影子价格及其在资源配置中的应用研究

为了应用影子价格实现资源在全社会的最优配置,本文通过线性规划的对偶理论和非线性优化问题的Kuhn-Tucker条件揭示了影子价格的本质,在资源配置优化问题中线性规划模型中的影子价格就是其对偶问题的最优解,非线性规划模型中的影子价格就是与最优解相对应的拉格朗日乘数。根据松紧定理解释了资源影子价格与资源限量之间的关系,还对线性规划模型与非线性规划模型中影子价格的不同表现进行了分析。最后阐明了影子价格在资源配置中的应用。     

影子价格及其灵敏度分析

影子价格真实地反映了资源在经济结构中最优决策下对总收益的影响和贡献大小，是实现资源合理配置的重要依据。本首先介绍影子价格的经济意义和计算方法，然后从影响影子价格变化的因素入手对影子价格进行灵敏度分析，最后探讨影子价格在经济管理中的应用。     

国民经济最优规划中的共轭问题研究

本论文针对稀缺资源提出国民经济最优化的共轭问题．由共轭定理得到了共轭问题解一致的可能性及其成立的条件，共轭定理为检验国民经济协调发展提供了理论依据和方法．论文着重讨论了以劳动资源为稀缺资源的国民经济规划共轭问题，给出其约束条件的影子价格的经济意义，证明了同一约束条件的影子价格是成比例的，劳动资源的影子价格是国民财富的影子价格的倒数．同时指出产品与资源等价替代系数与其影子价格有关，影子价格是产品与资源的短缺性、产品与资源的平衡的度量．最后讨论了影子价格与生产活动的消耗、劳动消耗与效益的关系．     

多种资源灵敏度分析和影子价格的探讨

本在原有的线性规划灵敏度分析和影子价格理论的基础上，讨论了多种资源变化的灵敏度分析中影子价格的调节作用，提出资源最佳数量的LP模型，指出在多种资源变化的情况下，影子价格的应用可以而且应该超越传统的观点，以统筹调配各种资源，追求总的目标函数值达到最优。     

最优化方法与影子价格──再谈数学与经济

本文给出了影子价格严格的数学定义，并根据定义用四个定理严格证明了在线性规划，二次规划、非线性规划中影子价格的计算公式。然后，从资源原采购、资源投向，投资方向和科学确定商品的地区差价等方面，对影子价格的经济应用进行了实证分析。     

电力行业碳排放权资源影子价格模型:以海南为例

在电力行业碳排放受限情况下,碳排放权成为电力企业生产必须获取的一种资源。碳排放权资源影子价格可以成为排放权交易定价机制构建和碳税税率制订的重要参考。本文构建了以系统发电总成本最小化为目标的电力系统数学规划模型,利用对偶原理求解碳排放权的影子价格。以海南电网为案例,得到电力系统碳排放权的影子价格并分析了其主要影响因素。研究结果表明,碳排放权影子价格随着碳排放总量上限的降低呈现阶梯状增长走势。碳排放强度高的煤电和排放强度低的风电对排放权的影子价格影响截然相反。     

基于投入产出线性规划模型的燃料乙醇影子价格研究

影子价格能够反映资源的稀缺性及对国民经济的贡献程度.应用投入产出与线性规划相结合的分析方法,构建了投入产出线性规划模型,并基于笔者编制的2005年燃料乙醇投入产出表,针对燃料乙醇制造业部门的不同发展速度,运用投入产出线性规划模型对燃料乙醇的影子价格进行了具体测算.     

影子价格在经济管理中的应用

本讨论了如何利用影子价格为企业的决策提供有价值的信息。     

影子价格与影子成本

本文根据线性规划问题对偶变量和影子价格的经济意义,给出了影子成本的概念,讨论了影子成本与对偶价格的关系.通过灵敏度分析给出了影子成本的动态表示,并进一步阐明了影子价格和影子成本的惟一性以及影子成本在经济管理中的应用.     

影子价格在经济管理中的应用

本文讨论了如何利用影子价格为企业的决策者提供有价值的信息 .     

Generalized average shadow prices and bottlenecks

Usually some of the constraints of a 0-1-Mixed Integer Linear Programming problem correspond to resources and in this paper we suppose that they may be redefined. For the availability of the resources the average shadow price is the maximum price that the decision maker is willing to pay for an additional unit of the package (i.e. a combination) of resources defined by some direction. In this paper we present a generalization of the average shadow price and its relation with bottlenecks including the analysis relative to the coefficients matrix of resource constraints. The generalization presented does not have some limitations of the usual average shadow price. A mathematical programming approach to find the strategy for investment in resources is presented.     

A comment on “solving the puzzles of structural efficiency”

In a recent paper by Li and Cheng [Li,S.K., Cheng, Y.S., 2007. Solving the puzzles of structural efficiency. European Journal of Operational Research 180(2), 713–722], they developed the shadow price model to solve the existing puzzles of structural efficiency theoretically. However, we observe that the optimal shadow price vector in the shadow price model by Li and Cheng (2007) is not always unique. As a result, the decomposition of the structural efficiency is arbitrarily generated, depending on the shadow price vector we choose. Finally, an example with multiple inputs and outputs is used to illustrate the phenomenon.     

Economic planning with institutional price constraints for a decentralized economy

This paper describes the relationship between market prices and shadow prices when the economy has general types of institutional price constraints. We consider a decentralized linear economy where market prices quide the decentralized behavior of each activity and the shadow prices measure the social values of resources. To measure the social values, we introduce a social objective criterion. Hence, our approach could be regarded as a central economic price control with institutional price constraints for a decentralized economy. A simple example is employed to graphically illustrate the wedges between market prices and shadow prices. It has been shown that our problem can be solved through mixed integer linear programming techniques.     

Average shadow prices in mathematical programming

We develop the concept of average shadow price in mathematical programming. This concept measures the value of resources along a direction in an average sense, in contrast to traditional marginal analysis; it serves as a useful standard price for management decisions about resources, particularly when there are nonconvexities. We give it an economic interpretation. We also develop simple computational schemes for obtaining and improving the bounds of the average shadow prices and illustrate them in two important classes of nonconvex programs: convex maximization problems and mixed integer programs.     

影子价格的价值公度性及资源临界特性

阐述了影子价格的概念,提出影子价格价值公度性的概念,讨论了在实际应用中较容易造成混淆的临界特性,对资源分配问题进行了较细致的分析,有助于最优资源分配方案的决策和最大利润的实现.     

Average shadow price and equilibrium price: A case study of tradable pollution permit markets

Shadow prices indicate implicit values of limited resources at the margin and provide important information in decision making for resource management. In continuous economic models, shadow prices associated with demand-supply balance constraints represent consumers’ willingness to pay and producers’ marginal cost, hence they correspond to market equilibrium prices. As well known, however, marginal analysis fails in the case of discrete optimization, such as mixed integer programming. An alternative concept has been introduced in the literature to measure the value of an extra unit of a limited resource in such cases. This concept is based on average rather than marginal values, thus called the average shadow price, and interpreted in the same way as conventional shadow prices. Whether average shadow prices in a discrete economic model can serve as market equilibrium prices has not been addressed in the related literature. The present paper addresses this issue in an empirical setting. Using a tradable pollution permit market as an example, where firms’ YES/NO type technology adoption decisions are represented by binary variables, we show that the average shadow price of tradable permits can be interpreted as the equilibrium price only when certain conditions related to the cost structure and emission levels hold. On the other hand, we show that an iterative procedure based on individual firms’ cost minimizing behavior presents a better approach for finding a price that can eliminate or reduce the gap between demand and supply of permits in the market.     

疫情环境下价格导向的防护物资最优生产分配机制研究

新型冠状病毒疫情导致防护物资匮乏,增加了医护人员受感染的风险.现构建了防护物资最优生产-分配-定价模型,并在此基础上提出了广义影子价格的概念,以此作为防护物资定价的参考和依据,通过价格引导生产型企业合理扩大生产规模,以解决当前防护物资短缺的困难.广义影子价格反映了企业产能提升成本等因素,相比传统影子价格更适用于为防护物资统一定价.另外,利用广义影子价格与拉格朗日乘子集合之间的联系,提出了一个线性规划模型用以计算广义影子价格.数值仿真结果说明了广义影子价格在防护物资定价上的适用性.