Supply functions in the ubiquitous Gorman class are examined for their homogeneity properties. Homogeneity places surprisingly strong restrictions on functional forms. These forms facilitate testing of aggregability given homogeneity or homogeneity given aggregability or testing both.

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.

Gorman’s theory of demand is extended comprehensively to incomplete systems. The incomplete systems approach 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 up and 0º homogeneity determines the functional form and there is no functional form restriction for an incomplete system. We prove that every full rank system and reduced rank systems with a minimal level of degeneracy can be written as a polynomial in a single function of income. A complete set of closed form solutions for the indirect objective functions of this class of models is derived. A simple method to nest rank and functional form for incomplete systems is presented.

Gorman Engel curves are extended to incomplete systems. The roles of Slutsky symmetry and homogeneity/adding up are 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 reduced rank Gorman system has a representation as a polynomial in a single function of income. This generates a complete taxonomy of indirect preferences for Gorman systems. Using this taxonomy, we develop models of incomplete Gorman systems that nest rank and functional form and satisfy global regularity conditions. All results are completely derived with elementary and straightforward methods that should be of wide interest.

A structural inter-temporal model of agricultural asset arbitrage equilibrium is developed and applied to agriculture in the North-Central region of the U.S. The data is consistent with unifying level of risk aversion. The levels of risk aversion are more plausible than previous estimates for agriculture. However, the standard arbitrage equilibrium is rejected; perhaps this is due to the period and the shortness of the period studied.