Point Estimates of Ordinates of Concave Functions

A method is developed for obtaining maximum likelihood estimates of points on a surface of unspecified algebraic form when ordinates of the points are required to satisfy a set of linear inequalities. A production function with one variable input is considered in some detail. In this case the restrictions follow from the assumption of non-increasing returns. An illustrative computation is worked out using a procedure based on equivalence between the estimation problem and a certain saddle point problem. Alternative procedures for production functions with two variable inputs are sketched.