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Like in the previous chapter we try to collect production functions that may prove useful in a global dynamic analysis. In particular we focus varieties of the constant elasticity of substitution function with negative exponents which have been hardly used at all, but which prove most useful if we want to incorporate capacity constraints in production and cost functions. Combined with “putty/clay” ideas of malleable versus fixed capital during investment periods from the 1970s this much facilitates the discussion of evolving competition among few big firms to many small firms.

In container shipping practices, containers owned by the shipping lines and leasing companies are generally regarded as homogeneous factor inputs and can substitute each other perfectly in providing the shipping service. Based on industry-wide data, this study surprisingly finds that the behavior of container selection for container shipping lines does not follow the pattern of perfect substitution, but rather the pattern of fixed proportions technology, through a constant elasticity of substitution production function. Combined with the observed relationship between the approximately constant leasing rates and the shrinking price premiums for leasing companies over the past two decades, the empirical results suggest that concerns with both the capital cost and strategic means may play key roles in determining the mix of owned and leased containers for the shipping lines. Several strategic concerns including the long-term leasing contract, supplier diversity program, and option contract are discussed and suggested as approaches that can be applied by the shipping lines to arrange their leasing policies with lessors and to moderate the competition of these two parties in expanding their container fleets. These approaches not only can reduce the costs and the associated risks for the shipping lines, but can also alleviate the situation of over-supplied containers in the global container shipping industry.

In this paper, we introduced three-nested Constant Elasticity of Substitution (CES) production function into a static Computable General Equilibrium (CGE) Model. Through four levels of factor productivity, we constructed three nested production function of land use productivity in the conceptual modeling frameworks. The first level of factor productivity is generated by the basic value-added land. On the second level, factor productivity in each sector is generated by human activities that presents human intervention to the first level of factor productivity. On the third level of factor productivity, water allocation reshapes the non-linear structure of transaction among first and second levels. From the perspective of resource utilization, we examined the economic efficiency of water allocation. The scenario-based empirical analysis results show that the three-nested CES production function within CGE model is well-behaved to present the economy system of the case study area. Firstly, water scarcity harmed economic production. Government investment on water projects in Gansu thereby had impacts on economic outcomes. Secondly, huge governmental financing on water projects bring depreciation of present value of social welfare. Moreover, water use for environment adaptation pressures on water supply. The theoretical water price can be sharply increased due to the increasing costs of factor inputs. Thirdly, water use efficiency can be improved by water projects, typically can be benefited from the expansion of watersaving irrigation areas even in those expanding dry area in Gansu. Therefore, increasing governmental financing on water projects can depreciate present value of social welfare but benefit economic efficiency for future generation. (C) 2015 Elsevier Ltd. All rights reserved.

We reconsider the effect of elasticity of substitution on: income per-capita, growth rate of capital-labor ratio, growth rate of income per-capita, the steady-state capital-labor ratio and the steady-state income per-capita, respectively. We demonstrate that: first, both income per-capita and growth rate of capital-labor ratio are decreasing functions of elasticity of substitution. Second, we find out that an increase in substitution elasticity leads to an increase or a decrease in the growth rate of income per-capita depending on initial-terminal conditions of the production function. Moreover, we demonstrate that at steady-state an increase in elasticity of substitution decreases both growth rate of capital-labor ratio and growth rate of income per- capita. Finally, we revise the erroneous result that there is a threshold of elasticity of substitution for which there is no steady-state equilibrium and for which ever-sustained growth is entailed. Instead, as a policy instrument increasing the minimum marginal product of labor is demonstrated to increase the growth rate of income per-capita.

Economic value of water and economic analysis of water use management in Gansu Province of China have attracted widespread public attention. With the socioeconomic development, research on water resources has become more important than before. In this study, we define “water productivity” as the changes of economic production outputs of sectoral activities in every cubic meter of water input, which is also the technical coefficient of water resource use in each sector. According to Computable General Equilibrium (CGE) framework, based on the Input–Output Table 2007 and water resources bulletin of Gansu Province, we introduced the water into the ORANI-G (A Generic Single-Country Computable General Equilibrium model) model through the nested constant elasticity of substitution (CES) production function to analyze the changes of economic productions caused by water supply changes. We then examined water productivity in different sectors. Empirical results showed that current water productivity is underestimated. Agricultural water productivity is lower than that of the secondary and tertiary industries, even although agricultural water use is the largest part of water use in Gansu Province, and therefore improving agricultural water productivity can greatly mitigate the water shortage. Simulation results indicate that industrial transformation and development of water-saving industries will also mitigate water scarcity. Moreover, sensitivity analysis shows that the empirical results are robust under different scenarios. The results also show that higher constant elasticity of substitution rate (CES) between water and other production factors will contribute to sustainable development.

Before restructuring in the electricity industry, the primary decision-makers of the electricity market were deemed to be power generation and transmission companies, market regulation boards, and power industry regulators. In this traditional structure, consumers were interested in receiving electricity at flat rates while paying no attention to the problems of this industry. This attitude was the source of many problems, sometimes leading to collapse of power systems and widespread blackouts. Restructuring of the electricity industry however provided a multitude of solutions to these problems. The most important solution can be demand response (DR) programs. This paper proposes an economic DR model for residential consumers in liberalized electricity markets to change their consumption pattern from times of high energy prices to other times to maximize their utility functions. This economic model is developed based on constant elasticity of substitution (CES) utility function known as one of the most popular utility functions in microeconomics. Simulation results indicate that the proposed model is adaptable to any group of residential consumers with any disposition toward participation in DR programs and can be adjusted for any time period according to the preference given by the residential consumer.

Applying constant elasticity of substitution (CES) functions in general equilibrium integrated assessment models (GE-IAMs) for the substitution of technical factor inputs (e.g., replacing fossil fuels) fails to match historically observed patterns in energy transition dynamics. This method of substitution is also very sensitive to the structure of CES implementation (nesting) and parameter choice. The resulting methodology-related artifacts are (i) the extension of the status quo technology shares for future energy supply relying on fossil fuels with carbon capture, biomass, and nuclear; (ii) monotonically increasing marginal abatement costs of carbon; and (iii) substitution of energy with non-physical inputs (e.g., knowledge and capital) without conclusive evidence that this is possible to the extent modeled. We demonstrate these issues using simple examples and analyze how they are relevant in the case of four major CES-based GE-IAMs. To address this, we propose alternative formulations either by opting for carefully applied perfect substitution for alternative energy options or by introducing dynamically variable elasticity of substitution as a potential intermediate solution. Nevertheless, complementing the economic analysis with physical modeling accounting for storage and resource availability at a high resolution spatially and temporally would be preferable.

A multicriteria economic problem is considered: the basic production assets and the labor resources define a set of feasible solutions (alternatives), labor costs, costs of the basic production assets (to be minimized), and cost of the manufactured products (to be maximized) are objective functions. The production function with constant elasticity of substitution is used. The decision maker's (DM's) preferences are introduced as follows: lower labor costs and costs of the basic production assets have the greater importance than higher income, and vice a versa. The fuzzy preferences along with the compromise have a degree of its confidence. Such crisp and fuzzy information is applied in the axiomatic approach of the Pareto set reduction by V. D. Noghin. We show how to construct a set, which is an upper bound of the optimal choice and belongs to the Pareto set of the problem in crisp and fuzzy cases. In fuzzy case one should solve a three crisp multicriteria problems. Thus, upon the crisp and fuzzy DM's preferences a narrower upper bounds of the optimal set of resources with respect to criteria and additional information are obtained., Poc. of 2017 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON), Novosibirsk, Russia. 2017

The supply-use system of production is extended to a social accounting matrix by and enriched with alternative model specifications in the blocks of final demand, production, and factor markets. Domestic, import and export prices are accommodated and different composite prices face industries, households, government and the Rest of the World, accounting for taxes and other margins. These price equations second the quantity equations. Alternative macroeconomic closure rules enable the determination of equilibrium values of output and prices, either by Leontief inversion or iteration. The demand function for private consumption nests different forms, including Cobb-Douglas, translog and the Almost Ideal Demand System. Production and trade are also generalized, using constant elasticity of substitution or translog functions, including for labor and capital demand and supply. Household consumption can be extended to a dynamic framework, to explain savings. The models, from static input-output to full-fledged computable general equilibrium are presented explicitly, in a unified manner.

The transport sector offers limited options to reduce greenhouse gas emissions as compared with other sectors, such as power generation and industrial sectors. To understand the potential reduction of energy consumption and associated emissions through fuel substitution or transportation service demand reduction, this study estimates own- and cross-price elasticities of various fuels used for transportation. The analysis shows, like many previous studies, that an increase in fuel prices would not have a large effect on transport sector carbon dioxide emissions, due to limited substitution possibilities among fuels for transportation. The study also finds that price-induced changes that lead to an increase in the rate of adoption of fuel-efficient vehicles would be more effective than a policy to cause fuel substitution.

Water resources play a vital role in human life and agriculture irrigation, especially for agriculture-dominant developing countries and regions. Improving agricultural water use efficiency has consequently become a key strategic choice. This study, based on Zhangye City’s economic characteristics and data, applies a static Computable General Equilibrium (CGE) model with a constant elasticity of substitution (CES) composited water−land resources account to assess the impact of improving agricultural water use efficiency on economy, water conservation and land reallocation. Results reveal that: Zhangye City’s GDP increases by 0.10% owing to an increasing average technical level by improving agricultural water use efficiency; total water consumption decreases by 122 million m3, 69% of which comes from a reduction of surface water use; and land demand increases by 257.43 hectares mainly due to agricultural land demands. With respect to the sectors’ output, export-oriented sectors with higher water intensities in the agricultural sectors benefit most. In contrast, land-intensive sectors contract the most, as the rental price of land rises. Therefore, agricultural water conservation technology should be introduced considering more in surface water. Furthermore, higher demand for agricultural land would reduce land availability for other sectors, thus inhibiting urbanization pace on a small scale.

Despite substantial interest in the role of energy in the economy, the degree of substitutability between energy and other production inputs, and the way energy should be included in the production function remain unresolved issues. Our study provides industry-level parameter estimates of two-level constant elasticity of substitution (CES) functions that include capital, labour and energy inputs and allow for technological change for Canada. In contrast to many existing studies, we do not impose prior restrictions on the order of input nesting, and we report the estimates for three possible specifications. We find that a nested production structure which first combines labour and energy into a composite good that is then combined with capital, fits the Canadian data best, in terms of respecting the restrictions imposed by cost minimization. We also find rather low elasticities of substitution between capital and labour, and limited evidence of exogenous technological change.

This paper analyzes the evolution of Chinese marine economic development policy and the characteristics of regional differentiation in the coastal regions. The contributions of the elements of the marine economy to regional economic growth in China are deduced by using a multi-factor production function model with a constant elasticity of substitution. The results indicate that the contribution of the Chinese marine economy to the national economy increased from 6.46% to 13.83% between 2000 and 2011, and the average annual growth rate during that same period was 7.17%. This contribution mainly resulted from marine capital׳s contribution to the national economy, which amounted to roughly two-thirds of the marine economy׳s contribution to the national economy. With respect to regional differentiation, the contributions of the marine economy to the regional economies in China are ranked by region from greatest to least as follows: the Circum-Bohai Sea Region, the Yangtze River Delta and the Pearl River Delta region. Finally, Liaoning׳s marine economy made the largest contribution to the national economy from 2000 to 2011.

Under constant elasticity of substitution (CES) preferences and Cournot (or Bertrand) competition, a larger market induces exits of domestic firms, lower prices, and larger production of surviving firms because of competition from more foreign firms, even without resorting to the selection effects of Melitz. The elasticity of the number of firms to population decreases with substitutability between goods, and it reaches 0.5 under Cournot competition with homogeneous goods: empirical evidence supports this structural relation against the unitary elasticity of monopolistic competition. The results hold also in a Heckscher–Ohlin model with imperfect competition generating inter- and intra-industry trade due to comparative advantage or comparative preferences.

This article studies optimal taxation in a general equilibrium macroeconomic model with endogenous entry. We compare the constant elasticity of substitution (CES) model to three alternative demand structures: oligopolistic competition in prices, oligopolistic competition in quantities, and translog preferences. Our economy is characterized by two distortions: a labor distortion due to the misalignment of markups on goods and leisure, and an entry distortion due to the misalignment of the consumer surplus effect and the profit destruction effect of entry. The two distortions interact in determining the wedge between the market-driven and optimal level of product diversity. We show how optimal labor and entry taxes depend on the prevailing demand structure, the nature and size of entry costs, and the degree of substitutability between goods.

I propose an application of the pure-consumption version of the Grossman model of health care demand, where utility depends on consumption and health status and health status on medical care and health technology. I derive the conditions under which an improvement in health care technology leads to an increase/decrease in health care consumption. In particular, I show how the direction of the effect depends on the relationship between the constant elasticity of substitution parameters of the utility and health production functions. I find that, under the constancy assumption, the ratio of the two elasticity of substitution parameters determines the direction of a technological change on health care demand. On the other hand, the technology share parameter in the health production function contributes to the size but not to the direction of the technological effect. I finally explore how the ratio of the elasticity of substitution parameters work in measurement and practice and discuss how future research may use the theoretical insight provided here.

Top-down computable general equilibrium models of energy–economy interactions have a limited representation of the electricity sector, typically using constant elasticities of substitution between generation types. Detailed bottom-up electricity models generally have embedded load duration curves with the electricity price determined by the marginal cost of generation. This study incorporates a simple representation of electricity generation with these bottom-up features directly into the GTAP general equilibrium model. The motivation for this study is to help project generation adjustments and macroeconomic costs associated with policies and shocks affecting the electricity sector. Various scenarios are shown using a simple hypothetical model with Base, Mid and Peak generation types: introducing an incremental output tax on Base generation, assuming mobile capital and then fixed capital; flattening the load duration curve; and introducing an intermittent generation source. Key results are: different responses in electricity generation, price and GDP to a simple constant elasticity of substitution treatment; higher macroeconomic costs associated with a faster tax introduction due to merit order switching and capital decommissioning; an increase in GDP and a shift towards Base generation from flattening the load duration curve; and a displacement of Base generation from the introduction of an intermittent generation source, with variability leading to an increase in Peak generation and a cost to GDP. The model code is made available for replication of results and further application and development.

We propose a theory of firm production that requires diverse inputs. We show that in a competitive labor market, firms differ in their skill composition. Organizations with higher total factor productivity (TFP) are larger and hire from a broader range of skills. Technological progress leads to an increase of all wages and results in downsizing. Quantifying productivity using our model shows that a constant elasticity of substitution (CES) production function generates unbiased estimates of TFP but biased estimates of marginal product and elasticity of substitution across skills. Our model also generates estimates of the TFP distribution based on CEO compensation alone.

Elasticities are key parameters for any economic analysis. Using the World-Input–Output Database, we estimate substitution elasticities for a three-level nested constant elasticity of substitution KLEM production structure using up to date nonlinear least squares estimation procedures. This allows us for the first time to use one coherent data set for the estimation process. Furthermore, it gives us the opportunity to derive elasticities from the same data which researchers can use to calibrate their models. On the basis of our estimations, we demonstrate that the practice of using Cobb–Douglas or Leontief production functions in economic models must be rejected for the majority of sectors. We provide a comprehensive set of estimated substitution elasticities covering a wide range of sectors. Our results suggest that no substantial change in input substitutability takes place during the time period we consider. Moreover, there is no substantial variation in substitution elasticities across regions.

This paper examines the ‘small share’ problem inherent within the constant elasticity of substitution Armington specification. As a de facto research tool in the quantitative trade literature, this structural bias plagues the results of numerous multi-region CGE studies. Kuiper and van Tongeren (2006) proposed a fusion of gravity and CGE specifications to remedy said bias, which the current paper further develops. With a pervasiveness of ‘small-share’ examples on Mercosur–European Union trade owing to the latter's restrictive tariff regime, the results reveal that significant additional trade led gains to Mercosur under a potential preferential trade agreement when compared with the standard Armington treatment.

Power-law (PL) formalism is known to provide an appropriate framework for canonical modeling of nonlinear systems. We estimated three stochastically distinct models of constant elasticity of substitution (CES) class functions as non-linear inverse problem and showed that these PL related functions should have a closed form. The first model is related to an aggregator production function, the second to an aggregator utility function (the Armington) and the third to an aggregator technical transformation function. A q-generalization of K-L information divergence criterion function with a priori consistency constraints is proposed. Related inferential statistical indices are computed. The approach leads to robust estimation and to new findings about the true stochastic nature of this class of nonlinear—up until now—analytically intractable functions. Outputs from traditional econometric techniques (Shannon entropy, NLLS, GMM, ML) are also presented.

As input ows of secondary raw materials show high volatility and tend to behave in a chaotic way, the identification of the main drivers of the dynamic behavior of returns plays a crucial role. Based on a stylized productionrecycling system consisting of a set of nonlinear difference equations, we explicitly derive parameter constellations where the system will or will not converge to its equilibrium. Using a constant elasticity of substitution production function, the model is then extended to enable coverage of real world situations. Using waste paper as a reference raw material, we empirically estimate the parameters of the system. By using these regression results, we are able to show that the equilibrium solution is a Lyapunov unstable saddle point. This implies that the system is sensitive on initial conditions that will hence impede the predictability of product returns. Small variations of production input proportions could however stabilize the whole system. (authors' abstract)

The proportion of resource-based industry groups in the industrial structure in Indonesia is 42.01%, yet its productivity is low because of its labor-intensive nature and limited capital, despite the direct contribution of the use of capital and labor to the creation of output. To optimize production, an input can be substituted by another input. However, it depends on the elasticity of substitution of the two inputs. The main objective of this research is to analyze the level of substitutability of inputs used in the natural resource-based industry group in Indonesia. Using the function of Constant Elasticity of Substitution (CES), the results of the study show that the substitutability level of capital and labor is inelastic, meaning that input substitution is relatively difficult. The results of this study imply that to increase its productivity, this industry group needs to strengthen the support from (government) policies to improve its workforce quality.

This paper examines the capacity determination factors of medical services at a national level through the analysis of a mathematical model that maximizes social welfare, which consists of the consumption of private goods and the medical capacity provided by the society. A sensitivity analysis is conducted to investigate the impact of these factors on the medical capacity provided. Furthermore, a case example based on the data provided by the government is presented to discuss the results derived from the theoretical analysis. The results of the sensitivity analysis indicate that individual disposable income, the medical expenditure for each treatment, the level of premium payments, and substitution parameters have a positive impact on medical capacity, while the medical costs and preference parameter negatively affect medical capacity. The results of the correlation analysis based on the data of the case example are consistent with the findings of the theoretical analysis.

The most commonly used parameterizations of constant elasticity of substitution functions (CES) have the disadvantage that the share parameter has no meaningful interpretation over the range of possible elasticities of substitution. This note introduces a slightly reformulated CES function which avoids the problem.

This paper examines the implications of product market imperfection for a dynamic economy in a two-commodity and two-factor open economy model in which the home country produces a consumption good (capital good) in a perfectly competitive (monopolistic) market. Based on a social utility function of constant elasticity of substitution variety, excess demand for the goods, volume of trade, and patterns of specialization are analyzed vis-a-vis the standard case where the capital-good market is perfectly competitive. Further, it is shown that the presence of imperfect capital-good market structure does not preclude the possibility of long-run steady-state economic growth.

We derive the aggregate normalized CES production function from idea-based microfoundations where firms are allowed to choose their capital- and labor-augmenting technology optimally from a menu of available technologies. This menu is in turn augmented through factor-specific RD if they are independently Pareto-distributed, then it is Cobb–Douglas. Third, by disentangling technology choice by firms from R&D output, one can draw a clearcut distinction between the direction of R&D and the direction of technical change actually observed in the economy, which are distinct concepts. Fourth, it is argued that the Weibull distribution should be a good approximation of the true unit factor productivity distribution (and thus the CES should be a good approximation of the true aggregate production function) if a 'technology' is in fact an assembly of a large number of complementary components. This argument is illustrated with a novel, tractable model of directed (factor-specific) R&D. Finally, it is shown that all our results carry forward to the general case of n-input production functions.

Top–down models usually include piecewise-smooth functions to describe marginal cost curves, while bottom–up models use step function curves. When a bottom–up cost curve is available, we can explicitly represent this curve with a top–down model in order to replicate its shape instead of using arbitrary assumptions. We propose several methods to approximate a piecewise function from a step function using constant elasticity of substitution technologies. Specifically, we consider a pollution abatement sector and calibrate the parameters of the abatement function in order to allow proper assessment of the economic effects of an environmental policy. Our methodology can be applied to any sector characterized by decreasing returns to scale technologies. We conclude that the elasticities of substitution need not be estimated only on the basis of historical data, but can be precisely calibrated on the basis of engineering estimates of technology potential.

This paper presents an agroeconomic approach to assess the economic impact of improving nitrogen and irrigation management practices in California’s Tulare Lake Basin and the Salinas Valley. The approach employs a self-calibrated mathematical programming model with a constant elasticity of substitution production function and two nests: one for irrigation and one for nitrogen. Agricultural crop yields are maintained as a worst-case for improving nitrogen use efficiency. Small reductions (

The long-debated issue of the business value of information technology (IT) to the firm (country) has received a great deal of attention in the literature. But the studies have rarely examined the dynamic patterns of the IT value as measured by the firm’s productive efficiency over time. The objective of this paper is to apply the three-factor constant elasticity of substitution (CES) time-varying stochastic production frontier models and use the same data set as used in several previous studies to investigate the dynamic patterns of IT value over time in connection with the issues of inputs substitution and complement and the productivity paradox. This paper adopts two analytical skills, collective and individual, to analyze the empirical results. Collectively, we find that the dynamic patterns of IT value are closely related to the substitution and complement of three inputs and the IT productivity paradox. Individually, we identify five common dynamic patterns of the IT value measured by productive efficiency and interpret their implications for the productivity paradox as summarized in a two by two matrix of practical applications and strategies. This matrix accounts for four different scenarios of the relationship between the average productive efficiency and the IT productivity paradox, illustrates some practical applications by the analytical results, and provides some business insights and managerial strategies for IT decision makers and PO/IS managers. This represents a new contribution to the understanding of the dynamic influence of IT investments upon the value of IT over time.

This paper develops a novel approach to modeling preferences in monopolistic competition models with a continuum of goods. In contrast to the commonly used constant elasticity of substitution preferences, which do not capture the effects of consumer income and the intensity of competition on equilibrium prices, the present preferences can capture both effects. The relationship between consumers’ incomes and product prices is then analyzed for two cases: with and without income heterogeneity.

This short note estimates using the Kmenta's (1967) approximation, a constant elasticity of substitution (CES) production function for Australia for 1960–2004. It is found that the elasticity of substitution is 2.44, technical progress is capital augmenting and the steady-state growth rate (SSGR) of Australia is about 0.34%.

Unlike the case of competitive equilibria for which there is the index theorem, almost nothing is known about multiple equilibria in Nash games. Multiple Nash equilibria are hard to find computationally accounting for spare prior literature discussion. Existing numerical literature on tariff games either assumes uniqueness or uses restrictive functional forms that guarantees this is the case. Here, we show for pure exchange Constant Elasticity of Substitution (CES) two country models with tariffs both how the introduction of a tariff can generate multiple competitive equilibria and related examples of widely separated multiple Nash equilibria. These typically occur when substitution elasticities are low, although implied import demand elasticities can still be high if the shares of trade in consumption are small. The implication seems to be that as one moves away from the constant elasticity excess demands (offer curve) formulations used in the optimal tariff literature to explicit structural models of in...

The document proposes a new entropy-based approach for estimating the parameters of nonlinear and complex models, i.e. those whose no transformation renders linear in parameters. Presently, for estimating such class of functions, various iterative technics like the Gauss Newton algorithm are applied and completed by the least square methods approaches. Due to conceptual nature of such methods, de nitely estimated functions are di erent from the original nonlinear one and the estimated values of parameters are in most of cases far from the true values. The proposed approach, being related to the statistical theory of information, is very di erent from those so far applied for that class of functions. To apply the approach, we select a stochastic non-homogeneous constant elasticity of substitution aggregated production function of the 27 EU countries which we estimate maximizing a non-extensive entropy model under consistency restrictions related to the constant elasticity of substitution model plus regular normality conditions. The procedure might be seen as an attempt to generalize the recent works (e.g. Golan et al. 1996) on entropy econometrics in the case of ergodic systems, related to the Gibbs Shannon maximum entropy principle. Since this nonlinear constant elasticity of substitution estimated model contains four parameters in one equation and statistical observations are limited to twelve years, we have to deal with an inverse problem and the statistical distribution law of the data generating system is unknown. Because of the above reasons, our approach moves away from the normal Gaussian hypothesis to the more general Levy instable time (or space) processes characterized by long memory, complex correlation and by a convergence, in relative long range, to the attraction basin of the central theorem limit. In such a case, fractal properties may eventually exist and the q non extensive parameter could give us useful information. Thus, as already suggested, we will propose to solve for a stochastic inverse problem through the generalized minimum entropy divergence under the constant elasticity of substitution model and other normalization factor restrictions. At the end, an inferential con dence interval for parameters is proposed. The output parameters from entropy formalism represent the long-run state of the system in equilibrium, and so, their interpretation is slightly di erent from the ceteris paribus interpretation related to the classical econometrical modeling. The approach seems to produce very e cient parameters in comparison to those obtained from the classical iterative nonlinear method which will be presented, too.

This paper builds on earlier work that used a general-equilibrium model to show that reducing employment of unauthorized immigrants in the United States through a tighter border-security policy lowers the average income of legal residents. Here we exploit further the detail available in the general-equilibrium model to look at distributional effects, recognizing that the policy increases wage rates for low-paid legal workers. We assess the social welfare effect on legal workers using a constant elasticity of substitution social welfare function. We contrast our general-equilibrium approach to immigration analysis with the more commonly used partial-equilibrium, econometric approach. (JEL D63, J61, C68)

Investment behavior of a price regulated service firm facing fluctuating demand is investigated with a Cobb-Douglas type of production function using optimal control theoretic model. Both machinery and labor are assumed to be capital goods. Rates of change of demand, attrition rate of labor and the depreciation rate of capital are the primary parameters determining optimal investment behavior. Switching times between four phases of investment where (1) both labor and capital investment are positive, (2) capital investment is zero but labor investment is positive,(3) capital investment is zero but labor investment is positive and (4) where both investments are zero are identified. The same analysis is repeated using Constant Elasticity of Substitution (CES) type of production function.

Employing a neoclassical growth model with a constant elasticity of substitution production function, we develop a comparative static and dynamic analysis of the effects of the elasticity of substitution between inputs on the steady state growth path, growth threshold, speed of convergence and savings rates. Unlike earlier studies along these lines, we incorporate human capital, along with physical capital and raw labor, as a third input in the production function. We prove that a higher elasticity of substitution between inputs can lead to a higher steady state level for income per effective unit of labor. To illustrate the quantitative significance of the elasticity of substitution, we consider two ways in which human capital enters the production function. Employing cross country data, we find estimates for the normalized CES production functions with human capital to be significantly below unity.

As a result of catastrophic events, firms and other organizations are faced with input shortages and price shocks. Firms can respond to these events using a variety of “resilience” actions, or tactics. Here we provide a microeconomic foundation for analyzing a comprehensive range of these tactics, incorporating both inherent and adaptive concepts of resilience. We classify these tactics and derive optimality conditions for production with the use of each class of resilience in the context of a nested Constant Elasticity of Substitution (CES) function consisting of aggregated Capital (K), Labor (L), Infrastructure (I), and Materials (M). The framework has broad applicability, including measurement and scoring of resilience, cost-effectiveness assessment of resilience tactics individually and as a group, calculation of resilience indices, and supply-chain management.

Chapter 3 analyzes the real side of the Soviet economic development, focusing on long-term productivity growth. Given the simple structure of the Soviet monetary economy, productivity almost directly reflected how efficiently funds were utilized. Consequently, a chronic stagnation in productivity growth probably caused a parallel accumulation of low-productivity material assets in the enterprise sector and of nonperforming financial assets in the household sector. The empirical analysis using the extended Solow residual calculation and the direct estimation of the normalized constant elasticity of substitution production function that were developed for this book indicated a long-term decreasing trend in Soviet productivity growth. The bottom-line evaluation of the Soviet monetary management was that it could not contribute to increasing productivity.

This study quantifies the uneven welfare gains from trade between firm owners and workers in a multi-country model of monopolistic competition under a demand system of constant elasticity of substitution (CES). An agent decides to start up her own firm or to be employed as a worker according to her level of innate capability, which determines the productivity of her potential launched firm. Although keeping this model isomorphic to Melitz's (2003) heterogeneous firm model in terms of the aggregate welfare gains from trade, we are able to examine the welfare gains for firm owners and workers, respectively. Theoretically, we find that countries with lower domestic expenditure shares display higher disparities in welfare gains from trade between firm owners and workers. Taking the model to data, we illustrate the application of the methodology by calculating the respective average welfare gains (compared to autarky) of firm owners and of workers for 14 countries, including G7, BRIC, Korea, Singapore, and Taiwan. Among them, Singapore has relatively lower domestic expenditure shares and shows dramatically large disparity in welfare gains between these two occupations. Taking the year of 2006 as an example, the gap in welfare gains in Singapore reaches to 445.03% while the same measure in the United States is only 9.95%.

We study a model of selfish resource allocation that seeks to incorporate dependencies among resources as they exist in modern networked environments. Our model is inspired by utility functions with constant elasticity of substitution (CES) which is a well-studied model in economics. We consider congestion games with different aggregation functions. In particular, we study $L_p$ norms and analyze the existence and complexity of (approximate) pure Nash equilibria. Additionally, we give an almost tight characterization based on monotonicity properties to describe the set of aggregation functions that guarantee the existence of pure Nash equilibria.

Many researchers have used quadratic utility function to study its influences on economic games with product differentiation. Such games include Cournot, Bertrand, and a mixed-type game called Cournot-Bertrand. Within this paper, a cubic utility function that is derived from a constant elasticity of substitution production function (CES) is introduced. This cubic function is more desirable than the quadratic one besides its amenability to efficiency analysis. Based on that utility a two-dimensional Cournot duopoly game with horizontal product differentiation is modeled using a discrete time scale. Two different types of games are studied in this paper. In the first game, firms are updating their output production using the traditional bounded rationality approach. In the second game, firms adopt Puu’s mechanism to update their productions. Puu’s mechanism does not require any information about the profit function; instead it needs both firms to know their production and their profits in the past time periods. In both scenarios, an explicit form for the Nash equilibrium point is obtained under certain conditions. The stability analysis of Nash point is considered. Furthermore, some numerical simulations are carried out to confirm the chaotic behavior of Nash equilibrium point. This analysis includes bifurcation, attractor, maximum Lyapunov exponent, and sensitivity to initial conditions.

In many situations, the dependence of the production or utility on the corresponding factors is described by the CES (Constant Elasticity of Substitution) functions. These functions are usually explained by postulating two requirements: an economically reasonable postulate of homogeneity (that the formulas should not change if we change a measuring unit) and a less convincing CSE requirement. In this paper, we show that the CES requirement can be replaced by a more convincing requirement—that the combined effect of all the factors should not depend on the order in which we combine these factors.

We focus on the role of the government in the provision of investment in China, through the medium of a Dynamic Stochastic General Equilibrium model of the economy in which the form of the production function reflects this governmental role. Using indirect inference, we estimate and test for the elasticity of substitution between government and nongovernment capital in both Constant Elasticity of Substitution (CES) and Cobb–Douglas technologies. The results underscore the strong substitution relationship between government and nongovernment capital from 1949, supporting CES rather than the Cobb–Douglas technology. They also show that the orientation of public investment changed after the start of the ‘Socialist Market Economy’ in 1992: government capital became more complementary to nongovernment capital as it focused more on infrastructure and withdrew from industrial production, intervening only in times of crisis, for stabilization purposes, indirectly via the state banks.

Since 1970, housing's relative price, share of expenditure, and ``unaffordability'' have all grown. We estimate housing demand using a novel compensated framework over space and an uncompensated framework over time. Our specifications pass tests imposed by rationality and household mobility. Housing demand is income and price inelastic, and appears to fall with household size. We provide a numerical non-homothetic constant elasticity of substitution utility function for improved quantitative modeling. An ideal cost-of-living index demonstrates that the poor have been disproportionately impacted by rising relative rents, which have greatly amplified increases in real income inequality.

A recent and growing area of research applies latent factor models to study the development of children's skills. Some normalization is required in these models because the latent variables have no natural units and no known location or scale. We show that the standard practice of “re-normalizing” the latent variables each period is over-identifying and restrictive when used simultaneously with common skill production technologies that already have a known location and scale (KLS). The KLS class of functions include the Constant Elasticity of Substitution (CES) production technologies several papers use in their estimation. We show that these KLS production functions are already restricted in the sense that their location and scale is known (does not need to be identified and estimated) and therefore further restrictions on location and scale by re-normalizing the model each period is unnecessary and over-identifying. The most common type of re-normalization restriction imposes that latent skills are mean log-stationary, which restricts the class of CES technologies to be of the log-linear (Cobb-Douglas) sub-class, and does not allow for more general forms of complementarities. Even when a mean log-stationary model is correctly assumed, re-normalization can further bias the estimates of the skill production function. We support our analytic results through a series of Monte Carlo exercises. We show that in typical cases, estimators based on “re-normalizations” are biased, and simple alternative estimators, which do not impose these restrictions, can recover the underlying primitive parameters of the production technology.Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

This paper describes calibration methods for models of agricultural production and water use in which economic variables can directly interact with hydrologic network models or other biophysical system models. We also describe and demonstrate the use of systematic calibration checks at different stages for efficient debugging of models. The central model is the California Statewide Agricultural Production Model (SWAP), a Positive Mathematical Programming (PMP) model of California irrigated agriculture. We outline the six step calibration procedure and demonstrate the model with an empirical policy analysis. Two new techniques are included compared with most previous PMP-based models: exponential PMP cost functions and Constant Elasticity of Substitution (CES) regional production functions. We then demonstrate the use of this type of disaggregated production model for policy analysis by evaluating potential water transfers under drought conditions. The analysis links regional production functions with a water supply network. The results show that a more flexible water market allocation can reduce revenue losses from drought up to 30%. These results highlight the potential of self-calibrated models in policy analysis. While the empirical application is for a California agricultural and environmental water system, the approach is general and applicable to many other situations and locations.

Understanding fossil fuel supply behaviour is crucial for interpreting carbon leakage and assessing the potential effectiveness of border measures in climate policy. In most computable general equilibrium models, this fossil fuel supply is derived from a constant elasticity of substitution production function, in which a natural resource is treated as a fixed factor. We show that this leads to endogenously decreasing supply elasticities and sharply increasing marginal leakage rates for large coalitions that have ambitious emissions targets, particularly when fuel exporters participate in the coalition. We propose an alternative production function that has a constant elasticity of fuel supply, which results in more stable leakage rates and a different share of trade-related leakage. The role of this model variation for the assessment of border measures in climate policy turns out to be limited. In those cases where the model versions differ most (i.e. large coalition, ambitious targets), border measures have a small effect anyway.

In this paper, we study an optimal consumption–leisure, investment, insurance and retirement choice problem of an infinitely lived economic agent with constant elasticity of substitution (CES) preferences. We incorporate random insurable losses that are independent of risky asset returns (negative monetary shocks) and impose short-sale constraint on the risky asset to formulate this optimal choice model. When the wealth process is subject to insurable negative monetary shocks produced by a general marked point process, the challenge is to derive an optimal allocation of the agent’s wealth between a portfolio investment and an insurance (costly) strategy. Without imposing the level of insurance to be within interval \(\left[ {0,1} \right]\); we capture the agent’s instantaneous preferences for consumption and leisure via CES preference, while integrating the optimal consumption–leisure–work tradeoffs, the optimal portfolio selection, optimal level of insurance and his/her optimal retirement time. We use the Martingale technique to formulate the optimization problem and solve the optimal policies of the agent by applying the variational inequality arising from the dual functions of the optimal stopping times. Our results demonstrate that a lack of insurance against large negative monetary shocks is positively correlated with lower participation rate in the equity market and high savings rates when short-sale constraint is binding. The optimal retirement time is characterized as the first time when his/her wealth exceeds a critical level of wealth.