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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.

Indonesia has undergone a transformation from agriculture to the manufacturing industry in 1971-1997. In the 2001-2015 period there was de-industrialization in developed countries. Likewise, Indonesia which shows a decrease in the contribution of GDP and manufacturing sector workforce to the economy. However, deindustrialization in Indonesia is premature / too fast. One of the policies to overcome this problem is with attention to the creative industry. With the existence of the creative industry, it can achieve several SDGs goals, namely the 8th goal, namely decent work and economic growth, the creative economy can increase economic growth, create jobs and increase exports (UNCTAD, 2010). However, the creative industry GDP growth that is below the RPJMN target is thought to indicate low productivity of the creative industry. According to IBS data, the craft sub-sector creative industry has a low production value. To see productivity can use technical efficiency. This study aims to evaluate the technical efficiency of creative industry in the craft sub-sector as well as to analyze the trend of variables that affect technical judgments. The method used is the CES production function and Data Envelopment Analysis. The results show that industries that have high total production factor values have a tendency to have high technical efficiency values as well. Furthermore, those arranged according to technical categories and binary logistic regression are used to determine trend variables that affect technical judgments. The technical efficiency of the craft, significantly by wages, investment status and company scale.

Includes supplementary material for the online appendix The link between income inequality and progressive taxation has long been considered a fundamental normative foundation for income tax progressivity. This paper furnishes necessary and sufficient conditions on primitives, in terms of the elasticity of income with respect to ability, under which various subclasses of progressive taxes are inequality reducing. The distributional effects of progressive income taxation are decomposed into two conditions on the wage elasticity of income, the tax rate effect and the subsidy effect, each capturing different aspects of the transition between before-tax and after-tax income distributions. The results confer a degree of useful flexibility to the theory, in that they allow the analyst to expand the universe of consumer preferences by suitably restricting the set of marginal-rate progressive taxes. As an illustration of the results’ practical implications, we provide a precise characterization of the subclass of (progressive) taxes that are inequality reducing for the constant elasticity of substitution (CES) and the quasi-linear utility functions. This paper benefited from valuable comments made by the anonymous referees. Llavador acknowledges financial support from the Spanish Ministry of Economy and Competitiveness through the Severo Ochoa Programme for Centers of Excellence in R&D (SEV-2015-0563), the AEI/FEDER-UE (PGC2018-096370-B-100) and the AEI/FEDER-EU (ECO2017-89240-P).

Studies of childhood development have suggested human capital is accumulated in complex and nonlinear ways. Nonetheless, empirical analyses of this process often impose a linear functional form. This paper investigates which technology assumptions matter in quantitative models of human capital production. I propose a general‐to‐restricted procedure to test the production technology, placing constraints on a modified McCarthy function, from which transcendental, constant elasticity of substitution, log‐linear and linear models are obtained as special cases. Applying the procedure to data on child height from the Young Lives surveys, as well as cognitive skills, I find that the technology of human capital production is neither log‐linear nor linear‐in‐parameters; rather, past and present inputs act as complements. I recommend that maintained hypotheses underlying functional form choices should be tested on a routine basis.

This paper provides the first comprehensive review of the empirical and theoretical literature on the determinants of the elasticity of substitution between capital and labor. Our focus is on the two‐input constant elasticity of substitution (CES) production function. We start by presenting four concise observations that summarize the empirical literature on the estimation of σ. Motivated by these observations, the main part of this survey then focuses on potential determinants of capital–labor substitution. We first review several approaches to the microfoundation of production functions where the elasticity of substitution (EOS) is treated as a purely technological parameter. Second, we outline the construction of an aggregate elasticity of substitution (AES) in a multi‐sectoral framework and investigate its dependence on underlying intra‐ and inter‐sectoral substitution. Third, we discuss the influence of the institutional framework on the extent of factor substitution. Overall, this survey highlights that the effective elasticity of substitution (EES), which is typically estimated in empirical studies, is generally not an immutable deep parameter but depends on a multitude of technological, non‐technological, and institutional determinants. Based on these insights, the final section identifies a number of potential empirical and theoretical avenues for future research.

We present a modified Heckscher–Ohlin model featuring product differentiation and monopolistic competition. Consumer preferences take the constant elasticity of substitution form. Production technology has constant returns to scale. The analysis shows, that in the movement from autarky to free trade the change in the wage/rental ratio following from an increase in the number of differentiated product varieties is due to the pattern of relative substitutability between the differentiated and the homogeneous good.

In this article, we propose a new class of production functions in the new classical theory of economics and study its qualities based on Euler’s relation of quasi-homogeneous functions. In a market economy environment, it is crucial to establish a firm’s profitability and draw conclusions about the operation and to make a variety of assumptions using a function that is more consistent with reality in the future. We showed that the quasi-homogeneous function is a general form of the well known production functions such as Cobb-Douglas and Constant Elasticity of Substitution (CES). We have made some qualitative and quantitative analysis and compare our results with the classical models using statistical data of Japan.

This paper aims to place Indonesian migrant workers based on a mapping from the estimation of the demand function of foreign workers and the efficiency of production costs. The demand function of foreign workers and the function of production costs are obtained through a derivation in the function of Constant Elasticity of Substitution (CES) production. The mapping of Indonesian migrant workers placement applies five scenarios by the assumption that local wage constantly increased using panel data from the Malaysian manufacturing industries, period 2002-2015. The result found that the relationship of all foreign workers with local workers at various levels of skills in the manufacturing industry is substitution. The priority for high-skilled which is a priority for placing Indonesian migrant workers is manufacturing industries with CA code and CI code, middle-skilled is manufacturing industries with CB code, CI code, and CJ code, low-skilled is manufacturing industries with CA code, CL code, and Other manufacturing industries.

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.

The present paper sheds new light on the growth implications of gender inequalities in the Moroccan labour market. We confront two different approaches. The first one is based on firm data to estimate gender complementarity in production and uses this information for simulations based on a simple macroeconomic model. The second relies on country panel variation to relate growth to the relative employment of women and, also, suggest simulations for Morocco. Both approaches lead to similar conclusions regarding the potential economic gains from increased female participation in this country.

In order to realize the East Asian Low-Carbon Community, a comprehensive energy and economic evaluation model must be developed. The model can be used to formulate future emission reduction plans and quantitatively evaluate the economic and environmental impacts of an East Asian Low-Carbon Community, including the effects of economic and technological measures and international cooperation. This chapter develops an integrated energy and economic evaluation model—the Glocal Century Energy Environment Planning (G-CEEP) model. First, we introduce the model framework and explore the modeling method, including the two-level constant elasticity of substitution (CES) production function, technological learning, the macroeconomic model, environmental evaluation, and the objective function. Using the G-CEEP model, we project a business-as-usual (BAU) scenario and a CO2 mitigation scenario to 2050, for China, Japan, and Korea. Then we evaluate co-benefit effects, considering SO2 and NOx. Finally, a policy perspective based on the analysis is provided.

A large body of literature estimates the relative wage impacts of immigration on low- and high-skill natives, but it is unclear how these effects map onto changes of the wage distribution. I document the movement of foreign-born workers in the U.S. wage distribution, showing that, since 1980, they have become increasingly overrepresented in the bottom. Downgrading of education and experience obtained abroad partially drives this pattern. I then undertake two empirical approaches to deepen our understanding of the way foreign-born workers shape the wage structure. First, I estimate a standard theoretical model featuring constant elasticity of substitution technology and skill types stratified across wage deciles. Second, I estimate reduced-form quantile treatment effects by constructing a ceteris paribus counterfactual wage distribution with lower immigration levels. Both analyses uncover a similar monotone pattern: a one percentage point increase in the share of foreign-born leads to a 0.2–0.3 (0.2–0.4) percent wage decrease (increase) in the bottom (top) decile and asserts no significant pressure in the middle. When analyzing the drivers of this pattern, I find suggestive evidence for a novel mechanism through which local labor markets absorb foreign-born workers: occupational differentiation of immigrants relative to natives.

Large-scale electricity outages have the potential to result in substantial business interruption losses. These losses can be reduced through a number of tactics within the broader strategies of mitigation and resilience. This paper presents a methodology for analyzing the tradeoffs between mitigation and three categories of resilience. We derive optimality conditions for various combinations of strategies for a Cobb-Douglas damage function and then explore implications of a less restrictive Constant Elasticity of Substitution damage function. We also calibrate the model and perform Monte Carlo simulations to test the sensitivity of the results with respect to changes in major parameters. Simulation results highlight the possibility that substitution away from mitigation towards resilience may lower total expected costs from large-scale outages for a given level of risk reduction expenditure when the marginal benefit of resilience is high relative to the expected marginal benefit of mitigation.

We relax two common assumptions in the Hotelling model with third-degree price discrimination: inelastic demand and exogenously assumed price discrimination. Based on the constant elasticity of substitution representative consumer model, we allow firms to endogenously choose whether to acquire consumer information and price discriminate. We find that when the information cost is sufficiently low, there exist two symmetric sub-game perfect Nash equilibria irrespective of the demand elasticity: both firms acquiring information and price discriminating, and neither firm acquiring information and charging a uniform price. This implies that the widely discussed prisoners’ dilemma, in which both firms are exogenously assumed to price discriminate, is not in fact a dilemma. A comparison of social welfare shows that when the demand elasticity is large enough, price discrimination improves social welfare. This is in contrast to the finding—price discrimination harms social welfare—in the existing literature assuming perfect inelastic demand.

It is now established that the consumption discount rate is determined by the growth of consumption multiplied by the elasticity of marginal utility, but distributive concerns are rarely reflected in the literature. Assuming a social welfare function with inequality aversion, we consider a consumption discount rate that can be decomposed into the growth effect and the intragenerational distribution effect. The framework is then extended to include population change and inequality in the environment as an amenity in a utility with constant elasticity of substitution. Numerical examples illustrate that distributional effects turn non-negligibly negative, that may reduce consumption discount rate by 1–3% for plausible parameters, once distribution is adjusted for both population and the environment.

Purpose In this paper, the authors assume that the matter of a good quality of air will grow in importance in the future, and that it could be a noticeable part of a quality system to be used for communication purposes. The authors propose some synthetic indicators for air quality and discuss them in-depth to provide robust indexes suitable for ranking a set of alpine destinations. Design/methodology/approach The authors use locally based data on three pollutants with reference to 25 alpine touristic destinations. Starting from hourly data for 62 days of the 2014 summer season for each pollutant, the authors end with a single synthetic air quality index for any locality. The aggregation methodologies are at the core of the paper; in particular, the authors propose a constant elasticity of substitution (CES) function – a well-known tool in Economics – to aggregate the pollutants the authors deal with. Because the degree of substitution among them is unknown, the authors simulate two extreme cases and an intermediate one to rank the localities on the bases of the synthetic air quality index. Findings All the Alpine destinations the authors considered have – or had in summer 2014 – an excellent open-air quality, and this was a permanent trait of that period. Ranks look robust (stable), as they do not depend significantly on the available options of the techniques the authors used. Originality/value The originality of the paper is inherent first in the idea that high quality air can be an issue of interest for touristic goals, especially in the case of mountain destinations, which have all proven to offer an excellent open-air quality. Second, from a methodological perspective, the paper frames dispersed and sectorial approaches into a single flexible one which has the property of being theoretically grounded into the economics mainstream and, at meantime, suitable to deal with some lack of information and research.

The policy debate surrounding the employment of immigrant workers in U.S. agriculture centers around the extent to which immigrant farmworkers adversely affect the economic opportunities of native farmworkers. To help answer this question, we propose a three-layer nested constant elasticity of substitution (CES) framework to investigate the substitutability among heterogeneous farmworker groups based on age, skill, and legal status utilizing National Agricultural Workers Survey (NAWS) data from 1989 through 2012. We use farmwork experience and type of task performed as alternative proxies for skill to disentangle the substitution effect between U.S. citizens, authorized immigrants, and unauthorized immigrant farmworkers. Results show that substitutability between the three legal status groups is small; neither authorized nor unauthorized immigrant farmworkers have a significant impact on the employment of native farmworkers.

International audience; We analyze a cheap talk game in a two-dimensional framework, with complementarities between the dimensions. A receiver chooses a two-dimensional costly effort in a productive activity. The Receiver's effort profile is determined by his individual ability profile, of which he is unaware. He is advised by an informed Sender, who makes one of two recommendations to maximize the Receiver's output. Output is a Constant Elasticity of Substitution function of the Receiver's two one-dimensional contributions. The credibility constraint on the Sender's recommendations requires her to truthfully contrast the Receiver's abilities. As a result, the Receiver associates greater (resp. less) effort with greater (resp. less) perceived ability in one (resp. the other) dimension. However, when there are strong complementarities, the Sender becomes more interested in the mismatch between effort and ability. Thus, strong complementarities preclude the Sender from making credible recommendations. By contrast, weaker complementarities allow the Sender to make credible recommendations, using either: (i) a symmetric comparison of abilities; or (ii) an asymmetric comparison, in which one ability could be perceived as greater, even if it is not. Sufficient complementarities make the asymmetric information revelation more stable and more productive.

Consumption of supply in transportation systems has generally always followed a First-Come-First-Served (FCFS) rule. This article proposes new control policies based on the concept of envy-freeness which outperform FCFS in both efficiency and fairness. We call an allocation envy-free when no agent feels any other agent’s allocation to be better than their own, at the current price. Envy-free allocations are thus considered fair. Several new contributions are made: we first present a conceptual theoretical supply-demand framework which formally introduces the new supply paradigm. We propose and simulate a new problem, queue-jumping operations on highways, in which vehicles can skip positions in a queue and compensate the overtaken vehicles with a payment. We present a new concept, dynamic envy-freeness, and provide a new envy ranking criterion, Constant Elasticity of Substitution Envy Intensity (CESEI) that is applied to PEXIC, an exchange-based traffic signal control scheme.

We investigate the effect of higher house prices or rental costs on family size. We provide a static model of a household's choice of family size assuming constant elasticity of substitution preferences between children, leisure, and other goods, and Cobb–Douglas household production of children using parental time and housing. We then explore the wealth and substitution effects that changing house prices or rental costs have on desired family size. Renters are predicted to have fewer children in response to higher rents. Home owners are predicted to have more children in response to higher house prices only if they have sufficient initial housing and low substitution between family size and other consumption, and fewer children otherwise. Finally, we provide exploratory correlations between the change in lagged house prices or rental costs and the change in number of children born to women using aggregated census units in New Zealand. We find weak negative correlations in both cases.

This paper presents a new, non-calculus approach to solving the consumer’s utility–maximization problem with constant elasticity of substitution (CES) utility function, as well as with Cobb-Douglas utility function in case of \(n\ge 2\) commodities. Instead of using the Lagrange multiplier method or some other method based on differential calculus of several variables which might give complicated terms and equations difficult to handle, the utility–maximization problems are solved by using Jensen’s inequality and weighted arithmetic-geometric mean (weighted AM–GM) inequality. In comparison with calculus methods, such approach does not require checking first and second order conditions.

This paper examines optimal monetary policy in a new Keynesian model with sectoral inflation persistence. It focuses on the welfare differential between timeless perspective (TP) and a purely discretionary monetary policy. Sectoral inflation persistence renders the central bank’s optimization problem more complicated under both cases of constant elasticity of substitution consumption index and generalized rule-of-thumb price setting. We find that there are substantial gains from employing a TP policy. This paper addresses the fact that this gain is robust with any changes in key structural parameters.

The ease with which firms can substitute away from energy to other inputs is an important determining factor in the costs of climate change mitigation policies. Climate policy simulation models usually represent this substitutability by using the Constant Elasticity of Substitution (CES) function with parameter values often taken from econometric studies. Hence, the accuracy of the estimated substitution parameters has a strong influence on the validity of the climate policy simulation. In this article, we attempt to replicate the results presented in a widely cited article in this field: Kemfert (1998) (‘Estimated substitution elasticities of a nested CES production function approach for Germany’, Energy Economics, 20, 249–264). We first use the data and software reported in that article and compare our results with those reported in the original study. We then test the same data and a new, more recent, data set on German industrial data with an improved econometric approach. Despite applying various approaches and modifications, we are not able to replicate the results in Kemfert (1998). We furthermore conclude that the data sets that are typically used to estimate nested CES functions often have too few observations and too little independent variation of the explanatory variables to obtain reliable estimates when using a direct non-linear approach. The ease with which firms can substitute away from energy to other inputs is an important determining factor in the costs of climate change mitigation policies. Climate policy simulation models usually represent this substitutability by using the Constant Elasticity of Substitution (CES) function with parameter values often taken from econometric studies. Hence, the accuracy of the estimated substitution parameters has a strong influence on the validity of the climate policy simulation. In this article, we attempt to replicate the results presented in a widely cited article in this field: Kemfert (1998) (‘Estimated substitution elasticities of a nested CES production function approach for Germany’, Energy Economics, 20, 249–264). We first use the data and software reported in that article and compare our results with those reported in the original study. We then test the same data and a new, more recent, data set on German industrial data with an improved econometric approach. Despite applying various approaches and modifications, we are not able to replicate the results in Kemfert (1998). We furthermore conclude that the data sets that are typically used to estimate nested CES functions often have too few observations and too little independent variation of the explanatory variables to obtain reliable estimates when using a direct non-linear approach.

This paper provides the first comprehensive review of the empirical and theoretical literature on the determinants of the elasticity of substitution between capital and labor. Our focus is on the two‐input constant elasticity of substitution (CES) production function. We start by presenting four concise observations that summarize the empirical literature on the estimation of . Motivated by these observations, the main part of this survey then focuses on potential determinants of capital–labor substitution. We first review several approaches to the microfoundation of production functions where the elasticity of substitution (EOS) is treated as a purely technological parameter. Second, we outline the construction of an aggregate elasticity of substitution (AES) in a multi‐sectoral framework and investigate its dependence on underlying intra‐ and inter‐sectoral substitution. Third, we discuss the influence of the institutional framework on the extent of factor substitution. Overall, this survey highlights that the effective elasticity of substitution (EES), which is typically estimated in empirical studies, is generally not an immutable deep parameter but depends on a multitude of technological, non‐technological, and institutional determinants. Based on these insights, the final section identifies a number of potential empirical and theoretical avenues for future research.

In the decades to come, seawater desalination is expected to be an important source of potable water in water-stressed countries bordering oceans and seas, in particular in regions with fast population growth where further decline of natural freshwater availability is expected due to climate change. Israel, being part of the “thirsty Middle East region”, faces natural water scarcity that was exacerbated by the five-year drought started at 2013. This has led to an ever-growing reliance on alternative water sources, where seawater desalination has been the main source for addressing the shortages. Desalination plants currently provide about a quarter of the potable water supply with plans to expand the desalination capacity. In this chapter, I assess the economic value of seawater desalination which increases the water supply and diminishes the effects of natural freshwater shortages. The analysis employs the Israeli Computable General Equilibrium (CGE) model—IGEM, which estimates the benefit of desalination gained by reducing water shortages that cause an economic loss with impact on the entire Israeli economy. IGEM assesses the impact of water shortages on key economic indicators, where the shortage values are equivalent to the amounts of desalinated seawater—current and planned. The different qualities characterizing the five water types, which account for constraints associated with crop salinity-tolerance and food-safety regulations, are reflected in the model by the constant elasticity of substitution (CES) rates between different irrigation water types. The results reveal that the value of desalinated seawater due to its role in diminishing potable water shortages is about $4 per m3—much higher than its direct cost.

Is the variation in bilateral trade flows across countries primarily due to differences in the number of exporting firms (the extensive margin) or in the average size of an exporter (the intensive margin)? And how does this affect the estimation and quantitative implications of the Melitz (2003) trade model? The benchmark Melitz model with Pareto-distributed firm productivity and fixed costs of exporting, predicts that, conditional on the fixed costs of exporting, all variation in exports across trading partners should occur on the extensive margin. This paper subjects this theoretical prediction to a reality check drawing upon the World Bank's Exporter Dynamics Database (EDD) which has firm-level exports from 50 developing countries to all destinations. Around 50 percent of the variation in exports across trading partners is shown to be along the intensive margin, contradicting the benchmark Melitz-Pareto model. The paper finds that moving from a Pareto to a lognormal distribution of firm productivity allows the Melitz model to successfully match the role of the intensive margin evident in the EDD. The paper then studies the implications of our findings for quantitative trade theory. Using likelihood methods and the EDD, a generalized Melitz model with a joint lognormal distribution for firm productivity, fixed costs and demand shifters is estimated, and exact hat algebra is used to quantify the counterfactual effects of a decline in trade costs on trade flows and welfare in the estimated model. Finally, these effects are compared to those that would be predicted by the Melitz-Pareto model, with the Pareto shape parameter chosen to match the average trade elasticity implied by the estimated Melitz-lognormal model. The paper shows that the effects on welfare turn out to be quite close to those in the standard Melitz-Pareto model even though the effects on trade flows remain different.

The question of appropriate factor proportions and concern for the low absorption of labor in LDC manufacturing have made these issues important areas for research and policy in the developing countries. This is especially so in Malaysia since unemployment increased from a rate of 3 percent in 1970 to 8.7 percent in 1987, despite large investments within this period;In this study, econometric analysis of capital-labor substitutability is conducted for the Malaysian manufacturing sector for the period 1963-1984. Estimates of the elasticity of substitution are computed using the Constant Elasticity of Substitution (CES) production function approach, the translog cost approach and the CES-translog cost approach. Comparisons of alternative estimates of the elasticity of substitution between capital and labor are also made;The statistical analysis shows that most of the Malaysian industries at the 5-digit industrial classification level exhibit relatively low elasticities of substitution between capital and labor. This provides a clearer understanding of the relatively low labor absorption in the Malaysian manufacturing sector. Other factors which may be responsible for the choice of inappropriate factor proportions including biases in government policy as well as private decisions by firms are also discussed.

In standard production models, wage volatility is far too high, and equity volatility is far too low. A simple modification–sticky wages because of infrequent resetting together with a constant elasticity of substitution (CES) production function leads to both smoother wages and higher equity volatility. Further, the model produces several other hard-to-explain features of financial data: high Sharpe ratios, low and smooth interest rates, time-varying equity volatility and premium, a value premium, and a downward-sloping equity term structure. Procyclical, volatile wages are a hedge for firms in standard models; smoother wages act like operating leverage, making profits and dividends riskier.

Staffing decisions are crucial for retailers since staffing levels affect store performance and labor-related expenses constitute one of the largest components of retailers’ operating costs. With the goal of improving staffing decisions and store performance, we develop a labor-planning framework using proprietary data from an apparel retail chain. First, we propose a sales response function based on labor adequacy (the labor to traffic ratio) that exhibits variable elasticity of substitution between traffic and labor. When compared to a frequently used function with constant elasticity of substitution, our proposed function exploits information content from data more effectively and better predicts sales under extreme labor/traffic conditions. We use the validated sales response function to develop a data-driven staffing heuristic that incorporates the prediction loss function and uses past traffic to predict optimal labor. In counterfactual experimentation, we show that profits achieved by our heuristic are within 0.5% of the optimal (attainable if perfect traffic information was available) under stable traffic conditions, and within 2.5% of the optimal under extreme traffic variability. We conclude by discussing implications of our findings for researchers and practitioners.

This article studies an economy with both centralized and decentralized monetary exchanges under search frictions. A degenerate asset distribution is featured under a broad class of preferences including, for example, constant return to scale, constant elasticity of substitution, CARA and others from a range of macroeconomic literatures. Some novel applications impossible under quasi-linear preferences, for example endogenous growth, are illustrated under this class of preferences. This article finds that the welfare cost and growth loss of inflation can be much higher in these applications than previous estimates.

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.

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.

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.

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.

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.

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.

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%.

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.

In recent years models with a nested constant elasticity of substitution utility function and heterogeneous firms involved in some form of competition have become popular in the international trade literature. This paper considers one particular model of this class — with firms competing in prices — and shows continuity of the model as the elasticity of substitution between goods goes to infinity. This result contrasts with the conjecture of prior literature. Continuity of the model ensures consistency of its outcomes when the elasticity of substitution approaches infinity. Therefore, researchers who were reluctant to use this model because of the lack of proof of continuity can now rely on this paper’s result to employ the model in their research.

This article estimates using the Bayesian methods a Constant Elasticity of Substitution (CES) production function for Singapore for 1960–2009. It is found that the elasticity of substitution is 0.6, technical progress is labour augmenting and the Steady-State Growth Rate (SSGR) of Singapore is about 1.8%.

When the Asia Pacific Economic Cooperation (APEC) formally adopted the principle of “open regionalism” (OR) in its trade liberalization in 1991, many were optimistic that this approach suggested the bloc as a stepping stone toward global free trade. This optimistic view was reinforced by the economic theorizing of Sang-Seung Yi (1996). This paper shows formally via a simple model why OR may fail. We unpick Yi (1996) systematically and explain that OR works in his model because of quasilinear preferences and Ricardian technology assumptions. Once these assumptions are replaced with constant elasticity of substitution (CES) preferences and increasing marginal costs, OR fails to ensure global free trade as an equilibrium when the world consists of a country that is sufficiently larger than the rest of the world.

This article deals with the feasibility of a tradable emission permit system (TEPs) for urban motorists. The objective is to develop a new microeconomic theoretical model to reduce urban pollution. We suppose that the city's regulating authority sets up a tradable emission permit system based on the number of kilometres covered by private cars. By the use of a Constant Elasticity of Substitution (CES) function, we determine the equilibrium under an environmental constraint and analyse the effects of a TEPs on social welfare. The aim is to find the optimal quantity of permits leading to the desired environmental objective. The analytical and numerical results of the model show the instrument's feasibility and efficiency. An important variable in the model must be taken into account: the knowledge of environmental damage. This variable will clearly influence the tool's success.

PurposeThe purpose of this paper is to understand technology diffusion in the banking sector in India by analyzing ATM (automatic teller machine) technology and its replacement of the teller (labor). ATMs are fast emerging as an important IT investment for a bank in India. Hence, in this paper the authors use the ATM as a proxy for capital and the teller as a proxy for labor.Design/methodology/approachThe debate on the “IT paradox” is the motivation for this paper. The constant elasticity of substitution (CES) model is used, as the degree of substitution can be estimated. The degree of substitutability of one form of input for another namely, ATM (capital) for teller (labor), is discussed by developing an appropriate model to understand the same.FindingsThe rapid diffusion of the ATM was clearly large from 1998, nine years after it was first adopted. This was also a time when the number of tellers was falling and the wage bill for tellers increasing. The CES production function model used in this paper is clearly a good predictor of the data compared with the other cases. The estimate shows that the degree of substitutability of the teller by the ATM is high. However, the ATM is not a perfect substitute. By running counterfactual experiments, it can be concluded that both a fall in the price of ATMs and an increase in the wage bill for tellers contributed to the diffusion of the ATM.Practical implicationsThe excess labor in public sector banks needs to be redeployed rapidly, or staff need to be trained in other functions as do private banks, so that they do not become redundant as technology diffuses.Originality/valueThe paper is original in its data, its model building and testing in the banking sector.

In very different fields of economics, economic inference and policy evaluation require economists to parametrize a production function that links measures of input factors to measures of output. While doing so, strong assumptions are implicitly made about microeconomic variables governing the shape of the aggregate production function. In this paper, I develop an assignment model that provides a microeconomic foundation for aggregate production functions. The shape of the production function depends crucially on the distribution of workers and jobs and the type of technological changes depends crucially on the evolution of these distributions. Sufficient and necessary conditions are provided for the production function to be of the Constant Ratio of Elasticities of Substitution form, a form nesting the broadly used Constant Elasticity of Substitution form. This model provides a way to evaluate how stringent assumptions about the type of production function or technological change are by comparing the implied distribution of jobs and its evolution over time to observations of the distribution of jobs and its evolution over time.

Jelen írásban röviden bemutatom az egyes növekedéselméletek fejlődését, számba véve az egyes fejlődési szakaszokban a növekedés legfontosabb forrásainak tekintett tényezőket. Mivel a termelési függvény egyik fontos paramétere, a helyettesítési rugalmasság értéke nem egységnyi, ahogyan azt a nemzetközi vizsgálatokban alkalmazott Cobb–Douglas-termelési függvény feltételezi, és a helyettesítési rugalmasság értéke 1-től eltérő is lehet, szükséges egy általánosabb, CES típusú (Constant Elasticity of Substitution – állandó helyettesítési rugalmasságú) „termelési függvény”-család alkalmazása is. Technikai kérdésként felmerül a termelési tényezők csoportosítása is. A helyettesítési rugalmasság egyben hatékonysági tényező is, ezért a termelési függvény ezen jellemzője kiemelt szerepet kap az elemzésben. Végül összefoglalom azokat a legjelentősebb irodalmakat, amelyek főként a növekedés összetételével (growth accounting) foglalkoznak, és megpróbálnak választ találni arra a kérdésre, hogy mely faktorok játszanak jelentős vagy kevésbé jelentős szerepet a gazdasági növekedésben. A growth accounting erősen összekapcsolódik a növekedéselméletekkel, így a megfelelő pontokon visszautalok az egyes növekedéselméletekre is. Journal of Economic Literature (JEL) kód: E13, O47

A framework that uses a Constant Elasticity of Substitution (CES) production function with skill differentiation and integrated national labor markets has predictions for the employment effect of immigrants at the local level. The employment (rather than wage) response to immigration by skill in a state reveals the production substitutability–complementarity between native and immigrant labor. This, in turn, reveals the degree to which immigrants stimulate or depress the demand for native labor. To estimate this elasticity, I use a novel instrument based on demographic characteristics of total Central American migrants or of the Mexican Population to predict immigration by skill level within California. Looking at immigration to California between 1960 and 2005 these estimates support the assumption of a nationally integrated labor market by skill and they support the hypothesis that natives and immigrants in the same education-experience group are not perfectly substitutable. This explains the counter-intuitive fact that there is a zero correlation between immigration and wage and employment outcomes of natives in the state.

The production function explains a basic technological relationship between scarce resources, or inputs, and output. This paper offers a brief overview of the historical significance and operational role of the production function in business and economics. The origin and development of this function over time is initially explored. Several various production functions that have played an important historical role in economics are explained. These consist of some well known functions, such as the Cobb-Douglas, Constant Elasticity of Substitution (CES), and Generalized and Leontief production functions. This paper also covers some relatively newer production functions, such as the Arrow, Chenery, Minhas, and Solow (ACMS) functions, the transcendental logarithmic (translog), and other flexible forms of the production function. Several important characteristics of the production function are also explained in this paper. These would include, but are not limited to, items such as the returns to scale of the function, the separability of the function, the homogeneity of the function, the homotheticity of the function, the output elasticity of factors (inputs), and the degree of input substitutability that each function exhibits. Also explored are some of the duality issues that potentially exist between certain production and cost functions. The information contained in this paper could act as a pedagogical aide in any microeconomics-based course or in a production management class. It could also play a role in certain marketing courses, especially at the graduate level.

In this article we defend that the adoption of a non-linear approach, theoretically framed on complexity theories can make some contribution to the bottom-up approach, which explains the levels of satisfaction with life as a whole through the combination of the levels of satisfaction in different life domains. Two approaches have been tested: (Rojas in J Happiness Stud 7:467–497, 2006) constant elasticity of substitution model and the model with quadratic terms and interaction effects (Gonzalez et al. in Soc Indic Res 80:267–295, 2006; Gonzalez et al. in Qual Quant 42:1–21, 2008). In order to prevent obtaining false non-linear relationships they have been analysed twice taking into account or not limited measurement of satisfaction with life as a whole. Results show that: (a) any of the two non-linear models fits better than the linear one; (b) any of the models failing to take into account limited measurement fits worse; (c) the non-linear model with quadratic terms and interaction effects fits better than Rojas’. The implications for the study of psychological well-being are discussed.