We extend the set of full rank nominal and deflated income demand systems to rational demand systems of any rank and … present a unifying expression for the indirect preferences of all full rank demand models. …

dramatically increases this class of models. The separate roles of symmetry and adding up are identified in the rank and the … functional form of this class of models. We show that symmetry determines rank and the maximum rank is three. We show that adding … system. We prove that every full rank system and reduced rank systems with a minimal level of degeneracy can be written as a …

isolated in the rank and functional form restrictions for Gorman systems. Symmetry determines the rank condition. The maximum … rank is three for incomplete and complete systems. Homogeneity/adding up determines the functional form restrictions in … complete systems. There is no restriction on functional form in an incomplete system. Every full rank and minimal deficit …

Agricultural production is subject to supply risk. Expected and realized farm outputs and output prices are unknown and … decisions of owner/operators who face output and output price risk, and who have opportunities to invest in a conditionally risk …, investment, and consumption under risk. We apply this model at the national-level to crop and livestock production for the years …

physical highway assets or system usage only under certainty or risk, this research focuses on the management of an entire … certainty, risk, or uncertainty, the software outputs match with the results of actual highway programming at least 85 percent …

stocks. The analysis leads to the conclusion that the risk entailed in stock investment is reduced relative to the yield as …