ZELLNER, KMENTA, AND DRfEZE in a recent article [3] specified for the firm a Cobb-Douglas production model in which the traditional profit maximization assumption was modified to explicitly recognize the stochastic nature of profits. Assuming that firms maximize the mathematical expectation of profits, the authors found that under conditions of pure competition least squares estimation of the production function from cross section data on firms' output and inputs provides consistent estimates of the production function parameters if certain reasonable specifying assumptions are satisfied. Since considerable attention has recently turned to the more general CES production function, the purpose of this note is to point out that use of the Zellner, Kmenta, and Dreze framework with a CES production function will also result in a model which permits consistent estimation of the production function parameters from single equation estimation of the production function relation itself. Section 1 below is devoted to demonstration of this conclusion. In addition, in Section 2 attention is turned to specification and estimation of a related model for a firm operating as a pure monopolist.