This monograph is intended as a contribution to applied work in production theory by treating: a) The measurement problems involved whenever several outputs are jointly produced, and b) The (possible) econometric framework for estimating production function parameters whenever (relative) prices vary sufficiently over the observations. Thus, the "pure" theory of production, and the theory of non-linear regression is not treated in sufficient detail: for these topics we refer to the available literature~ for a comprehensive list of references we refer to Uebe (1975). Some years ago, papers by L. J. Lau and W. E. Diewert initiated my interest in duality within production theory, and then I started to appreciate R. W. Shephard's fundamental contribution to this topic. This monograph is a (minor) revision of a Ph. D. dissertation submitted to the Department of Economics, The University of Wisconsin, Madison, in August 1973. The Graduate School and the Social Systems Research Institute provided funds for the reported computer work, Lawrence R. Klein and Laurits R. Christensen provided data, and as a Graduate Student I received financial support in form of an University Fellowship~ all this is very much appreciated. With some nostalgia I think back to the enjoyable period of learning during the preparation of my diFosertation~ I appreciate the spirit within the department, and the guidance of my committee Arthur S. Goldberger, Dennis J. Aigner, and Laurits R. Christensen.