数学附录 15二元凹函数和拟凹函数的判别: Assume that f( x,y is defined on a convex set X and fis C2. Then f is concave if f <0 and f XXy -(fx)2>0 A necessary and sufficient condition for a function f defined on a convex set crn to be quasi-concave is that all the superior sets s(y) are convex; f is strictly quasi-concave if all the superior sets s(y) are convex, and for any two points xand x in any superior set S(y), the points on the line segment x=(1-mx+x: nEIO, I expect possibly the two endpoints are all contained in Int(s(y))数学附录 • 15 二元凹函数和拟凹函数的判别： • Assume that f(x,y) is defined on a convex set X and f is C2 . Then f is concave if f xx < 0 and f xx fyy –(f xy ) 2 > 0. • A necessary and sufficient condition for a function f defined on a convex set Xn to be quasi-concave is that all the superior sets S(y) are convex; f is strictly quasi-concave if all the superior sets S(y) are convex, and for any two points x’ and x” in any superior set S(y), the points on the line segment {x=(1-)x’+x”: [0, 1]} expect possibly the two endpoints are all contained in Int(S(y))