Совокупная общая производительность факторов и совокупная эластичность замещения в моделях с промежуточными товарами
We consider the dependence of the growth arte on the elasticity of substitution within the framework of a model with the agents' mutual dependence. This model is interpreted as a network structure. the development is explined as the agents' valus increase in a dynamic system described by functions which display constant elasticity of substitution (CES). We investigate the cases of high and low complementarity of activities. In particular, we receive conditions allowing to identify the cases when the elasticity of substitution has the positive (negative) effect on growth rate under high (low) complementarity of activities. Additionally we analyse the influence of the individual agent's productivities on the growth rate. Finally we give a potential generalisation of the model allowing for different growth rates of the agents.
Relation between curvature and the elasticity of substitution is the old question important for economic theory. Opinions of economists concerning presence or absence of a link between these two concepts radically diverge. Also now there is a steady trend of the use of the Arrow-Pratt coefficient of relative risk aversion and the coefficient of relative prudence as characteristics of utility functions and production functions even in non-stochastic models, and these two coefficients are also commonly interpreted as measures of curvature. The purpose of the paper is to contribute to clarification of the links between all these concepts. We suggest a simple unifying approach based on the notions of prototype functions and osculating curves. In framework of this approach we easily derive the classic geometric curvature and show the relations between the Arrow-Pratt coefficient, the prudence coefficient, the elasticity and the elasticity of substitution. As an example, demonstrating the role of such relations in economic models, we study a simple macroeconomic model with a non-homothetic production function.
A class of Solow production functions is a natural extension of the class of the CES functions and the Cobb--Duglas functions. We give a complete descriptions of this class in terms of various differential characteristics such as various elasticity measures. We use also differential description of quasi-homogeneous functions. We give also new characterization of the class of multifactor production functions which such that the elasticity of substitution of each factor by another one is constant and the same for each pairr of factors. We show also that each quasi-homogeneous multifactor function which can be linearized via an autonomous scaling of its arguments is a Solow function.
The second edition of a paper from `Economics and Mathematical Methods' in a collection of selected works of George Kleiner in occasion of his 70th birthday.
This article is focused upon the survival of democratic regimes and successfulness of democratization. The dynamical mathematical model is presented in the paper. The model’s departing point is the hypothesis of S.M. Lipset and A. Przeworski that the growth of the welfare leads to a mitigation of the interest groups` conflict over the redistribution of resources. This mitigation is met as a result of interrelated processes of broadening of a «compromise space», which is a range of mutually accepted policies, and of a convergence of different groups` preferences over the redistribution in an area of moderate policies.
The presented model illustrates how social capital (more precisely – its component responsible for trust between strangers) and institutional quality favor the stabilization of democratic regimes through the increase of economic productivity and welfare. According to the predictions of the model, total factor productivity (TFP) – understood as the opportunity of individuals and/or firms to cooperate efficiently – increases the overall wealth of the society given the same stock of human capital. It fosters the consolidation of democracy due to reduction of social tensions and improvement of functioning of democratic mechanism of economic policy elaboration. Following these results the hypothesis of positive impact of TFP on the survival of democracy is formulated.
The hypothesis was tested by means of survival analysis on the quantitative database on episodes of democratization («Regimes in the World»). The survival analysis showed that TFP is a significant and important predictor that lowers the risk of unsuccessful ending of the democratization episode (of the return back to more autocratic regime). The increase in TFP on 10 percentage points is ceteris paribus associated to the decrease of risk of leaving the track of democratization in 1.2-1.4 times. The obtained results are robust to the changes in the model specification or in a list of control variables.