Showing papers on "Elasticity (economics) published in 1970"

Large elastic deformations

Abstract: In a previous chapter, the foundations of the classical theory of elasticity have been presented. It is concerned with the description and explanation in terms of a unified theory of the relations which are observed between load and deformation for elastic solids of various shapes, sizes, and compostions. The elastic character of the materials to which the theory is applicable may be loosely described as follows: If a body of elastic material is subjected to a load, it will be deformed and on the removal of the load will regain its initial dimensions and shape. In the concept of the elastic solid is also contained the assumption that the mechanical system constituted by an elastic solid and a system of forces applied to it is a system in which energy is conserved. The work done by the applied forces during the iso thermal deformation of the body is balanced by potential energy stored in the elastically deformed body and the kinetic energy of the various parts of the body and the members through which the deforming forces are applied.

The mechanical properties of bone

Abstract: 2 Department of Anatomy and Highway Safety Research Institute, The University of Michigan, Ann Arbor, Mich. 48104. BONE is the material with which the orthopaedic surgeon deals. Consequently, some knowledge of its mechanical properties is of importance for an understanding of the mechanism and management of fractures, as well as the design of prosthetic or orthotic appliances and protective gear, e.g., crash helmets. The behavior of a body under a load or force is a function not only of the form and structure of the body, but also of the mechanical properties of the material composing the body. For example, a steel beam will support a higher load before breaking and will behave differently under loading than will an oak beam of exactly the same shape and dimensions because of differences in the mechanical properties and structure of steel and of wood.

Regimes of Elastohydrodynamic Lubrication

Abstract: The different regimes of behaviour in the elastohydrodynamic lubrication of rollers are displayed on a chart whose rectangular co-ordinates express the influence of elasticity of the solids and var...

Contact problem of the theory of elasticity

Abstract: : The first chapter of the book is devoted to methods of the solution of fundamental equations of the contact problem. The second part contains, together with the classical investigations, an account of certain works of Soviet mathematicians on the two-dimentional contact problem of the theory of elasticity, including my works, part of which has been published for the first time. These include: a new formulation of the problem on the pressure of a stamp on an elastic half-plane, and the periodic contact problem. An attempt is made to calculate surface deformations, which up till now were not calculated in the theory of the contact problem. A number of new solutions are given for an axisymmetric contact problem of the theory of elasticity. The book should be regarded as a division of the mathematical theory of elasticity, since it is devoted to the solution of basic contact problems of the theory of elasticity.

On the empirical relevance of the ces production function

Abstract: W ITH the pathbreaking article by Arrow, Al Chenery, Minhas and Solow [1] introducing the constant elasticity of substitution (CES) production function, interest in production theory has multiplied. No longer is the Cobb-Douglas function the workhorse for neoclassical theory; rather, the role of the production function has been examined anew in the theory of the firm, in growth theory, and in the theory of international trade. This re-examination has taken the form (1) of theoretical analysis of the role of the elasticity of substitution, (2) of empirical estimation of the elasticity, and (3) of the introduction of new forms for the production relation, e.g., Zellner and Revankar [14] and Revankar [8]. Unfortunately, knowledge about the appropriate micro-economic or macro-economic production function seems further away now than before 1961, the year of the ACMS article [1]. Nerlove [7, p. 58] reports that "even slight variations in the period or concepts tend to produce drastically different estimates of the elasticity [of substitution] " and he presents a summary of empirical studies of the CES production function to support his conclusion. In this paper it is first shown that Nerlove's conclusion on the definition of time periods is an inappropriate interpretation of previous estimates (however, part of the difficulty was outside Nerlove's control); that in fact changes in period do not produce significantly different estimates of the elasticity. To demonstrate this contention, estimates of the elasticity from the factor demand equation for labor for two consecutive years are obtained. However, evidence of serial correlation leads to a correction of the labor and wage rate variables for quality variation in the workers over states. Since this correction does not remove the serial correlation, the estimation is then undertaken using the efficient estimation technique of Zellner [12] and the results suggest that use of different time periods does not produce different estimates of the elasticity. Second, the estimates of the elasticity are constrained to be equal for the two years and the efficient estimation techniques are again used with the labor quality correction included. A test on the null hypothesis that the elasticity of substitution equals one for each industry indicates that the elasticity does not in general depart significantly from one. This conclusion from estimates of the labor demand equation supports a similar conclusion of Griliches [3, p. 292] based upon least squares regressions for two-digit manufacturing industries. However, he uses a smaller sample (only 1958 data) than here, and his estimates are biased toward one because labor quality variation was not included in his two-digit industry estimates (he only considers labor quality variation in his estimates for manufacturing as a whole). Third, direct estimates of the CES production function are obtained for each industry using Kmenta's approximation [5]. Again, using efficient estimation and correcting for labor quality differences across states, the elasticity of substitution is not in general significantly different from one. It is incidentally shown that returns to scale can be accepted as being equal to unity for most industries.

A method for measuring human skin elasticity in vivo with observations of the effects of age, sex and pregnancy.

Abstract: SUMMARY 1. A method is presented for the measurement of the elasticity of human skin in vivo. A simple suction cup device is applied to the intact skin and the distortion produced in response to pre-determined negative pressures recorded. By the use of appropriate formulae stress and strain may be calculated and a stress/strain curve drawn, the gradient of which represents the elastic modulus for intact skin. 2. The test, which is simple to perform and entirely innocuous to the patient, has been shown to achieve acceptable standards of accuracy and reproducibility. 3. In the present study, the physiological variation in skin elasticity that occurs in respect of age, sex and pregnancy is investigated and the implications concerning the physiological changes that occur in skin collagen discussed. The elastic properties of skin have interested physicians for a considerable period of time. However, no satisfactory method has been evolved of measuring skin elasticity in the living subject and enabling the result to be expressed in absolute terms. A number of workers have measured the elasticity of human and animal skin in vitro using the conventional ‘strip’ method on specimens of skin removed from the body (Rollhauser, 1950; Dirnhuber & Tregear, 1966). An alternative technique was introduced by Dick (1951). By this method, a circle or diaphragm of skin is clamped peripherally and uniform pressure is applied from below by raising the pressure in a water-filled chamber (Fig. 1). The distortion produced represented by the height of the resulting dome of skin can be measured by a suitable recording device. Tregear (1966), using the standard formulae that represent pressure changes across spherical membranes, evolved the following formulae to express stress (T) and strain (S) in this system in mathematical terms.

A New Approach to Plasticity and Its Application to Blunt Two Dimensional Indenters

Abstract: The classical slip line field solution for a two-dimensional punch is found to give a constraint factor (2.57) which i s too small when the specimen beneath the punch is extensive. A new approach based on elasticity provides a constraint factor of 2.75. The new method of analysis also enables residual stresses to be estimated and indicates that plastic $ow occurs not only when the specimen i s loaded, but also when i t i s unloaded. Several details concertzing the performance of hardness indenters are explained by the new theory for the first time.

Tissue Conditioners: II. Rheologic Properties

Abstract: The rheology of proprietary and experimental tissue conditioners was studied. Viscoelastic properties were examined to evaluate the role of ethanol in the liquid component and the effect of temperature. Experimental materials were prepared that corresponded closely to the proprietary materials in their viscoelastic properties.

Stability of a Relaxation‐Type Viscoelastic Fluid with Slight Elasticity

Abstract: A viscoelastic fluid of a relaxation type having a single relaxation time is studied. The effect of slight elasticity on the hydrodynamic stability of a plane Poiseuille flow is investigated by the linearized method of small two‐dimensional disturbances since it is shown that Squires' theorem is valid for the fluid chosen. The resulting equation is a modified Orr‐Sommerfeld equation. The equations are solved numerically, and it is shown that the critical Reynolds number is lowered as the magnitude of the relaxation number is increased.

A method of estimating tensile properties of materials tested in indirect tension

Abstract: Equations were developed for estimating values of modulus of elasticity, Poisson's ratio, and tensile failure strains for circular specimens based upon total horizontal and vertical deformations created in the specimen during indirect tensile testing. A study was undertaken to verify the theoretical relationships for estimating the elastic constants of modulus of elasticity, Poisson's ratio, and tensile strains. To substantiate the equations a circular aluminum specimen, which is considered to exhibit a high degree of elasticity, was tested in indirect tension. The aluminum specimen was instrumented with rosette strain gages at the center. The results indicated that the elastic properties can be obtained from total horizontal and vertical deformations of an elastic material tested in indirect tension. Additional tests were conducted to evaluate the effect of the dimensions of the curved loading strip used in the indirect tensile test and to evaluate the effect of loading rate (vertical strain rate). The results indicated that for best results a 1/2-inch-wide curved loading strip should be used to estimate the modulus of elasticity and Poisson's ratio from total deformation information. It was also found that the dimensions of the curved loading strip used had no significant effect on the tensile strain at the center of the circular aluminum specimen. The loading rate had a significant effect on Poisson's ratio but had no practical engineering effect on the modulus of elasticity.

Price and Output Response of Marketed Surplus of Foodgrains: A Cross-Sectional Study of Some North Indian Villages

Abstract: If foodgrains producers are also the major consumers, price elasticity of production and price elasticity of marketed surplus should be distinguished. While the former is likely to be positive, the latter may theoretically assume either sign, and this introduces a complication in deriving the long‐run price elasticity of marketed surplus. Village‐level, cross‐sectional data are used to get a direct regression estimate of the short‐run price elasticity of marketed surplus for northwest India. The estimate seems to indicate negative elasticity. Other variables with statistically significant influence on marketed surplus are production level of foodgrains and income from milk.

A Cobb-Douglas Production Function with Variable Returns to Scale

Abstract: T HE OBJECTIVE of this paper is to present a production function with variable returns to scale over the range of the function. A modified form of the Cobb-Douglas function is developed for this purpose. Data from a sample of farms are used to estimate the parameters of the modified function utilizing single-stage least-squares estimation. The empirical results are presented and some implications of the estimated elasticities of production are discussed. Many attempts have been made in the past to find algebraic forms that are theoretically appropriate and empirically useful for describing and estimating the functional relationships between inputs and outputs [7]. Each alternative functional form has advantages, but each usually imposes certain limitations on the input-output relationship. The conventional Cobb-Douglas function, for example, assumes unitary elasticity of factor substitution and partial and total production elasticities that do not vary over ,the range of the function. Recent efforts to develop more general forms of production functions have focused almost exclusively on the elasticity of factor substitution. Examples of such efforts include the constant elasticity of substitution function [1], the class of homothetic isoquant production functions [2], transcendental production functions [5], and the variable elasticity of substitution production function [6]. These new functional forms elevate the elas-

The equation of state for rubber elasticity: the effect of swelling on the front factor.

Abstract: : The 'front factor' in the equation of state for fubber elasticity has been measured for a poly (dimethylsiloxane) network swollen in a series of swelling agents. The intrinsic viscosity of a linear poly (dimethylsiloxane) polymer in these swelling agents was also measured. Comparison of the intrinsic viscosity and 'front factor' values indicate that the change in modulus of the network upon swelling arises from the change of preferred conformation of the network chains due to interaction with the swelling agent. (Author)

Identification and Specification Analysis of Alternative Equations for Estimating the Elasticity of Substitution

Abstract: The elasticity of substitution between capital and labor is a fundamental parameter describing the structure of production in an economy or its component sectors. This elasticity is a measure of the relative ease with which these factors may be substituted in production; and for this reason, it plays a crucial role in most modern partial and general equilibrium models of income distribution [1, 3, 8, 11, 12, 13, 14, 15, 21, 22, 23, 25, 27, 28, 37, 38], international trade [3, 24, 26], and economic growth [1, 3, 13, 31, 36, and comments on 31, in 6, 32]. Following the introduction of the constant elasticity of substitution (CES) production function by Arrow, Chenery, Minhas, and Solow (referred to hereafter as ACMS) [3], a great deal of professional interest has centered on the estimation of the elasticity of substitution (a) in the aggregate U.S. economy and among its industries or sectors. In particular, ACMS showed that under the assumptions of (i) constant returns to scale, and (ii) purely competitive product and factor markets, the elasticity of substitution could be estimated from the