Note that just monotonic transformation of a concave function isnot necessarily concave: consider, for example f (x) = x and g (z) = z 3 .Thus the concavity of a function is not ordinal, it is cardinal property.Economic ExampleSuppose production function f (x) is concave and the cost function c (x) is convex.ote that just monotonic transformation of a concave function isnot necessarily concave: consider, for example f (x) = x and g (z) = z 3 .Thus the concavity of a function is not ordinal, it is cardinal property.Economic ExampleSuppose production function f (x) is concave and the cost function c (x) is convex.