The Law of Demand versus Diminishing Marginal Utility

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 DMU. The examples are accompanied with the geometry and basic mathematics of the utility functions and the implied ordinary/Marshallian demands.     

INCOMPLETE DEMAND SYSTEMS AND SEMILOGARITHMIC DEMAND MODELS

The methodology of LaFrance and Hanemann for analysing the structure of incomplete demand systems is applied to models that are linear or logarithmic in quantities, prices and/or income. The structure of each model is presented when the implications of consumer choice theory are satisfied. The usefulness of the approach is illustrated. It is shown that considerable prior information is obtained from the theory of consumer choice when it is applied to this set of functional forms for demand equations.     

Agricultural arbitrage and risk preferences

A structural intertemporal model of agricultural asset arbitrage equilibrium is developed and applied to agriculture in the North Central region of the US. The data are consistent with a 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.     

DO INCREASED COMMODITY PRICES LEAD TO MORE OR LESS SOIL DEGRADATION?

In this paper, a dynamic economic model is used to analyze the conflicting impacts of crop increasing/land degrading inputs with those of soil conserving/crop reducing inputs in problems of soil degradation in agriculture. Soil is a renewable resource that is generated naturally at a slow, essentially autonomous rate. Cultivation enhances crop production and degrades the soil, while conservation is unproductive for the crop but improves the soil resource. If the effects of cultivation dominate the effects of conservation in the soil dynamics, an increase in the price of the crop accelerates the rate of soil degradation In the short-run and decreases the long-run stock of the soil resource. On the other hand, if the effects of conservation dominate the effects of cultivation, an increase in the price of the crop decelerates the rate of soil degradation in the short run and increases the long-run stock of the soil resource. It is shown that subsidies on conservation activities or taxes on cultivation intensity may well decrease the long-run soil stock, although strong conditions must be satisfied for either of these results to hold. It also is shown that a reduction in the real discount rate or a direct per unit tax on soil losses is certain to increase the long-run soil stock and reduce the short-run rate of soil degradation.     

Imperfect Price Deflation in Production Systems

Numéraire prices that are measured with error create challenges for econometric estimation. A straightforward approach for a model with linear input demands, such as generated from a quadratic normalized profit function, is proposed where the numéraire price is measured with error. Numéraire measurement error is likely because expected output price is measured imperfectly by actual output price. An approach using generalized method of moments is developed to estimate such errors-in-variables (EIV) systems that avoids use of extra-sample data or additional structural specifications. Monte Carlo examination of small sample properties shows promise. Measurement error is statistically significant using aggregate U.S. agricultural data.     

The structure of US food demand

An exactly aggregable system of Gorman Engel curves for US food consumption is developed and implemented. Box-Cox transformations on prices and income nest functional form. The model nests rank up to rank three. The model is estimated by nonlinear three-stage least squares with annual time series data on 21 foods, 17 nutrients, age and race demographics, and the distribution of income for 1919–1941 and 1947–2000. Results are consistent with full rank three. Point estimates for the Box-Cox parameters on income and prices are 0.86 and 1.09, respectively, strongly rejecting zero and one in both cases. No statistical evidence of serial correlation, specification errors, or parameter instability is found.     

Homogeneity and Supply

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.     

Linear demand functions in theory and practice

Integrability conditions for an incomplete system of linear demand functions are considered. The parameter restrictions consistent with integrability are identified, and the structure of the conditional preference map is obtained. It is found that the conditional preferences for a set of linear demand functions are either quadratic or Leontief from a translated origin. Welfare analysis with linear demand models is also considered.