Allocatable fixed inputs, such as land, are a potentially important source of jointness in agriculture. As with other causes of jointness, they necessitate multiple‐product systems for modeling product supply and input demand. In other important ways, however, their analytical implications are very different from other causes of jointness. Model specification differs. Demand functions for the quantities of each input used in the production of individual commodities can be derived if a primal approach is used, but such allocation equations cannot in general be identified from a dual specification. Available allocation data are not even useful in such dual estimations.

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We are indebted to Lynne for a thought-provoking comment. He has made the following main points: (a) As traditionally represented, jointness exists only with nonallocatable inputs and is synonymous with technical interdependence.(b) Equidistant isoresource (or isocost) curves imply traditional nonjointness.(c) Separability of costs among outputs means that production is technically independent and inputs are allocatable.(d) Separability of the profit function in output prices does not imply separability of the cost function in output quantities.(e) We mistakenly assumed away the allocatable, fixed input case in our "jointness in supply" tests by using separability conditions [our equations (6a)-(6b)] from the unrestricted profit function [our (5)].(j) Additional terminology is needed to distinguish between "jointness in technology" due to technical interdependence and "jointness in supply" due to allocating fixed inputs.We will respond to these points in order. Our conclusion, however, remains that the traditionally cited tests (as well as the one proposed by Lynne) are ambiguous on the issue of which type of jointness exists. We close with some comments about procedures that could indicate jointness type from the data. Traditional Jointness DefinitionsWe thank Lynne for his comments on the various definitions of nonjointness. A rereading of Carlson documents that he is correct in his interpretation of the single-variable input [x in our (3) and Xl in his (1)] as total input quantity. We erred in regarding it as just the input allocation to output Yt-Contrary to our assertion, the Lau (1972) definition of nonjointness in inputs [our (1)] does imply the Carlson definition [our (3)] with this interpretation and common regularity assumptions on each production function. Lynne is further correct that Carlson con-C. Richard sidered only the case of nonallocatable inputs in discussing jointness.However, the two traditional "jointness in technology" definitions cited by Lynne are not fully consistent even for a single-variable input. While Lau nonjointness implies Carlson nonjointness, the reverse is not implied. For example, consider the case where Y2 is technically independent of Yl but the quantity of Y2 results in horizontally parallel shifts in the total productivity curve (production function) for Yl. 1The production function for Yl in (22) clearly violates Lau nonjointness (because it cannot be written as a function only of inputs allocated to its production), but it does not violate Carlson nonjointness [our (3)] since X in (24) is additive in Y1 and Y2' Thus, one may choose one of these definitions for nonjointness but not both.Lynne is further correct that we erred in applying the Carlson definition to the allocation of an input [see our equations (8}-(l3)]. However, since X 2 is constant in our example and X is the sum of X 1 and X 2 , our (13) is the same regardless of whether the cross partial derivative is taken for Xl or x.Like Lynne, we have also struggled to seek a meaningful interpretation of the trad...