14.8
In the Edgeworth Box diagram, any reallocation within this region can improve both individuals' utilities. However, the Pareto-efficient allocation occurs at points where the indifference curves of Taylor and Alex are tangent to each other.
At the points where the curves are tangent, Taylor's marginal rate of substitution (MRS) equals Alex's MRS. This ensures that both individuals maximize their utilities, given the allocation of resources.
This condition is crucial because it reflects exchange efficiency. If the MRS for one individual differs from the other's, there is still potential for mutually beneficial trade.
For instance, if Taylor’s MRS of oranges for apples is higher than Alex’s MRS at a particular allocation, it means Taylor is willing to give up more oranges to obtain one additional apple compared to Alex's.
In this scenario, Taylor might trade some of their oranges for more apples. Meanwhile, Alex, whose MRS of oranges for apples is lower, values oranges more relative to apples and might happily agree to the trade.
The exchange continues until their MRS equalizes, indicating that both have maximized their utilities and reached Pareto efficiency.
交换效率发生在两个人无差异曲线的切点处。在这一点,两个人的边际替代率(MRS)是相等的。边际替代率衡量的是一个人在保持效用水平不变的情况下愿意放弃多少其中的一种商品来换取另一种商品。当边际替代率相等时,任何一个人都无法在不降低对方满意度的情况下进一步提高自己的满意度。
例如,以泰勒和摩根两个人为例,…