During the twenty years or so since some early estimations of production functions in agriculture there has been considerable discussion of many of the technical problems associated with such estimation. Although the simultaneous nature of production decisions, leading to the determination of input levels in the production function, was pointed out early in the piece by Marschak and Andrews, little attention has been paid to this aspect of the problem until comparatively recently. The only systematic treatment of these problems is that of Hoch, although there appeared recently in the Economic Record an extended controversy between Konijn and Soper. The purpose of the present paper is to demonstrate that when the profit maximisation conditions are cast in a slightly different form, Hoch's conclusions concerning the existence of simultaneous equations bias cannot be sustained, although there is similarity of assumptions throughout. The treatment initially will be in terms of farms producing a single output. However, the examination of the simultaneous equation problem will be extended to the multiple output case where it will be shown that problems of an entirely different nature arise. The Cobb-Douglas form of production function will be adhered to throughout.