General Equilibrium Conditions Research Articles

Symmetry and reversibility in social exchange

In this paper, the equilibrium properties of Coleman's (1973) model of social exchange are explored as a prelude to making interpretations about the dynamics implicit in static models of exchange in general, this model in particular. The model is first presented in the conventional way—as an exchange condition embedded within more general equilibrium conditions, and the subsequent analysis of the model is enriched by examining its equilibrium at aggregate as well as disaggregate levels and by interpreting the model as a set of flows or networks. Its equilibrium properties are then described. First, it is shown how a model in which the exchange condition is a function of its equilibrium, defines an equilibrium which is reproducible and reversible in the stochastic sense. Tests for reversibility are given which show how the equilibrium conditions can be computed from inspection of the data set. Second, an underlying flow structure to the model is assumed, and it is shown how equilibrium in this structure is...

Spatial majority voting equilibria and the provision of public goods

This paper develops general equilibrium conditions for urban areas where a pure public good is provided at a level decided upon by majority voting. Models with a property tax and a head tax and external land ownership are analyzed, and equilibrium solutions are compared using a specific form for the utility function. Optimal cities are characterized and compared to those emerging from the majority voting equilibria. Models where aggregate land rent is divided equally among the urban residents are also developed.

An Analysis of Lattice Dynamical Angular Force Models for Body Centered Cubic Metals

Abstract Present angular force models for lattice dynamical behaviour of body centered cubic (bcc) metals have been analysed for the satisfaction of rotational invariance and general equilibrium conditions. It has been found that most of the angular force models (except that due to Clark et al.) are deficient and leave the lattice under stress. Further it has been inferred that either the axially symmetric or the central pair potential schemes, incorporating the concept of electron pressure, provide the realistic picture of lattice excitations in metals.

Welfare and Savings Effects of Indexation

WE SEEK TO ACCOMPLISH two goals in this paper. First, we provide a clarifying discussion of the welfare implications of the introduction of indexed debt contracts in a financial market, an issue that has been discussed in [ 1, 9, 11] in this journal, as well as in [3, 12, 13]. We show that doubts about the Pareto-superiority of indexed debt contacts that have been raised in some of this literature are methodologically incorrect, and that, not surprisingly, the introduction of indexed debt contracts at an equilibrium of the nonindexed economy does indeed lead to a Pareto-superior allocation. Second, we derive and examine the implications of suffcient general-equilibrium conditions for (aggregate) savings to rise or decline as a result of the introduction of indexed debt. These conditions allow for general utility functions and take into account the fact that, in general, all prices may change as a result of the introduction of a contract that changes the asset economy. As a result, the conclusions derived are, in their rigor, generality and (as it turns out) simplicity, a significant improvement on the results of Levhari and Liviatan [4, 5] on the same issue. As in most of the literature in this area, our analysis is carried out in the framework of a two-period mean-variance model of consumption and portfolio choice, although

An elastic model of the large‐scale structure of duplex DNA

AbstractA general model for the large‐scale, time‐independent structure of duplex DNA is developed based on elastic considerations. The general conditions of elastic equilibrium are given. These equations are solved for the equilibrium shape of stressed duplex DNA, based on the assumption that the double helix behaves mechanically as a symmetric, linearly elastic rod. It is shown that, in general, two orders of superhelicity will arise at equilibrium. Several possible applications of this approach to the supercoiling of closed circular DNA are described.

Generalization of the classical theory of capillarity

Gibbs’ concept of dividing surfaces is supplemented explicitly by the concepts of dividing lines and dividing points. The general forms of the fundamental equations for dividing surfaces and lines are established by considering the proper extensive geometric properties, in addition to area and length. The detailed description of the fluid part of a capillary system by these fundamental equations is used to obtain the general conditions of equilibrium. Proper generalizations of the Laplace equation, the Neumann relation, and the Young equation are derived.

Imperfect Competition and the Resource Allocative Effects of Effective Protection

Given the importance of intermediate goods as inputs into production and in international trade flows, Corden [10] and others have argued that calculating effective rates of protection would yield more accurate information on the resource allocative effects of a given tariff structure than would calculations of nominal tariff rates. Subsequently, a number of authors have attempted to clarify the conditions under which particular measures of effective protection would be appropriate-appropriate in the sense of correctly indicating the resource allocative effects of a particular tariff structure. The principal concern has been to define an appropriate measure of effective protection when the input-output coefficients of intermediate inputs are variable. In fact, [1], [10], [11], [12], [13], [14] are but a few of the papers that have dealt with this question. A second major direction for enquiry has been the exchange rate effects of increasing or decreasing tariff protection. For example, [3], [11], [17] and [18] contributed to this literature and to the development of the concept of net effective protective rates. Recent work, including [3], [9], [11] and [19] has shed light on the affect of the existence of nontraded intermediate inputs on the formulation of an appropriate measure of effective protection. Finally [23] and [25] developed extensions of effective protection theory under general equilibrium conditions. The purpose of this note is to explore the effects of imperfect competition in input and output markets on the appropriateness of currently used measures of effective protection. Our simple contention is that market imperfections are as relevant and significant in their impact on whether or not effective protective rates will reveal the resource allocative effects of a given tariff policy as any of the factors already mentioned. To illustrate this point, we present a simple two-commodity, two-factor model in which each commodity is a fixed coefficient intermediate input into the production of the other. We assume that domestic production of importables occurs under conditions of pure monopoly. Under these conditions, we show that a tariff change leads to ambiguous results. The effect of tariff changes on the allocation of resources when factor markets are imperfectly competitive is explored in Section 2. Assuming that a labour union maintains wages in the importable goods sector at some fixed proportion above the wage rate in the production of exportables, we again demonstrate that the effects of a given tariff change on factor allocation, and production levels are uncertain.

THE IMPACT OF CORPORATE GROWTH ON THE RISK OF COMMON STOCKS

THE ORIGINAL WORK of Irving Fisher' on the application of the theory of consumer choice to the problem of allocating resources over time provides the classical economic foundation for the current theory of dividend valuation. If the future is known with certainty and capital markets are perfect the conditions of general equilibrium are such that the interest rate in each future period is equal to every individual's marginal rate of time preference for that period and the supply of loanable funds is equal to the quantity demanded. The theory is widely accepted as useful and it provides the rationale for discounting future income in order to arrive at its present value. The application of such discounting to the problem of common stock valuation is presented in the classic work of J. B. Williams.2 If the dividend per share of stock at the end of period t is denoted by Dt and if it denotes the general equilibrium rate of interest that reflects the marginal rate of time preference of every individual with respect to period t resource allocation then the value of the share at the end of period zero is given by

Physical principles of the theory concerning polymolecular adsorption films and capillary condensation of polar liquids

Analyzed are the general conditions of thermodynamic equilibrium in polymolecular adsorption films of polar liquids. Thermal equations of adsorption and a capillary condensation are derived for systems with a developed interphase boundary.

Model studies of capillary condensation. I. Cylindrical pore model with zero contact angle

The general conditions of equilibrium in capillary systems, and the production of entropy by irreversible processes during capillary condensation, are discussed with reference to a detailed consideration of the filling and emptying of a single uniform cylindrical capillary. The metastable states causing adsorption hysteresis in such a pore are identified. Exact calculations are presented for this model, and are verified by observations of these processes in macroscopic capillaries. Theoretical predictions of the entropy production accompanying the filling and emptying of a single model pore are given. The results are discussed in relation to experimental studies of real porous media.

The Moral Sanctity of Legal Functions

It has always been a matter of great philosophic import to clarify the relation of law to morality. There have been times, however, when the philosophical interest in clarifying this relation has become more intense because of a sense of urgency created by contemporary political upheaval. The present is such a time. One of the difficulties of philosophizing within a context defined by a sense of urgency is that prevailing political conditions and one's own immediate commitments concerning these conditions often lead one to philosophical extremes which do more to confound the philosophical issues involved than to clarify them. This confounding of issues is not only philosophically depressing but a cause for practical alarm since the practicing philosopher usually attracts some followers, if only among his students, who tend to act in accord with the espoused ideology. Given the fact that one either chooses or is forced to engage in direct political action because of the prevailing sense of urgency, the connection between one's philosophical position and his overt political action becomes rather intimate, more so than when one is lulled into inactivity by general conditions of social equilibrium. Unfortunately, sometimes a misguided ideology can discredit an entire position containing many valid points of real social significance which could stand without the accompanying ideology. In my judgment, many persons defending political anarchism at the present time, simply by virtue of their defense of that position, have done more to impede what otherwise are sound points of social criticism than they might have by simply remaining silent. What is particularly depressing is that some of the criticisms which they believe valid are ones which I believe to be valid. I am not urging that one disguise what he believes to be a correct political ideology for' reasons of political expediency, though in the appropriate circumstances such behavior might be quite desirable. What upsets me is that

Biochemical relationships and inorganic nitrogen equilibrium in semi-enclosed basins

In anoxic basins the oxidation of organic matter has so far been represented taking only the reduction of sulphate into consideration. Theoretical studies, however, show that anaerobic bacteria reduces nitrate prior to the reduction of sulphate. Hence, in representing the total redox reactants, the inclusion of ammonia gives a better representation of its relation to the total phosphate regeneration in stagnant basins. An attempt is made to study the state of equilibrium of the inorganic nitrogen compounds from measurements of the concentrations of nitrate-, nitrite-, and ammonia-nitrogen, using the parameter p E . The systems NO 2 ? - NO 3 ? , NH 4 + - NO 2 ? , and NH 4 + - NO 2 ? are applied for calculations. Studies are made of the variations of the three redox pairs in oxidising and in reducing environments. In narrow basins, under oxidising conditions, the system NO 2 ? - NO 3 ? is found to approach equilibrium values. From the proximity of the calculated values to the equilibrium values the system NO 3 ? - NO 2 ? - NH 4 + appears to exist at least in partial equilibrium, if not in total equilibrium conditions, in marine environments independent of the general equilibrium condition controlled by the system H 2 -H + -H 2 O. DOI: 10.1111/j.2153-3490.1969.tb00438.x

Biochemical relationships and inorganic nitrogen equilibrium in semi-enclosed basins<sup>1,2</sup>

In anoxic basins the oxidation of organic matter has so far been represented taking only the reduction of sulphate into consideration. Theoretical studies, however, show that anaerobic bacteria reduces nitrate prior to the reduction of sulphate. Hence, in representing the total redox reactants, the inclusion of ammonia gives a better representation of its relation to the total phosphate regeneration in stagnant basins. An attempt is made to study the state of equilibrium of the inorganic nitrogen compounds from measurements of the concentrations of nitrate-, nitrite-, and ammonia-nitrogen, using the parameter pE. The systems NO2- NO3, NH4+- NO2, and NH4+- NO2 are applied for calculations. Studies are made of the variations of the three redox pairs in oxidising and in reducing environments. In narrow basins, under oxidising conditions, the system NO2- NO3 is found to approach equilibrium values. From the proximity of the calculated values to the equilibrium values the system NO3- NO2- NH4+ appears to exist at least in partial equilibrium, if not in total equilibrium conditions, in marine environments independent of the general equilibrium condition controlled by the system H2-H+-H2O.

THE USES OF REGIONAL SCIENCE: POLICY PLANNING IN CHILE

Every scientific endeavor aims in some measure to be useful, either by deepening man's knowledge of the world or by extending his control over the objects of his knowledge. Regional science is no exception to this rule. Its fundamental concern is the changing pattern over time of relations between terrestrial space and society. We all know, of course, that the hoary distinction between the basic and applied sciences is badly misleading, especially when it suggests an hierarchical relation, with the basics peering down their noses upon an inferior species called planners or, with equal lack of logic, planners nodding condescendingly to useless basics. It is misleading because action itself generates knowledge and knowledge prompts action. Thus, an intimate relationship evolves between the two uses of science which, when it fails to be nourished, quickly leads to the debilitation of both. Action points to what is relevant; it insists on leading the scientist to the concrete problem itself. Science helps to define problems with greater precision and to choose the proper instruments for intervention. We propose to speak here as practitioners and planners, and, as such, we are perhaps more conscious of the great difficulties posed in passing from mathematical models that describe partial or general equilibrium conditions under highly artificial conditions to situations that are scientifically impure , imperfectly known, subject to change, and often uncomfortably real. And because we are engaged in trying to solve problems that matter to people, we always work under the pressure of great urgency and within a highly charged fieId of social values in tension. We do not dispose over unlimited time and our answers are never morally neutral. Nevertheless, the passage must be attempted. It would be fatal for regional science if its students resigned themselves to investigating the properties of abstract models--and damm the public and its problems! The theoretical and the practical must be joined in action. Should this require a change in the orientation of scientific behavior, let it be so. It is the way of all creative thought.

The equilibrium of heterogeneous systems including electrolytes. Part I.―Fundamental equations and phase rule

In his well-known memoir on the equilibrium of heterogeneous substances Willard Gibbs obtained the conditions of equilibrium in heterogeneous systems. The equations he obtained have been the basis of most subsequent applications of thermodynamics to material systems, and not a great deal of fundamental importance has been added. In one respect alone his results were comparatively meagre, namely in the case of electrolytes. The reasons for this Collected Papers. He there remarks: "The meagreness of the results obtained in my E. H. S. in the matter of electrolysis has a deeper reason than the difficulty of evaluation of the potentials. In the first place, cases of true equilivrium (even for open circuit) are quite exceptional. Thus the single case of unequal concentration of the electrolyte cannot be one of equilibrium, since the process of diffusion cannot be stopped . . . Again, the consideration of the difference of potential in electrolyte and electrode involves the consideration of quantities of which we have no apparent means of physical measurement, while the difference of potential in 'pieces of metal of the same kind attached to the electrodes' is precisely one of the things we can and do measure. The first of these reasons is no longer valid since many cases of electrode equilibria have been measured with as great or greater precision than equilibria of other types. It is still true that no reliable means of determining the single potential difference between two phases has been discovered, but it will be found to be of importance to proceed with the formulation of the conditiions of equilibrium in cases in which such differences of potential must be taken into account, for these are essential factors determining equilibrium not only in galvanic cells but between phases containing electrolytes in general. In this paper the method of Gibbs is employed to obtain the general conditions of equilibrium in systems containing electrolytes. Although a number of partial expressions are to be found in the literature, a complete statement does not appear to have been attempted before.