Partial Production Functions and the Analysis of Farm-Firm Costs and Efficiency*

"Partial production functions " relating output to part of, rather than the entire array of, inputs employed are quite common in the production analysis of the biological subprocess in the farm-firm. This article attempts to outline the framework within which this approach is reconcilable with the accepted theory of the firm. It also traces the derivation of the various cost functions from a set of partial production functions which, under certain conditions, may replace the single comprehensive one. An empirical example demonstrates the usefulness of this approach in relating cost variations to factor intensities or economics of scale which characterize a sub-process rather than the process of production as a whole. XONCE PT of a single production function re-lating the firm's output to the entire ar-ray of inputs it employs underlies the analysis of costs and efficiency within the frame-work of the conventional theory of the firm in its simplest form. Following this concept, the estimation of an empirical production function plays a major role in numerous studies con-cerned with various aspects of costs and effici-ency in various groups of farm-firms. Yet, a con-siderable number of these studies are directed to the estimation of a functional relationship, known as the "biological function " [5], which relates the output of a farm product to a limited rather than the entire array of inputs employed by the farm-firm. Focusing on these "biologi-cal " inputs, and deliberately overlooking other inputs, these studies were concerned with a partial relationship which may be looked upon as a "partial production function." Contemplating the possible modifications in the conventional theory, which implicitly underlie the empirical studies of the biological function, we arrive at the model of a hypothet-ical farm-firm outlined in the first part of this article. This model consists of a set of partial production functions, each of which character-izes a distinct part or subprocess in the process of production. The set, as a whole, addresses it-self to the entire array of farm inputs and thus allows for the derivation of the farm-firm total costs schedules. The second part of this article • Acknowledgment is gratefully given to Gad Bental, formerly a graduate student at Rehovot, now an economi