Uniqueness of Positive Fixed Points for Increasing Concave Functions on : 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 ⁿ to ⁿ satisfying these properties has a unique positive fixed point. Journal of Economic Literature Classification Number: C62.