Jeffrey T. LaFrance

Fat Taxes: Big Money for Small Change

In an attempt to improve the nations health, many U.S. policy makers have or are considering imposing taxes on the fat in food. Dairy products constitute a large portion of at home fat consumption of particularly harmful types of fat, and nearly all U.S. households consume these products. We estimate a demand system for dairy products, which we use to simulate substitution effects among dairy products and the welfare impacts of fat taxes on various consumer groups. We find that even a 10 percent ad valorem tax on the percentage of fat would reduce fat consumption by less than a percentage point. Given that the demand for most dairy products is inelastic, a fat tax is an effective means to raise revenue. However, these fat taxes are unattractive because they are extremely regressive, and the elderly and poor suffer much greater welfare losses from the taxes than do younger and richer consumers.

The Dual Structure of Incomplete Demand Systems

Integrability of incomplete demand systems is discussed. The concepts of weak integrability, quasi-expenditure function, quasi-indirect utility function, and quasi-utility function are defined. Their relationships to the expenditure function, indirect utility function, and utility function are developed. The dual structure of the quasi-functions permits exact welfare analysis and reveals the conditional preference structure for the commodities of interest. New results relating the uniqueness and exactness of consumers surplus to the structure of the expenditure and indirect utility functions are obtained.

Linear demand functions in theory and practice

Abstract 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.

An Econometric Model of Cattle Inventories

Dynamic regression equations are estimated for each beef cattle breeding herd and beef cattle inventories at two levels of aggregation, the U.S. and Montana. The analysis for Montana was utilized as a guide for specification of the national equation to reduce the inference problem associated with letting the sample data help specify the model. Rational lags on average price received by farmers for calves and the ratio of fed beef to corn prices at Omaha constitute the primary explanatory variables. The equations perform exceedingly well over the sample period (1950–80) and in post-sample forecasts with the sample truncated back to 1970.

The envelope theorem in dynamic optimization

Abstract The dynamic envelope theorem is presented for optimal control problems with nondifferential constraints. Some of these constraints may switch from binding to nonbinding, or vice versa, along the optimal path. Twice continuous differentiability of the optimal performance function and intertemporal symmetry and reciprocity conditions are shown to follow from the envelope theorem and twice continuous differentiability of the integrand, state equations, and constraints. Conditions implying convexity or concavity of the optimal performance function in the parameters are derived. Dynamic versions of Hotellings Lemma, Roys Identity, and the Slutsky equation are presented for an intertemporal consumption problem.

Regulation in a Dynamic Market: The U.S. Dairy Industry

An econometric model of the U.S. dairy market is estimated for the period 1950–80. The economic costs of the dairy program for the period 1965–80 are calculated using ex ante, ex post, and long-run demand and supply functions. Results indicate that the costs of the dairy program averaged from 430 to 590 million 1980dollars per year, depending upon the choice of economic surplus measure. The cost estimates depend only slightly on the year that the dairy program is assumed to have been terminated.

The Structure of Constant Elasticity Demand Models

The demand model with constant price and income elasticities has been used extensively in applied agricultural economics. This paper analyzes the structure of incomplete systems of constant elasticity demand functions. It is demonstrated that there is a duality theory for incomplete demand systems that is analogous to the duality theory for complete systems. This theory permits the recovery of that portion of the direct and indirect preferences pertaining to the goods of interest, and we can calculate exact welfare measures for changes in income and in the prices of these goods. For an incomplete system of constant elasticity demands, the Slutsky symmetry restrictions for integrability are presented and the implied structure of the direct and indirect preferences with respect to the prices and goods of interest is derived.

Weak Separability in Applied Welfare Analysis

The focus of this paper is the impact on welfare measurement of a common assumption in applied demand analysis, weak separability. A standard empirical practice is to estimate conditional demand models for a set of goods which are assumed to be weakly separable from all other goods with expenditure as a right-hand-side variable, tacitly assuming that expenditure is predetermined (Alston and Chalfant 1987, 1991; Alston, Carter, Green, and Pick; Blackorby, Boyce, and Russell; Blisard and Blaylock; Brown and Heien; Cashin; Choi and Sosin; Clements and E. Selvanathan; Clements and S. Selvana-than; Deaton 1975; Goddard and Amuah; Gould, Cox, and Perali 1990, 1991; Heien; Heien and Pompelli 1988, 1989; Murray; Safyurtlu, John-son, and Hassan; Theil 1976, 1980; Van Ko-oten; Yen and Chern). Once estimated, such separable demand models often are used to cal-culate exact welfare measures, or changes in the true cost of living index, of the economic effects on consumers due to changes in the prices of the goods under study (Heien; Heien and Pom-pelli 1989; Van Kooten; Blisard and Blaylock). This practice is shown here to produce biased results. There are two sources of the bias and both can be traced to the inappropriate treatment of expenditure as predetermined. In an empiri-cal application to the U.S. dairy program, a comparison of estimates from an incomplete demand system specification versus a weakly separable specification suggests a negative bias of around 17% of the compensating variation due to eliminating price discrimination in federal milk marketing orders in 1990. Results from a Monte Carlo simulation suggest that the downward bias is closer to 40%. I first present the analysis of weak separability, then the empirical application, and a summary and conclusions.

Information theoretic measures of the income distribution in food demand

A new method to nest, estimate and test the rank and functional form of the income terms in an incomplete system of demand equations is developed. Information theory is employed to infer the U.S. income distribution from data on quintile and top five percentile income ranges and intra-quintile and top five percentile mean incomes. Maximum entropy income distributions are combined with data on the U.S. demand for 21 food items to estimate U.S. food demand over the period 1919–1995, excluding 1942–1946.

Inferring the Nutrient Content of Food With Prior Information

Given measurements on the nutrient content of the U.S. food supply and a coherent reduced form empirical model of the demand for foods, we can analyze the effect of agricultural farm and food policy on nutrition. Using unpublished documents from the HNIS, estimates of the percentages of seventeen nutrients supplied by twenty-one foods were compiled for the period 1952-1983. The Bayesian Method of Moments is applied to this data set to obtain a proper prior for the purpose of drawing year-to-year inferences about the nutrient content of the U.S. food supply for the period 1909-1994. Information theory and the Kullback-Leibler cross entropy criterion are used to formalize the inference problem.