An econometric model of annual per capita U.S. food and nutrition demand is developed. The model is a flexible, full rank two Gorman polar form. It is strictly aggregable across income, demographic variables, and variations in micro preference parameters. Parametric conditions for global quasi-concavity of the (quasi-)utility function are derived. The model is implemented with annual time series data on U.S. per capita food consumption for the sample period 1918-1994. A battery of new test statistics are developed for and applied to the following hypotheses: (1) strict exogeneity of income or total expenditures; (2) global symmetry and negative semidefiniteness of the Slutsky substitution matrix; (3) parameter stability in a multivariate, nonlinear regression model based on within sample residuals; and (4) weak separability of food items from all other goods in the representative consumer's preference function. The empirical results are very encouraging with respect to the strictures of economic theory, heretofore a virtually unheard of outcome. The model is used to analyze the food and nutrient consumption and consumer welfare impacts of the U.S. dairy program.

Theil's theory of rational random errors is sufficient for strict exogeneity of group expenditure in separable demand models. Generalized rational random errors is necessary and sufficient for strict exogeneity of group expenditure. A simple, robust, asymptotically normal t-test of this hypothesis is derived based on the generalized method of moments. An application to per capita annual U.S. food demand in the 20th century strongly rejects exogeneity of food expenditure in a model that in all other respects is highly compatible with the data set and with the implications of economic theory.

A flexible, full rank two model of food consumption that is globally consistent with economic theory, aggregates across income, demographic variables, and variations in micro demand parameters, and accommodates tradeoffs between tastes and nutrition is derived. The econometric demand model is estimated with per capita U.S. consumption of 21 foods on the time period 1919-1994, excluding the World War II years 1942-1946. An approach for inferring the percentage of nutrients available from individual commodities in the U.S. food supply is derived and implemented empirically on the time period 1949-1995 for the nutrients energy, protein, total fat, carbohydrates, and cholesterol. The two sets of model results are combined to generate time paths for income and Hicksian compensated price elasticities of demand for individual foods and macronutrients.

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.

A great deal of research on farm and food policy and consumer choice focuses on the link between food consumption and nutrition. This paper presents and applies a new method to analyze the demand for food and nutrients, and consumer welfare. The foundation for this method is the recent extension of the Gorman class of exactly aggregable demand models to incomplete demand systems. The purposes of this approach are to derive and implement coherent, flexible empirical models of food and nutrient demand, to estimate the model parameters consistently with aggregate data, and to make inferences on the impacts of farm and food policy changes on food and nutrient demand and consumer welfare of those policies. We apply this framework to annual per capita U.S. demand for food and nutrients 1919–-2000, excluding 1942-1946 to account for World War II. The empirical model is an incomplete system of Gorman Engel curves that is nonlinear in income. This class of demand models generates theoretically consistent, exactly aggregable systems of demand equations for which only a small number of summary statistics for the distribution of income are required to estimate the model’s parameters consistently using aggregate data. This model is estimated with 0° homogeneity, monotonicity, symmetry, and a negative semidefinite Slutsky matrix imposed globally, so that the results can be used directly for economic analyses. A complete time series of price and income elasticities of food and nutrient demand are obtained for the sample period.

Diminishing marginal utility(DMU)is neither necessary nor sufficient for downward sloping demand. Yet upper-division undergraduate and beginning graduate students often presume otherwise. This paper provides two simple counter examples that can be used to help students understand that the Law of Demand does not depend on diminishing marginal utility. The examples are accompanied with the geometry and basic mathematics of the utility functions and the implied ordinary/Marshallian demands.