Constant Elasticity Of Substitution Research Articles

Solution of the system of nonlinear PDEs characterizing CES property under quasi-homogeneity conditions

The constant elasticity of substitution (CES for short) is a basic property widely used in some areas of economics that involves a system of second-order nonlinear partial differential equations. One of the most remarkable results in mathematical economics states that under homogeneity condition i.e. the production function is a homogeneous function of a certain degree, there are no other production models with the CES property apart from the famous Cobb–Douglas and Arrow–Chenery–Minhas–Solow production functions. In this paper we generalize this classification result to a much wider framework of production functions under quasi-homogeneity conditions, showing in particular the existence of three new classes of production models with the CES property.

Моделирование динамики валового регионального продукта

The gross regional product is a key macroeconomic indicator that characterizes the development of the regional socio-economic system. Modeling the dynamics of this indicator, as the final product of the economic system, also involves the development of models for changing the values of aggregated cost factors associated with its production. One of the directions of using the developed models is the formation of short-term forecasts of the direct values of the gross regional product and the factors of labor and capital costs of the regional economy that determine them. Aim. Modeling the dynamics of the value of the gross product of the regional economy of the Yamal-Nenets Autonomous Okrug on the basis of the one-sector model of R. Solow for the formation of short-term forecasts of the value of this indicator. Materials and methods. The one-sector model of economic growth by R. Solow is used, in which the functioning of the regional economy is described by two-factor neoclassical functions with a constant elasticity of substitution of factors of production costs. Production functions are identified using retrospective sequences of indices of gross regional product and cost factors of the regional economy. Short-term forecasting of the gross product of the regional economy is carried out using a production function that provides a better approximation of retrospective data of the time interval of the previous forecasting year. Results. Neoclassical two-factor production functions with constant elasticity of substitution of cost factors of the regional economy of the Yamalo-Nenets Autonomous Okrug (YNAO) for the period from 2001 to 2018 were constructed.The values of the gross regional product and the average annual number of employed in the Yamal-Nenets economy were calculated for 2017–2019, which were compared with the corresponding data published by the Federal State Statistics Service of the Russian Federation, and the forecast values published by the regional administration. Conclusion. It has been established that the used production functions give acceptable estimates of the approximation of the actual values of the gross regional product of the considered regional economy in the considered time interval. Modification of the models for changing the values of cost factors made it possible to increase the accuracy of short-term forecasts, both directly of the values of the gross regional product and the values of factors of labor and capital costs.

Study on Agglomeration Level and Effect of Equipment Manufacturing Industry in the Yangtze Delta Urban Agglomeration

This paper analyzes the agglomeration level and agglomeration effect of 8 subindustries of equipment manufacturing industry and 26 prefecture-level cities in the Yangtze River Delta (YRD). From the perspective of industry, the agglomeration change trend of 8 subsectors of equipment manufacturing industry from 2006 to 2016 in the Yangtze River Delta Urban Agglomeration (YRDUA) is analyzed. From the perspective of cities, the spatial differences of equipment manufacturing agglomeration degree in 26 prefecture-level cities in the YRDUA are discussed. By using CES production function, the agglomeration effect of equipment manufacturing agglomeration is studied. The results show that the YRDUA has formed an agglomeration pattern of equipment manufacturing industry, with Shanghai as the core, and Hefei, Hangzhou, Suzhou, and Nanjing as the auxiliary cities, and the overall agglomeration effect in the region is relatively obvious.

The Neoclassical Growth Model and the Labor Share Decline.

The labor share may be declining in the data, but it is often assumed constant in neoclassical growth models (NGM). We assess the quantitative importance of this discrepancy by comparing alternative calibration approaches featuring constant and declining labor shares. We find little difference in model performance. Our results derive from strong general equilibrium effects: while a declining labor share mechanically lowers wage growth, the investment response pushes wages back up. Hence, different models deliver nearly identical paths of macro aggregates. Numerous robustness checks (including a CES production function, different time periods, and calculations of the labor share) reinforce the similarity of performance across model specifications. We conclude that the NGM with a constant labor share is still an appropriate choice to study many standard macro aggregates.

Assessment of CES Function Parameters in Oil-Rich CIS Countries

The article analyses balance between the capital and labor market in the CIS countries rich in hydrocarbon resources – Azerbaijan, Kazakhstan and Russia. For this purpose, the impact of capital (fixed assets) and labor (employed population) on the production volume (on GDP) was estimated based on the relevant statistical data from these countries using production function analysis. The parameters of CES production function were determined in the Mathcad system by the nonlinear least-squares method. The subject of the research has enhanced relevance due to the lack of extensive research of the problem posed in the oil and gas-rich countries of the CIS, and the research evaluates the balance between capital and labor markets for the first time in resource-abundant countries. From the results, it can be seen that for each of these three countries the distribution coefficient for capital is significantly higher than that for the labor factor. This means that there is an excess of capital that cannot be started. This is typical for the countries rich in natural resources. The main reason for this process is the complex structure of increasing capital with oil revenues and low level of specialization of the existing labor force to launch this capital. Moreover, according to the results obtained from the CES production function, the substitute elasticity coefficient in oil-rich countries of the CIS is less than one. The study summarizes the current problem as an imbalance between the capital (fixed assets created using modern technology) and the labor market (labor to leverage key assets using potential opportunities). Based on the analysis, the results obtained from modeling is formulated and scientifically grounded recommendations have been provided for the improvement of education and its quality in these three countries, especially in Russia and Azerbaijan.

Depth and breadth relevance in citation metrics

AbstractThe Euclidean length of a citation list is “depth relevant”: the metric increases when citations are transferred from less to more cited papers. We introduce “breadth relevance,” which favors consistent achievers over one‐hit wonders. The exponent of the CES aggregator then is less than unity rather than greater than unity, as for depth relevance. Using two datasets on citations of economists for the top 50 US and global universities, simply counting citations maximizes the correlation between the citation metrics of researchers and the peer‐reviewed rank of their department. However, citation depth may explain the allocation of researchers across lower‐ranked departments.

Định dạng hàm sản xuất CES bằng phương pháp hồi qui phi tuyến tính Bayes (Specifying a CES Production Function Using a Bayesian Non-linear Regression)

Vietnamese Abstract: Đa phần cac nghien cứu tại Việt Nam sử dụng ham sản xuất Cobb-Douglas va cac biến thể của no như một cong cụ trong phân tich va dự bao kinh tế. Dạng ham nay co nhược điểm la cac tiền đề của no qua cứng nhắc ma khong phu hợp với hiện thực trong nhiều trường hợp, đặc biệt trong phân tich động thai tang trưởng kinh tế. Ham CES (constant elasticity of substitution) với tiền đề linh hoạt hơn, cụ thể la hệ số co gian giữa vốn va lao động khac một, được sử dụng ngay cang phổ biến. Do vậy, nghien cứu nay được thực hiện nhằm định dạng ham CES dựa tren dữ liệu của cac doanh nghiệp phi tai chinh niem yết tren thị trường chứng khoan Việt Nam. Bằng việc sử dụng phương phap hồi quy phi tuyến tinh Bayes thong qua thuật toan lấy mẫu Random-walk Metropolis Hastings (MH), tac giả kham pha rằng, ham sản xuất được ước lượng cho cac doanh nghiệp phi tai chinh Việt Nam la dạng ham CES với hệ số co gian thay thế giữa vốn va lao động nhỏ hơn một, tức la lao động va vốn bổ sung nhau. Phat hiện nay cho thấy nền kinh tế Việt Nam co thế đối diện với đa trạng thai dừng (multiple steady-states) va cac bẫy ngheo đoi (poverty traps) nen chưa đạt được cac khả nang cho tang trưởng nội sinh (endogenous growth). English Abstract: Most studies in Vietnam use the Cobb-Douglas production function and its variants as a tool in economic analysis and forecasting. A great disadvantage of this functional form is that its propositions are extremely rigid, which is not in agreement with reality in many cases, especially in analyzing economic dynamics. The CES (constant elasticity of substitution)function with more flexible propositions, namely the elasticity of substitution between capital and labor different from unity, is used more and more popularly. Therefore, this study was conducted to specify a CES function based on data of non-financial businesses listed on Vietnam's stock market. By using a Bayesian non-linear regression through the Random-walk Metropolis Hastings (MH) sampling algorithm, the author finds that the estimated production function for Vietnamese non-financial enterprises is a CES one with the elasticity of substitution between capital and labor smaller than one. This finding shows that Vietnam's economy might face multiple steady-states and poverty traps, so it has not yet reached the possibilities of endogenous growth

Vertical mergers with input substitution: Double marginalization, foreclosure and welfare

We consider differentiated duopolists that face symmetric linear demands and produce using Cobb–Douglas technologies with a monopolized input and a competitively supplied input. A merger between the input monopolist and either firm eliminates double marginalization but – unlike​ with fixed-proportions technologies – can lead to foreclosure and reduce welfare. The same can occur under a CES technology with greater input substitutability than Cobb–Douglas. With identical Cobb–Douglas technologies, the merged firm raises the rival’s cost by more, and the welfare effects are worse, when the input it controls constitutes a low rather than high share of input costs. With different technologies, the welfare effects can be non-monotonic in that input’s share of costs.

Income and factor substitution: an investigation on the Solow growth model under the constant elasticity of substitution

PurposeThe purpose of this study is to examine whether the elasticity of substitution (ES) varies between developed and developing countries.Design/methodology/approachThe author derives the growth regressions from the Solow model under the constant elasticity of substitution production function by using the first-order Taylor series expansion and estimate them for each country group classified based on time-varying behavior of income per worker using the data-driven algorithm.FindingsThe ES is not unitary and varies among country groups. Developed countries generally have a higher ES than developing countries.Originality/valueFor the first time, the author uses the first-order Taylor series expansion to linearize the steady-state value of income per worker, as the author considers this approach to be relatively more straight-forward and tractable. Furthermore, the author estimates the equations using both cross-section and panel data techniques and employs the data-driven algorithm proposed by Phillips and Sul (2007) to classify countries.

KEY ASPECTS OF USING NUMERICAL METHODS IN THE MECHANISM OF INVESTMENT OF SMALL AND MEDIUM-SIZED BUSINESS ENTERPRISES

In today's realities of investment activities, small and medium enterprises are faced with the dilemma of choosing areas of investment of monetary and non-monetary resources. Determining the feasibility of a particular investment is based on the use of appropriate mathematical apparatus and economic-mathematical models. The article considers some of the most important aspects of the use of numerical methods in the mechanism of investment of small and medium enterprises, developed on the basis of research on the development of such economic entities. The logical basis of the proposed methods is a proven division of the term of operation of enterprises into several stages of the life cycle, which differ significantly in the characteristics of incoming and outgoing cash flows. It is proposed to determine the absolute expediency of founding small and medium enterprises by calculating the probabilistic values of profitability of the enterprise based on the calculation of the area of geometric shapes limited by the functions of income and expenses during all stages of the life cycle. It is proved that such calculations are expedient by calculating the indefinite integral and applying the Newton-Leibniz formula.With regard to the functions that characterize the income and expenses of small and medium enterprises throughout their existence, the article proves that the most optimal in this case is the use of production functions. Among the whole set of existing production functions, we have identified the most optimal for the task Cobb-Douglas production function, CES production function, Linear production function, Leontief production function, adapted to the conditions of the microlevel. To calculate the elementary areas limited by the corresponding production functions, the article examines the relevant existing methods. Studies have been conducted on the possibility of using to calculate the areas limited by the production functions of income and expenses of small and medium enterprises during each stage of the life cycle, the methods of rectangles, trapezoids and parabolas. It is determined that they have limited conditions for use due to the need to divide the time period of operation of enterprises at intervals that do not coincide with the stages of the life cycle. Therefore, studies were continued, as a result of which it was proved that the most optimal method of calculating the elementary areas limited by the target functions of income and expenditure of small and medium enterprises is the Gaussian method with different variations.

The dual Lovász extension operator and the Shapley extension operator for TU games

An extension operator assigns to any TU game its extension, a mapping that assigns a worth to any non-negative resource vector for the players. Algaba et al. (2004) advocate the Lovász extension (Lovász, 1983) as a natural extension operator. This operator is determined by the minimum operator representing one particular CES (constant elasticity of substitution) technology. We explore alternative extension operators, the dual Lovász extension and the Shapley extension, that are based on the only two alternative CES technologies that induce an economically sound behavior of extensions in some sense, the maximum operator and the average operator.

The wage premium and market structure: theory and empirical evidence from Chilean manufacturers

PurposeThis paper aims to examine how the “wage premium,” the percentage by which wages earned by skilled workers exceed those of unskilled workers, varies across industries characterized by different levels of competitiveness.Design/methodology/approachA theoretical model employing constant elasticity of substitution (CES) utility function and constant returns to scale production function is developed and analyzed to derive the effects of industry competitiveness on the wage premium. Econometric methods are applied to Chilean manufacturing data to test implications of theoretical model.FindingsOnce the relative factor endowment is being controlled, market competition significantly reduces the wage premium. More specifically, given with the same relative factor endowment, the wage premium is significantly higher under oligopolistic competition than under monopolistic competition. Empirical evidence from Chilean manufacturers supports our theoretical conclusions.Practical implicationsDuring economic development, the reallocation of production factors from unskilled labor-intensive to skilled labor-intensive industries raises the wage premiums received by skilled workers. Besides, skilled workers will earn higher wages by working in more highly concentrated industries instead of more competitive industries. This needs to be considered by government policymakers who must balance promotion of technical change with prevention of extreme the income inequality.Originality/valueThis paper examines how market structure affects wage premiums, providing new insights into a well-established literature that largely maintains that wage premiums are primarily a function of relative factor endowments or international trade.

The relationship between labor productivity and number of operating firms

This paper constructs a theoretical model matching empirically observed relationships between average labor productivity and the number of operating firms. The models in the related literature which utilize CES utility function find no relationship between average labor productivity and the number of operating firms in the economy (Melitz, Marc J. [2003. “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity.” Econometrica 71 (6): 1695–1725] and many versions of this model). Moreover, the models which utilize non-homothetic preferences with a numeraire good find a positive relationship between average labor productivity and the number of operating firms (Melitz, Marc, and Gianmarco I. P. Ottaviano [2008. “Market Size, Trade, and Productivity.” Review of Economic Studies 75: 295–316] and many versions of this model). However, the model developed in this paper provides a single theoretical framework that depending on the source, a rise in the average labor productivity may lead to an increase or a decrease in the number of operating firms. In line with our results, we provide empirical evidence from ten European countries for the 2008–2016 period, which shows that the correlation between these two variables is positive for some of the countries, while negative for the others.

Vertical Mergers with Input Substitution: Double Marginalization, Foreclosure and Welfare

We consider differentiated duopolists facing symmetric linear demands and using Cobb-Douglas technologies with two inputs: a monopolized input and a competitively supplied input. Unlike with fixed-proportions technologies, a merger between the input monopolist and either firm can reduce welfare. The merged firm raises the input price to the rival by more—sometimes inducing complete foreclosure—when that input constitutes a lower share of the rival’s input costs. If that share is sufficiently low then welfare declines, while rising elsewhere despite foreclosure. The merger also can reduce welfare under a CES technology with greater input substitutability than Cobb-Douglas, though the foreclosure and welfare effects are no longer monotonic in the monopoly input’s share of downstream costs.

Inverse problems in analysis of input-output model in the class of CES functions

Abstract The article proposes a modification of the approach to the analysis of inter-industry balance. Instead of linear models of inter-industry balance, based on the hypothesis of W. Leontief about the constancy of the cost standards of production factors, the article studies nonlinear models. For the case of production functions with constant elasticity of substitution (CES) an algorithm for solving the inverse problem is proposed, which allows to identify the model of nonlinear inter-industry balance based on the data of the symmetric input-output table. Based on the Young transform and Fennel duality, with the help of this model, we develop a technology for analyzing inter-industry relationships. The technology has been tested on the data of economic statistics of Russia.

General Equilibrium in a Heterogeneous-Agent Incomplete-Market Economy with Many Consumption Goods and a Risk-Free Bond

We study a pure-exchange incomplete-market economy with heterogeneous agents. In each period, the agents choose how much to save (i.e., invest in a risk-free bond), how much to consume, and which bundle of goods to consume while their endowments are fluctuating. We focus on a competitive stationary equilibrium (CSE) in which the wealth distribution is invariant, the agents maximize their expected discounted utility, and both the prices of consumption goods and the interest rate are market-clearing. Our main contribution is to extend some general equilibrium results to an incomplete-market Bewley-type economy with many consumption goods. Under mild conditions on the agents' preferences, we show that the aggregate demand for goods depends only on their relative prices and that the aggregate demand for savings is homogeneous of degree in prices, and we prove the existence of a CSE. When the agents' preferences can be represented by a CES (constant elasticity of substitution) utility function with an elasticity of substitution that is higher than or equal to one, we prove that the CSE is unique. Under the same preferences, we show that a higher inequality of endowments does not change the equilibrium prices of goods, and decreases the equilibrium interest rate. Our results shed light on the impact of market incompleteness on the properties of general equilibrium models.

The Effect of Recent Technological Change on US Immigration Policy

Did recent technological change, in the form of automation, affect immigration policy in the United States? I argue that as automation shifted employment from routine to manual occupations at the bottom end of the skill distribution, it increased competition between natives and immigrants, consequently leading to increased support for restricting low-skill immigration. I formalise this hypothesis theoretically in a partial equilibrium model with constant elasticity of substitution in which technology leads to employment polarization, and policy makers can vote on immigration legislation. I empirically evaluate these predictions by analysing voting on low-skill immigration bills in the House of Representatives during the period 1973-2014. First, I find evidence that policy makers who represent congressional districts with a higher share of manual employment are more likely to support restricting low-skill immigration. Second, I provide empirical evidence that representatives of districts which experienced more manual-biased technological change are more likely to support restricting low-skill immigration. Finally, I provide evidence that this did not affect trade policy, which is in line with automation having increased employment in occupations exposed to low-skill immigration, but not those exposed to international trade.

On the uniqueness of the solution of the cost minimization problem with generalized Sato production function

Whenever a firm is maximizing its profit, it necessarily has to minimize its cost. Thus, the cost minimization problem is one of the central problems in the theory of the firm. When presenting this problem, the majority of microeconomic textbooks use very well-known production functions, such as Leontief, Cobb-Douglas, or other CES production functions. The goal of this paper is to analyze the cost minimization problem with the generalized Sato production function. The generalized Sato production function is one of the non-standard production functions with variable elasticity of substitution. First, we show that the generalized Sato production function is continuous, strictly monotone, strictly quasiconcave and that a positive amount of output requires positive amounts of some of the inputs. Next, by using mathematical programming we show that the cost minimization problem with generalized Sato production function has a unique solution. This result is very important since it implies the existence of the corresponding cost function and conditional input demands.

Existence of non-trivial steady-state equilibria in an overlapping generations model: A CES production function of which elasticity of substitution is less than one case

Existence of non-trivial steady-state equilibria in an overlapping generations model: A CES production function of which elasticity of substitution is less than one case

Cooperative Federated Learning-Based Task Offloading Scheme for Tactical Edge Networks

In this study, we focus on the federated learning (FL) based tactical edge network platform to cooperatively operate computation-hungry tasks as efficiently as possible. Based on the incentive of FL model training, each individual device makes offloading decisions for their tactical tasks in resource-constrained network environments. According to the ideas of two different bargaining solutions - weighted average solution and constant elasticity substitution solution - edge server and IoT devices work together in a coordinated manner to approximate a well-balanced system performance. Therefore, we can reach an agreement while exploring the mutual benefits to leverage a reciprocal consensus between different viewpoints. The main novelty of our approach is to investigate the dual-interactive bargaining process based on the interdependent relationship between IoT devices and the tactical edge server. To the best of our knowledge, this is the first work that jointly considers different bargaining solutions to handle tactical edge-assisted task offloading services. Based on the numerical simulation, it is demonstrated that the proposed approach can increase the system throughput, device payoff and device fairness up to 10%, 15% and 20%, respectively, in comparison with existing protocols.