| 单词 | convexity |
| 释义 | convexity A property of sets whereby if any two points are members of a set, any convex linear combination of them is also a member. If points with coordinates shown by (a1, a2, a3,…,aN) and (b1, b2, b3,…,bN ) are members of a convex set, any linear combination (c1, c2, c3,…,cN ), where ci = λaI + (1 - λ)bi for all i, 0 < λ < 1, is also a member of the set. For example, if a and b are sets of goods which can be produced in an economy with constant returns to scale technology in all industries, then c can also be produced, using λ of all resources in the proportions used to produce a, and (1 - λ) of all resources in the proportions used to produce b. The country's production possibility frontier thus encloses a convex set. The horizontal axis represents good X, the vertical axis good Y. ABCD in Panel 1 is a convex set: every linear combination of any two members of the set is also a member of it. EFGH in Panel 2 is not a convex set: points in the triangle FGH can be expressed as linear combinations of members of the set, but are not themselves members of it. |
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