Resistive Magnetohydrodynamic Equilibria in a Torus

It was recently demonstrated that static, resistive, magnetohydrodynamic equilibria, in the presence of spatially-uniform electrical conductivity, do not exist in a torus under a standard set of assumed symmetries and boundary conditions. The difficulty, which goes away in the ``periodic straight cylinder approximation,'' is associated with the necessarily non-vanishing character of the curl of the Lorentz force, j x B. Here, we ask if there exists a spatial profile of electrical conductivity that permits the existence of zero-flow, axisymmetric r esistive equilibria in a torus, and answer the question in the affirmative. However, the physical properties of the conductivity profile are unusual (the conductivity cannot be constant on a magnetic surface, for example) and whether such equilibria are to be considered physically possible remains an open question.Comment: 17 pages, 4 figure

Cost Escalation in Nuclear Power

This report is concerned with the escalation of capital costs of nuclear central station power plants between the early 1960s and the present. The report presents an historical overview of the development of the nuclear power industry and cost escalation in the industry, using existing data on orders and capital costs. New data are presented on regulatory delays in the licensing process, derived from a concurrent study being carried on in the Social Science group at Caltech. The conclusions of the study are that nuclear capital costs have escalated more rapidly than the GNP deflator or the construction industry price index. Prior to 1970, cost increases are related to bottleneck problems in the nuclear construction and supplying industries and the regulatory process; intervenors play only a minor role in cost escalation. After 1970, generic changes introduced into the licensing process by intervenors (including environmental impact reviews, antitrust reviews, more stringent safety standards) dominate the cost escalation picture, with bottlenecks of secondary importance. Recent increases in the time from application for a construction permit to commercial operation are related not only to intervenor actions, but also to suspensions, cancellations or postponements of construction by utilities due to unfavorable demand or financing conditions

Toroidal Vortices in Resistive Magnetohydrodynamic Equilibria

Resistive steady states in toroidal magnetohydrodynamics (MHD), where Ohm's law must be taken into account, differ considerably from ideal ones. Only for special (and probably unphysical) resistivity profiles can the Lorentz force, in the static force-balance equation, be expressed as the gradient of a scalar and thus cancel the gradient of a scalar pressure. In general, the Lorentz force has a curl directed so as to generate toroidal vorticity. Here, we calculate, for a collisional, highly viscous magnetofluid, the flows that are required for an axisymmetric toroidal steady state, assuming uniform scalar resistivity and viscosity. The flows originate from paired toroidal vortices (in what might be called a ``double smoke ring'' configuration), and are thought likely to be ubiquitous in the interior of toroidally driven magnetofluids of this type. The existence of such vortices is conjectured to characterize magnetofluids beyond the high-viscosity limit in which they are readily calculable.Comment: 17 pages, 4 figure

A Case Study of Regulatory Programs of the Federal Energy Administration

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Artificial Markets and the Theory of Games

The theory of games has provided notable insights into the nature of bargaining processes. In this article I will apply co-operative game theory to a specific problem of air pollution control, as a device for designing and evaluating a set of institutions intended to eliminate certain transaction costs which appear to prevent profitable bargains from being consummated

Separable Externalities in Cost and Production Functions

The characterization of external effects as “separable” has played an important role in the development of the theory of externalities. The separable case is particularly well behaved when procedures for achieving an optimum allocation of resources in the presence of externalities are examined. Davis and Whinston (1962) find that separability assures the existence of a certain kind of equilibrium in bargaining between firms which create externalities, and that equilibrium does not exist without separability. Kneese and Bower (1968) argue that with separability the computation of Pigovian taxes to remedy externalities is particularly simple. Marchand and Russell (1974) demonstrate that certain liability rules regarding external effects lead to Pareto optimal outcomes if and only if externalities are separable. In each of these cases the problem is posed in terms of two firms related by technological externalities, and separability is defined in terms of a cost function. In this paper, we will characterize that class of production functions which give rise to separable cost functions, and show that the relation between production functions and separable cost functions is by no means as trivial as has been claimed

Competitive Equilibrium with Separable Externalities

The characterization of external effects as "separable" has played an important role in the development of the theory of externalities. The separable case appears particularly well behaved when procedures for achieving an optimum allocation of resources in the presence of externalities are examined. For example, Davis and Whinston (1962) find that separability assures the existence of a certain kind of equilibrium in bargaining between firms which create externalities, and that equilibrium does not exist without sepalability. Kneese and Bower (1968) argue that with separability the computation of Pigovian taxes to remedy externalities is particularly simple. Marchand and Russell (1974) demonstrate that certain liability rules regarding external effects lead to Pareto optimal outcomes if and only if externalities are separable. We will argue in this paper that whenever an externality affecting a firm is separable, the production set of that firm is not convex in a neighborhood of zero output. The proposition is established by redefining separability in a manner which allows for the fact that in the long run a firm will shut down rather than accept negative profits. These definitions yield the theorem that separability implies a non-convexity of the production function, which may result in a discontinuous supply correspondence

Stability of Pure Trade Equilibrium with Externalities

Sufficient conditions for the stability of competitive equilibrium in a pure trade economy with externalities are developed in this paper. Externalities are introduced through the assumption that each individual's utility depends on the consumption of every other individual. A two-level adjustment process is postulated. At fixed prices, individual strategies must be made mutually consistent. Each individual's strategy is stated as a relation which maps prices and the demands of all other individuals into the demand of that individual. The equilibrium of the externality adjustment process is a demand allocation, depending on price, which is feasible and maximizes utility for each individual at given prices. Sufficient conditions for stability of the externality adjustment process are proved and interpreted. The equilibrium demand functions are then used in a tatonnement process to investigate the stability of competitive equilibrium. All the standard theorems on excess demand functions which give sufficient conditions for stability apply to the equilibrium demand functions of an economy with externalities. It is established that the stability properties of an economy without externalities possess a certain type of continuity. Any sequence of economies with externalities which converges in the proper sense to an economy without externalities characterized by gross substitutability has the property that for all t > T the competitive equilibrium of the economy with externalities is stable. Weaker stability conditions on the limit economy can make this theorem fail

Separability and vanishing externalities

In one of the most influential papers written on the subject of externalities, Otto Davis and Andrew Whinston argue that corrective taxes and private bargaining are likely to achieve an optimum in the presence of mutual externalities between two firms only when externalities are separable, in the sense that marginal cost is independent of the level of externality. Further analysis of the concept of separability reveals that even this conclusion is too optimistic. I shall argue below that the assumptions needed to make taxes and negotiations work properly rule out the possibility of having externalities in any observable situation

Separability, Externalities, and Competitive Equilibrium

The characterization of external effects as "separable” has played an important role in the development of the theory of externalities. The separable case appears particularly well behaved when procedures for achieving an optimum allocation of resources in the presence of externalities are examined. Three examples can illustrate the range of conclusions which have been reached concerning separable externalities. Davis and Whinston [1962] find that separability assures the existence of a certain kind of equilibrium in bargaining between firms which create externalities, and that equilibrium does not exist without separability. Kneese and Bower [1968] argue that, with separability, the computation of Pigovian taxes to remedy externalities is particularly simple. Marchand and Russell [1974] demonstrate that certain liability rules regarding external effects lead to Pareto optimal outcomes if and only if externalities are separable. In these and other articles, an externality is defined as separable if the cost function of an affected firm has a specific form, stated in Definition 1 of this paper. With few exceptions, explorations of the implications of separability have assumed that equilibria and optima can be characterized in terms of classical first-order conditions of profit-maximization. Examination of the class of production functions which are compatible with separable externalities reveals, however, that separable externalities cause a distinctive non-convexity when the possibility that a firm will shut down rather than accept negative profits is introduced. Since numerous policies for dealing, for example, with environmental damage have been based on theoretical investigations of externalities, a defect in those investigations can have serious consequences. In this paper, we characterize the class of production functions which generate separable externalities. These results are used to show that all production functions in this class contain a nonconvex part. Some of the consequences of this non-convexity for market structure in the presence of separable externalities are examined. Finally, examples are given which suggest some conditions under which a competitive equilibrium may exist in the presence of externalities and some conditions under which it may not