Cobb-Douglas production functions estimated by least-squares methods have been widely applied in agriculture. Estimates based on cross-sectional samples of farms, as most studies have been, almost typically result in some elasticities for land and labor which are negative. These negative coefficients, which are meaningless, can arise for several reasons. One is the prevalence of multicollinearity in random or unstratified farm samples where farmers with large labor inputs also are those with larger inputs of land and various forms of capital. (A farm sample stratified by the various input categories and magnitudes much in the manner of a factoral, central composite or other experimental designs to estimate the physical production surface, would not encounter this problem to the extent of the typical farm survey.) Another reason is reporting or measuring bias. For example, regardless of whether he actually does so, a farmer generally will report that he works twelve months per year; he is unlikely to concede that he is idle part of the time. Finally, other inadequacies of data also pose the potential of negative labor elasticities in CobbDouglas functions and are hard to explain under existing knowledge. These negative coefficients confuse the analysis and leave the researcher more or less empty-handed. Among others obtaining these results, Sahota simply considered his results absurd and Srivastava and Nagadevara could not attempt to explain theirs. The production function analysis conducted by Agrawal and Foreman, and Suryanarayana also resulted in negative elasticities for labor and capital services. Heady and Dillon and, recently, Doll have proposed reasons for the prevalence of negative elasticities. We attempt to resolve the problem of negative elasticities with a Bayesian model incorporating relevant prior restrictions.