Uniqueness of positive fixed points for increasing concave functions on Rn:: An elementary result

The square root function has a unique positive fixed point. This function has the following properties: it is strictly increasing and strictly concave, with f (0) = 0, and there are points a > 0 and b > 0 such that f (a) > a and f (b) < b. It is shown that any function from R-n to R-n satisfying these properties has a unique positive fixed point. Journal of Economic Literature Classification Number: C62. (C) 2001 Academic Press.