the above.

Question

Quizplus · Accepted Answer

In a Pareto optimal allocation, the MRS of both individuals will be equal. For Ken, MRS = MUqs/MUws = Q_K/W_K For Barbie, MRS = MUqs/MUws = Q_B/W_B At the optimal allocation, both MRS values will be equal and hence we have: Q_K/W_K = Q_B/W_B Simplifying it gives: Q_K/Q_B = W_K/W_B This implies that Ken and Barbie will consume the goods in the ratio of their marginal utilities. Using Ken's utility function: MUqs/MUws = Q_K/W_K We know that Ken's endowment is 4 units of quiche and 10 units of wine. Hence, MUqs/MUws = Q_K/W_K = MUqs(4)/MUws(10) Similarly, using Barbie's utility function, her ratio of consumption will be: MUqs/MUws = Q_B/W_B = MUqs(8)/MUws(10) Equating both ratios gives us: MUqs(4)/MUws(10) = MUqs(8)/MUws(10) Simplifying this equation gives us MUqs(4) = MUqs(8), which implies that Ken and Barbie would consume quiche in the same ratio as their endowments, which is 4:8 or 1:2. Therefore, for every 20 units of wine, Ken would consume 12 units of quiche, which gives us choice (B) as the correct answer.

Ken's Utility Function Is U(QK, WK)= QKWK and Barbie's Utility

Ken's Utility Function Is U(Q_K, W_K)= Q_KW_K and Barbie's Utility