The Asynchronous Leontief Model

The traditional dynamic Leontief model is synchronous: every vertex acts simulaneously. A model with delays of action has been proposed, but it still remains synchronous. In this paper we propose an asynchronous version of the model that allows realistic computations. We furnish an algorithm and a program.     

Optimization in a Dynamic Leontief Model with Restricted Value Growth

The purpose of this paper is to develop a dynamic Leontief model of an msector economic system in which the production of all goods requires one time period and one primary factor, but no capital stocks of any good, and in which the total value of outputs from all sectors is required to grow at a specified rate in each period. The requirement of a fixed rate of total value growth is less restrictive than the familiar condition of balanced growth across all sectors, and it permits the definition and analysis of interesting finite-period optimization problems. Specific results of the paper include the following: (1) the proof that a value-added maximization problem with an unrestricted initial state will experience consumption in exactly one sector in each time period, and willyield an optimal value function which is linear in the variables that describe the terminal state of the system; (2) the development of an efficient Dantzig-Wolfe procedure for analysis of the total value-added maximization problem where both the initial and terminal states are specified; (3) the derivation of testable properties that will guarantee the attainability of a specified target state from a specified initial state of the system; (4) a formal comparison of some basic characteristics of total value growth and balanced value growth.     

A Dynamic Leontief Model with Non-renewable Resources

In this paper we study a generalization of the dynamic Leontief input–output model. We extend the standard dynamic Leontief model with the balance equation of non-renewable resources. Obviously, the non-renewable stocks will decrease, exploiting primary resources. In this study we examine the controllability of this extended model by taking the consumption as the control parameter. Assuming balanced growth for both consumption and production, we investigate how long these scarce resources will cover the input needs of production and how the lifetime of the system depends on the balanced growth rate and on the consumption. In doing so, we apply classic results from control theory and on eigenvalue problems in linear algebra.     

The Second Eigenvalue of the Leontief Matrix

According to Frobenius, a positive matrix possesses a unique positive eigenvector which belongs to a positive eigenvalue. This eigenvalue is of the largest absolute magnitude and the matrix admits no other positive eigenvector. If an arbitrary positive vector is repeatedly premultiplied by such a matrix, then the result tends towards this positive eigenvector. It is the second largest eigenvalue that determines the speed of convergence. The estimate of the second eigenvalue of a purely random flow coefficient matrix shows that its expected absolute magnitude declines monotonically with the size of the matrix. Hence, the larger the system is the faster is the convergence. A prescribed exactness of the eigenvector (of equilibrium prices or quantities) will be reached after a few—perhaps just a couple of—iterations in a large system.     

The Leontief Pollution Model: A Systematic Formulation

In a recent article in this journal, Qayum offered a reformulation of the Leontief pollution model. Here, a systematic formulation of this model is offered which integrates the numerical examples of both Leontief and Qayum.     

城市空间结构生态调控研究——以常州生态城市规划为例

城市空间发展应注重"质"的提高,而不应单纯追求"量"的扩张.本文认为生态城市规划建设的核心是城市空间结构生态化和城市功能群生态化,提出了基于自然、社会和经济特征的城市空间生态分区方案和建设导则,构建城市生态网架,优化调整城市空间整体布局以及城市产业和城市人居布局,并运用"三地动态平衡"理论对城市土地资源的开发利用进行时空安排与调控,从而引导城市空间形态的合理演化.     

The spatial structure of Latin American cities

"Using published census data, metropolitan area population and employment statistics are constructed for several large Latin American cities in 1950, 1960, and 1970, and compared to similar statistics from selected North American cities. The Latin cities are experiencing decentralization of population and some decentralization of employment. Overall population density patterns of large Latin cities resemble those in older North American cities; newer North American cities have lower densities and are much more decentralized than Latin cities. High-status groups are somewhat concentrated in the central cities of Latin American metropolitan areas, but their concentrations there are declining."     

Urban spatial structure: An analysis with a varying coefficient model

This paper proposes a varying coefficient model (VCM) to introduce city- and tract-specific variables into the exponential density functions used to study urban spatial structure. Since the selected city- and tract-specific characteristics may be subject to control by policy action and themselves comparatively easily projected on the basis of time, the VCM model can be used for both forecasting and policy analysis even though estimated from cross-sectional data. The results show that questions about the appropriateness of the exponential functional form and specification errors associated with the omission of city- and tract-specific variables can be handled by the VCM model. The paper demonstrates the usefulness of the VCM model as a tool for policy analysis and projection.     

信息技术与城市空间结构的优化

本文从空间相互作用、区位因子选择、功能空间替代入手,分析信息技术优化城市空间结构的机理,探讨在信息技术的推动下,城市在空间扩展、集聚运动、用地模式、功能分区、等级体系等方面所呈现的新变化和新景观,并提出中国城市利用信息技术优化和调整空间结构的具体建议.     

中国城市空间结构调整的性质

当前及相当长一段时期内 ,内外空间结构双重调整是中国城市空间结构演化的主要性质。竞争尚未成为城市关系、区域关系中的主要方面。由此决定了城市的理性选择应是有机结合的内外空间结构双重优化     

The approximation capabilities of the minflex-Laurents,translog, and generalized Leontief forms

This paper compares the approximation capabilities of the minflex-Laurents translog and minflex generalized Leontief cost functions with their translog and generalized Leontief counterparts in Monte Carlo experiments. The minflex Laurent specifications generally provided closer approximations to underlying technical and economic parameters. Imposition of nonlinear restrictions on some of the parameters of the minflex Laurent models yielded measurable improvement in estimated elasticities of substitutions, returns to scale, and rates of technical change.The refereeing process of this paper was handled through E. Appelbaum.     

A Consistent Formulation of the Leontief Pollution Model

We consider the environmental Leontief model, which is an input–output model augmented by pollution-generation and pollution-abatement sectors. Two formulations of this model, dating back to Leontief's work in 1970, can be found in the literature. One formulation treats an exogenously given vector of the tolerated level of pollutants (environmental standards) as a negative variable on the right-hand side of the model. The other formulation supposes that each industry eliminates a given proportion of the pollution that it creates, so that the proportions of gross pollutants which are subject to treatment by each sector enter as given parameters. Even in the case when the levels of production and abatement in the two different model formulations are equal, the solutions of the dual or price model are different for cases where some net pollution is left untreated. First, the analytical relationship between the two price models is established. Secondly, both models formulated in a linear programming framework are extended by imposing emission charges (effluent taxes) for untreated pollution. Finally, it will be shown how to estimate the level of emission charges for both model formulations such that they provide the same levels of production and abatement, as well as the same shadow prices. This is illustrated by a numerical example.     

煤炭清洁生产技术的开发与应用研究

文章在论述煤炭工业清洁生产必要性的基础上,对煤炭清洁生产技术,即洁净煤技术的开发和应用进行了介绍。     

Reconsideration of Non-negative Solutions for the Augmented Leontief Model

We consider the Leontief model augmented with pollution-generation and pollution-abatement sectors. The conditions to ensure the existence of non-negative solutions for the total output and for the vector of abatement activities, depending on the exogenously given final demand and environmental standards, are presented. They are extensions and modifications of the conditions for a single pollutant derived, for example, by Miller and Blair.     

The structure of technology in Brazilian sugarcane production, 1975–87: An application of a modified symmetric generalized McFadden cost function

Sugarcane-based ethanol has become a primary automotive fuel in Brazil over the past 15 years. Because sugarcane costs are over two-thirds of the costs of ethanol production, the economic efficiency of this renewable petroleum substitute hinges on the structure of technology in sugarcane production. In this paper a modified symmetric generalized McFadden (SGM) cost function for sugarcane is estimated and the presence of technical change and economies of scale are investigated. The original SGM proposed by Diewert and Wales (1987) is modified to allow for fixed factors of production. This allows the cost function to be applied to processes which have fixed factors. The results suggest that there is no empirical evidence of economies of scale and very little technical change, only in the north of Brazil. The implications for the future economic efficiency of this petroleum substitute are discussed.     

Income taxes and urban spatial structure

This paper examines the impact of an income tax in a monocentric city where households equilibriate their allocation of time between work, commuting, and leisure. An increase in the income tax rate lowers the implicit value of time, and hence transportation costs. “Compensated equilibrium” comparative statics analysis shows that under certain conditions, this results in a larger, more dispersed urban area, with lower land rents at the city center and less population within any given distance from the center. The welfare effect of an income tax rate change is also studied, and an expression for the marginal excess burden is derived. The income tax produces welfare losses both because it induces substitution in favor of leisure and in favor of travel—the latter accompanied by excessive spatial dispersion and consumption of space. The marginal excess burden depends not only on the compensated demand elasticity for leisure, but also on that for space. Finally, the problem of benefit measurement for transportation projects in this tax-distorted spatial economy is examined. Benefit measures should be deflated to adjust for the fact that further transportation improvements lead to reduction of land use intensity, exacerbating the problem of spatial resource misallocation in an already excessively dispersed urban area.     

On Hypothesis about the Second Eigenvalue of the Leontief Matrix

If an arbitrarily positive eigenvector is repeatedly premultiplied by a positive matrix, then the result tends towards a unique, positive (Frobenius) eigenvector. Brady has demonstrated that the expected absolute magnitude of the estimate of the second largest eigenvalue of a positive random matrix (with identically and independently distributed entries) declines monotonically with the increasing size of the matrix. Hence, the larger the system is, the faster is the convergence. Molnár and Simonovits examined Brady's conjecture in the case where entries of a stochastic matrix are close to 1/n. We prove this hypothesis for any stochastic and positive matrix.     

Efficiency and truthfulness with Leontief preferences. A note on two-agent,two-good economies

In exchange economies where agents have private information about their preferences, strategy-proof and individually rational social choice functions are in general not efficient. We provide a restricted domain, namely the set of preferences representable by Leontief utility functions, where there exist mechanisms which are strategy-proof, efficient and individually rational. In two-agent, two-good economies we are able to provide an even stronger result. We characterize the class of efficient and individually rational social choice functions, which are fully implementable in truthful strategies.Received: 28 April 2003, Accepted: 23 June 2003, JEL Classification: D51, D71The author thanks Matthew Jackson, Jordi Massó and James Schummer for fruitful discussions, William Thomson for many valuable comments on an earlier version. A particular thank to Salvador Barberá for his fundamental help.