| 单词 | concavity |
| 释义 | concavity A property of a function whereby if it is evaluated at three points, where a < b < c, its value at b is never less than, and may exceed, the appropriate weighted average of its values at a and c. If y = f(x), y is concave if f(b) ≥ [(b - a) f(a) + (c - b) f(c)]/(c - a), and it is strictly concave if f(b) > [(b - a) f(a) + (c - b) f(c)]/(c - a). A decreasing marginal utility function is thus concave, and a person with such a utility function is risk-averse. The horizontal axis shows consumption; the vertical axis shows total utility. U(C1) > [(C1 - C0 )/(C2 - C0 )] U (C0 ) + [(C2 - C1 )/(C2 - C0 )] U (C2 ). ABD shows the utility function. AED shows the straight line connecting A and D. If the utility function is strictly concave, B lies above E. If the utility function is weakly concave, B lies at or above E. |
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