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Positive Mathematical Programming (PMP) has become a popular method for regional production models. The standard approach estimates cost (or production) functions for each land-use activity separately from each other. This means that the same crop grown under two technologies is treated as if it were two separate crops, which may lead to unsatisfying results, for example, if agri-environmental programs are modeled. We present an extended version of PMP that leads to more plausible results than the standard version in such cases. The extended method is applicable to other problems where differences in the elasticity of substitution between activities are important. Copyright 2003, Oxford University Press.

We consider resource management with recursive preferences. These generalize expected utility while eliminating some well-known difficulties. Monotonicity and convergence properties of optimal decision rules are established using lattice programming methods. Empirical applications are rangeland and groundwater management. Decreasing the intertemporal elasticity of substitution implies greater (lower) resource usage with limited (abundant) stocks. This moderates stock evolution and stabilizes consumption. Increasing risk aversion implies the same or reduced usage over the state space. Intertemporal substitution has a substantial effect on the optimal decision rule and a moderate effect on the limiting distribution, while risk aversion has a very small effect. Copyright 1996, Oxford University Press.

In this paper we seek to reconcile low farm-level substitution elasticity between nitrogen, fertilizer, and land, with larger industry-level values for the corn sector. This is accomplished with a micro-simulation model which identifies twenty-three heterogeneous groups of corn farmers based on survey data for Indiana. After controlling for soil quality, slope, crop rotation, and natural nitrogen sources, considerable variation in fertilizer application rates remains. Model simulations indicate that the estimated substitution elasticity at the state level (1.15) is consistent with very low farm-level substitutability. The difference is attributable to compositional changes in the wake of relative price shocks. These compositional effects are potentially very important but they are ignored in most policy analyses. Copyright 1996, Oxford University Press.

This paper analyzes the demand for labor, capital, and energy in the U.S. food‐manufacturing industry using Allen and Morishima elasticities of substitution. The demand for capital is more elastic than for labor and energy, and these production factors are substitutable, especially between capital and labor.

sequence of low market integration and low substitutability between domestic and imported foods. In addition, if the geographical area over which these multipliers are calculated increases, the share of nontradables in the economy rises and multipliers are correspondingly larger. This leads the authors to praise the potential for a demand-led approach to both agricultural and industrial development, anchored in productivity gains in traditional exports. While the general proposition is reminiscent of the development strategies advanced by Mellor (1986), Adelman (1984), and Hazell (1984), and by now well accepted, the quantification of multiplier effects is inadequate. The model used makes unrealistic assumptions that systematically bias upward the size of the growth linkages induced by technological change in farm or nonfarm tradables. Denoting by T = tradables, T, = farm tradables, NT = nontradables, E = elasticity of supply response, ,qM = elasticity of substitution in consumption between output (q) and imports (M), and m, = income multiplier of an extra $1 of income from farm tradables, the key assumptions made by the authors are T: E = 0, , qM= o; and NT: E = o, YqM = a value which does not matter as long as E = oo. This yields local m, between 1.3 and 1.8 reported in table 2 of the Delgado et al. paper. Consider now the more realistic characteriza

Perhaps no single area of recent inquiry has had greater impact on production economics than the duality results of Shepard, McFadden, and Uzawa. As Lau, Binswanger, and others have argued, these dual approaches (cost and profit functions) have substantial advantages over primal specifications (production functions plus equilibrium conditions). Although cost minimization is attractive for some problems, like measuring the elasticity of substitution, it seems sensible to view output as endogenous. Thus, one must "explain" output changesat least for proper estimation. This leads to profit maximization or some other explicit behavioral assumption. The profit function approach is used increasingly in agricultural economics (Lau and Yotopolous; Weaver; Yotopolous, Lau, Lin). Generally, this approach is applied without formal recognition of risk or risk-averse behavior. The purpose of this note is to illustrate the changes in expected profit given various models of risk. It shows that risk aversion biases the certainty results regarding factor demands and output supplies derived from the profit function. The qualitative and quantitative nature of these biases also are analyzed. These results should help researchers discern problems with the certainty approach and the possible consequences in agricultural applications where risk is present.

In a recent paper, Freebairn, Davis, and Edwards (hereafter FDE) have examined an interesting and neglected aspect of the distribution of benefits from research. Agricultural production is seen to comprise three stages: input supply, farm production, and farm to retail marketing. FDE have explored the distribution of the benefit stemming from a downwards shift in the supply function at any one of the stages. They conclude these benefits are distributed according to the elasticities of consumer demand and supply facing each stage. Furthermore, under the special assumptions they employ, this distribution is independent of which of the three supply functions is shifted by research. They conclude, albeit with due caution, that the choice of agricultural research projects should not be limited to farm production research alone, especially in view of the cost shares of purchased inputs and marketing services in the retail value of food. "In fact," they argue "they [farmers] may receive greater benefits from off-farm-oriented research than from farm-oriented research" (p. 39). This finding has potentially important implications for agricultural research policy. It immediately spurs one to ask whether research funded by the farmer or the fisc might have neglected opportunities for research related to farm inputs or marketing. To reach their result FDE assume (a) all supply and demand curves are linear, (b) research induces parallel shifts in supply curves, (c) farmers cannot substitute nonfarm inputs for inputs supplied by farmers in production of the farm product, and (d) marketing firms cannot substitute marketing inputs for raw farm products in the production of retail commodities. The purpose of this note is to emphasize the importance of these elasticities of factor substitution in determining the distribution of research benefits between the three stages. To do this we use a simple but general two-factor model in which we focus attention on the elasticity of factor substitution between marketing services and raw farm products in the third stage, marketing. This model is not restricted to linear supply and demand curves, nor to an elasticity of substitution of zero. We maintain the assumptions of parallel shifts of supply curves induced by research and a perfectly elastic supply of marketing services. In a revision of FDE's application to the U.S. hog industry, the distribution of research benefits is shown to depend crucially on the elasticity of factor substitution. Their result, that such distribution is independent of the stage in which research shifts the supply curve downwards, follows only for the special case in which that elasticity is zero. This is clearly a restrictive assumption. A reexamination of some of the policy issues raised by FDE, once the assumption is relaxed, would seem to be warranted.

The impact on consumers and input suppliers of allowing substitution between farm and nonfarm inputs in food processing is a controversial issue. Freebairn, Davis, and Edwards (1982) assumed that no substitution between these inputs was possible and concluded that the distribution of surplus gains between producers and consumers is independent of the source of supply shift. Alston and Scobie pointed out that this conclusion depends on the assumption of no input substitution. Once input substitution is possible, farmers can no longer be indifferent about the supply shift since their share of total surplus gains is greater for shifts in farm supply than for marketing input supply. Furthermore, as the degree of input substitution increases, the farmers' share of surplus gains from a downward shift in the supply of marketing inputs decreases. Freebairn, Davis, and Edwards (1983) replied that, "while we tend to agree with Alston and Scobie that the elasticity of substitution in the case of pork is likely to be nonzero, we doubt that it is very large, and at this stage no satisfactory estimate is available" (p. 357). In this study, we obtain a lower-bound estimate of the elasticity of substitution and show

This paper draws out the implications of equilibrium in a two-product, two-factor model for elasticity of product supply, which is found to depend upon input supply elasticities, alternative product demand elasticity, elasticity of substitution between production inputs, relative factor intensity of the product, and relative importance of the product in its use of resources. These factors interact in a complex manner to determine supply elasticity. The author discusses related approaches of Buse, Muth, and Powell and Gruen, and considers several simplified examples in an attempt to provide an intuitive grasp of the workings of the model.

A declining labor share in agriculture is consistent with an elasticity of substitution between labor and other factors greater than unity. Using cross-section data drawn from a small sample of Colombian crop farms, this study develops a three-factor model and estimates the Allen-Uzawa partial substitution elasticities between the factor-pairs land, labor, and farm machinery. Both Ordinary and Generalized Least Squares estimation procedures provide elasticity estimates that agree with each other and with the results of recent and related research: a substitution elasticity between labor and machinery (capital) of about one and a half is strongly indicated.

In a multistage production system, research that reduces production costs at one stage provides benefits to producers at all stages and to consumers. Agricultural production is assumed to involve three stages: nonfarm input, farm, and marketing. Research causes a parallel drop of the supply curve. Benefits are measured as changes in economic surplus. With a competitive model, the distribution of research benefits is the same for research directed at each production stage. Implications for the distribution of research benefits of some forms of imperfect competition are investigated.

T HE OBJECTIVE of this paper is to present a production function with variable returns to scale over the range of the function. A modified form of the Cobb-Douglas function is developed for this purpose. Data from a sample of farms are used to estimate the parameters of the modified function utilizing single-stage least-squares estimation. The empirical results are presented and some implications of the estimated elasticities of production are discussed. Many attempts have been made in the past to find algebraic forms that are theoretically appropriate and empirically useful for describing and estimating the functional relationships between inputs and outputs [7]. Each alternative functional form has advantages, but each usually imposes certain limitations on the input-output relationship. The conventional Cobb-Douglas function, for example, assumes unitary elasticity of factor substitution and partial and total production elasticities that do not vary over ,the range of the function. Recent efforts to develop more general forms of production functions have focused almost exclusively on the elasticity of factor substitution. Examples of such efforts include the constant elasticity of substitution function [1], the class of homothetic isoquant production functions [2], transcendental production functions [5], and the variable elasticity of substitution production function [6]. These new functional forms elevate the elas