DEVELOPMENT OF AN OPTIMAL WATER ALLOCATION DECISION TOOL FOR THE MAJOR CROPS DURING THE WATER DEFICIT PERIOD IN THE SOUTHEAST UNITED STATES

ABSTRACT. We developed a dynamic economic model to optimize irrigation water allocations during water deficit periods for three major crops grown in the humid southeastern United States. Analysis involved the use of crop simulation models to capture (a) the yield water relationship and (b) soil moisture dynamics from one week to another week. A hy‐drological model was used to find the water supply; combinations of hydrological and simulation models were used to find the optimal water allocation during each week in corn, cotton and peanuts. Results indicated that farmers should irrigate the most valuable crop first (peanuts) before applying water to other crops (corn and cotton). Results also showed that, because of restriction on total water supply, an increase in crop acreage did not increase the net revenue of the farm in a proportionate amount. Results should provide guidelines to water managers, engineers, policy makers, and farmers regarding an optimal amount of water allocation that will maximize net returns when water shortage is a serious concern.     

有关判断决策单元的DEA有效性的新方法的探讨

为了判断决策单元是否(弱)DEA有效并克服现有的模型及[1]中模型在解决上述问题时的不足之处,本文将讨论的新模型是由CCR模型与CCGSS模型变来的,且定理的证明不同于[1]．还讨论了文中新模型的最优解的存在性,此外,研究了所有决策单元的输入输出的变化对某决策单元有效性的影响．     

风险资产的最优保险

本文采用期望方差方法，引入无风险投资；建立多元风险模型，从投保人角度讨论了最优保险决策，分析了投资风险，无风险投资收益和保费政策等因素对最优决策的影响，为现代企业采取综合措施降低风险提供了理论依据．     

Robustness of the efficient DMUs in data envelopment analysis

By means of modified versions of CCR model based on evaluation of a decision making unit (DMU) relative to a reference set grouped by all other DMUs, sensitivity analysis of the CCR model in data envelopment analysis (DEA) is studied in this paper. The methods for sensitivity analysis are linear programming problems whose optimal values yield particular regions of stability. Sufficient and necessary conditions for upward variations of inputs and for downward variations of outputs of an (extremely) efficient DMU which remains efficient are provided. The approach does not require calculation of the basic solutions and of the inverse of the corresponding optimal basis matrix. The approach is illustrated by two numerical examples.     

Analysing production and environmental risks in arable farming systems: A mathematical approach

In response to a growing environmental concern in Dutch society, sustainable production systems in arable farming have been developed. Amongst other things, a reduction of the dependency on chemical inputs is attempted. This paper addresses the role of risk in the adoption by farmers of new systems by means of a model that determines differences in production risks between conventional and sustainable farming systems (CAFS and IAFS).Timing of activities – setting out a management track – is particularly important in sustainable arable farming systems. Resource requirements of crop husbandry activities mainly depend on weather conditions. To assess risks caused by weather conditions, the major aspects of crop husbandry in various crops have been modelled. Using tactics in crop husbandry (decision rules) and weather uncertainty as input, crop husbandry models (HMs) calculate management tracks that require resources. The value distributions of resource requirements of crop husbandry according to different farming systems is calculated in different HMs represented by stochastic dynamic directed networks. Hence, production risks of CAFS and IAFS can be compared.On a farm, all the aspects of crop husbandry in the various crops are to be taken into account. Given the weather conditions, tactics for all the aspects are combined in an LP model of the whole farm where they compete for limited resources. In the LP model, tactics are re-assessed by means of the HMS, using information of the LP solution. This iterative procedure enables production risks of CAFS and IAFS to be compared, considering fixed, allocatable resources for the whole farm firm.     

MODELING OF A LANDLORD—TENANT AGRICULTURAL SYSTEM IN THE ENVIRONMENTAL CONTEXT

A hierarchical economic–environmental model is formulated to analyze the sustainable management of farming production in a landlord–tenant system. The problem under study is interdisciplinary and combines various agricultural, economic, social, and environmental factors. To maximize profit, the landlord chooses a rental payment and the duration of a lease contract. Tenants invest into farmyard fertilizer in order to improve future crop growth and maximize their profit. It is shown that the qualitative behavior of optimal trajectories in the landlord–tenant problem is mostly affected by environmental conditions rather than by the end‐of‐horizon and delay effects. A range of model parameters is identified, where the optimal trajectory coincides with the first‐best environmentally and socially efficient solution.     

DEGREE OF ECONOMIC UNSUSTAINABILITY IN THE MANAGEMENT OF RENEWABLE RESOURCES

A criterion commonly used to determine economic sustainability posits that the discounted welfare should not decrease over time. Resource management problems involving fluctuating stocks may be exacerbated by a lack of sustainable policies unless some violations of this condition are accepted. Moreover, sustainable policies may lead to the minimal welfare levels. To alleviate these problems, a new notion of sustainability is suggested. In this new form of sustainability, violations of nondecreasing welfare are accepted to a certain degree. The policies that maximize the discounted welfare under the constraint for the largest accepted violation for sustainability satisfy a dynamic programming type of fixed‐point condition that can be effectively utilized for finding optimal policies. The new notion of sustainability can also be utilized in defining an index for measuring the degree of overall unsustainability of resource management problems and different harvesting policies.     

THE DYNAMICS OF AN ANIMAL—VEGETATION SYSTEM: SHEEP FARMING

The paper studies the economy and ecology of sheep farming at the farm level in a Nordic context, with a crucial distinction between the outdoors grazing season and the winter indoors feeding season, and where climate conditions fix the length of the grazing season. Two different categories of animals, ewes (adult females) and lambs, and one plant species are included in our ecological model. The farmer is assumed to maximize present‐value profit where the revenue is made up income from meat and wool production. We find that livestock cycles may represent an optimal management policy. We also show that in a possible steady state with a constant number of animals and constant vegetation quantity, slaughtering either only lambs or only ewes is optimal.     

ECONOMIC EVALUATION OF BIOTECHNOLOGICAL PROGRESS: THE EFFECT OF CHANGING MANAGEMENT BEHAVIOR

Abstract The paper assesses the welfare effects of biotechnological progress, as exemplified by tree improvements, using a partial equilibrium model. Timber demand is assumed to be stochastic and the distributions of its coefficients known. The coefficients of a log‐linear supply function are determined by maximizing the expected present value of the total surplus of timber production, both in the presence and in the absence of genetically improved regeneration materials. The supply functions are then used to estimate the expected present values of the total surplus in different cases through simulation. These estimates enable us to assess the direct effect and the effect of changing harvest behavior on the expected present value of the total surplus. The main results of the study are (i) the presence of genetically improved regeneration materials has significant impacts on the aggregate timber supply function; (ii) the application of genetically improved regeneration materials leads to a significant increase in the expected present value of the total surplus; and (iii) a considerable proportion of the welfare gain results from the change in harvest behavior. A conclusion we draw from this study is that ignoring the influences of technological and policy changes on behavior can lead to significantly biased welfare estimates. We view the model as a potential approach to conducting counterfactual policy comparisons in economics without forward‐looking data.     

混合的DEA模型最优解的存在性

有ｎ个决策单元。设被评价的决策单元可以不是这ｎ个之一,且它们的输入或输出可以取负值,在这样情况下,给出了混合的ＤＥＡ模型存在最优解的必要条件或充分条件     

产出不确定条件下“公司+农户”型订单农业供应链协商模型研究

在农产品产出不确定性及零售价格受农产品产出率影响的条件下,研究了一类由风险规避农户和风险中性公司组成“公司+农户”型订单农业农产品供应链协调问题。在该农产品供应链中,农户和公司通过Nash协商谈判来分别决策最优的生产量和订单价格。研究结果表明,在农产品产出不确定及零售市场价格受农产品产出率影响的条件下,风险规避型农户和公司的Nash协商合作博弈存在均衡解。Nash协商谈判所达成的最优农产品产出量和订单价格均高于分散决策情形下的最优农产品产出量和订单价格。最优农产品产出量是关于农户风险规避度的单调增函数,而最优的订单价格是关于农户风险规避度的单调减函数。最后,通过与分散决策情形相比,证明了Nash协商谈判机制能够促使风险规避型农户和风险中性型公司均达到帕累托改进。     

混纺比测定中的数学方法及其遗传算法实现

测定纱线的混纺比在纺织工程的实践中有着重大的实际意义.在特征值提取环节,结合相关文献,从“径长”的角度提出面积系数、异形度、波动率等形态指标并利用其合理地构成特征向量.重点讨论鉴定纱线混纺比中聚类分析的数学方法.结合非线性优化模型和遗传算法,通过适当的编程计算,从而得出较好的聚类分析结果.     

A JUVENILE‐ADULT DISCRETE‐TIME PRODUCTION MODEL OF EXPLOITED FISHERY SYSTEMS

Abstract. Previous mathematical modeling of the population dynamics of Georges Bank Atlantic cod fishery employed discrete‐time models without age‐structure. To make use of a much wider variety of data on fisheries and fish stocks than was possible with an unstructured model, we introduce a juvenile‐adult age‐structured production exploited fishery model with a very general recruitment function. We use the age‐structured model to study the interaction between fish exploitation levels and recruitment dynamics. As case studies, we use our model results and historical fish population data from Georges Bank to investigate the impact of recent harvesting levels on the sustainability of cod fishery. We show that a constant harvesting policy with the same harvesting rate of 2007 would lead to the recovery and sustainability of Georges Bank cod fishery.     

REGIONAL ECONOMIC IMPACTS OF CLIMATE CHANGE: A COMPUTABLE GENERAL EQUILIBRIUM ANALYSIS FOR AN ALASKA FISHERY

We compute the effects on the Alaska economy of reduced pollock harvests from rising sea surface temperature using a regional dynamic computable general equilibrium model coupled with a stochastic stock‐yield projection model for eastern Bering Sea walleye pollock. We show that the effects of decreased pollock harvest are offset to some extent by increased pollock price, and that fuel costs and the world demand for the fish, as well as the reduced supply of the fish from rising sea surface temperature, are also important factors that determine the economic and welfare effects.     

WELFARE MEASUREMENT OF TECHNOLOGICAL AND ENVIRONMENTAL EXTERNALITIES IN THE RAMSEY GROWTH MODEL

This paper deals with the measurement of economic welfare within the framework of the Ramsey growth model, when there are anticipated technological and/or environmental changes. It is shown that, under such circumstances, the Hamiltonian along an optimal trajectory underestimates the maximum sustainable utility, meaning that the welfare measure suggested in several recent studies would be incorrect in this case. We also derive the appropriate welfare measure in the presence of technological and environmental changes. The second part of the study concerns the welfare implications of unanticipated technological change.     

生猪生产的最优利润

线性规划（ＬＰ）用于确定饲料最低费用配比已有多年的历史。但确定饲料配比仅是农场主所关心的一件事，他们的主要目的是为了从生产中获取最大的利润。本文提出了基于ＬＰ的饲料规划方案，以便使猪是佳地生长，同时也使养猪者获取更大的生产利润。在最大利润模型中，售价和重量的乘积作为收入，饲料费和间接费作为成本。解中包括猪饲料的总量和猪应有的最佳重量。为了把猪的生长模式引入到ＬＰ模型中，我们用数学生长函数来表达生长率和猪龄之间的关系。该函数是经过适当的转化，用回归方法估算出来的。猪在不同生长阶段的营养需求是依据其生长模型和饲料转化率分析的。把上述结果全都引用到ＬＰ模型中，这样可以使利润最优化。实际数据的检验表明：在实践中，ＬＰ模型的结果是合理的。     

A BIOECONOMIC SHEEP–VEGETATION TRADE‐OFF MODEL: AN ANALYSIS OF THE NORDIC SHEEP FARMING SYSTEM

Abstract. The paper studies the economy and ecology of sheep farming at the farm level and includes 2 different categories of the animals, ewes (adult females) and lambs. The model is analyzed in a Nordic economic and biological setting. During the outdoor grazing season, animals face limited grazing resources so that the weight gain of lambs is determined by the per‐animal vegetation consumption. On the other hand, the number of grazing animals, lambs as well as ewes, determines the grazing pressure. This problem is studied under the assumption of a rational and well‐informed farmer who aims to maximize profit in ecological equilibrium with zero animal and vegetation growth. We find that lamb‐only slaughtering is optimal and that it is never beneficial for the farmer to keep livestock that overgraze pasture. It is also shown that higher meat prices and more profitable slaughtering make it economically rewarding for the farmer to keep more animals. A numerical illustration indicates that the optimal sheep farming decision may be more sensitive to changes in pasture quality and productivity than changes in economic conditions.     

ROYALTY INCENTIVES AND GULF OF MEXICO OIL PRODUCTION

ABSTRACT. This paper employs field‐specific estimates of Pindyck's (1978) widely cited model of natural resource supply to simulate effects of changes in federal royalty rates on the timing of exploration and output by firms in the deepwater Gulf of Mexico oil industry. Results suggest that deepwater Gulf oil production is highly inelastic with respect to changes in royalty rates. Royalty rate decreases are shown to increase early period exploration effort, result in little change in reserve additions and future production. Policy implications of this study suggest that public officials should be wary of arguments that large increases in deepwater Gulf oil field activity can be obtained from reductions in federal royalty rates‐particularly reductions in the early years of oil field development.     

基于经验分布的条件VaR计算方法研究

本文以基于股票价格的条件收益率为出发点,研究在不能确定价格P与收益率R的联合分布类型时,利用历史数据刻画其经验条件概率分布函数,并据此测算一定价格水平下的VaR值。本文的研究重点在于如何确定能近似描述价格Pt时收益率分布特征的最佳样本数据。     

Choosing weights from alternative optimal solutions of dual multiplier models in DEA

In this paper we propose a two-step procedure to be used for the selection of the weights that we obtain from the multiplier model in a DEA efficiency analysis. It is well known that optimal solutions of the envelopment formulation for extreme efficient units are often highly degenerate and, consequently, have alternate optima for the weights. Different optimal weights may then be obtained depending, for instance, on the software used. The idea behind the procedure we present is to explore the set of alternate optima in order to help make a choice of optimal weights. The selection of weights for a given extreme efficient point is connected with the dimension of the efficient facets of the frontier. Our approach makes it possible to select the weights associated with the facets of higher dimension that this unit generates and, in particular, it selects those weights associated with a full dimensional efficient facet (FDEF) if any. In this sense the weights provided by our procedure will have the maximum support from the production possibility set. We also look for weights that maximize the relative value of the inputs and outputs included in the efficiency analysis in a sense to be described in this article.