A note on aggregation of CES-type production functions

In this note we shall be concerned with the aggregation of the constant elasticity of substitution (CES) type of production function. In particular we will derive the error made by using the arithmetic averages as they are usually published, rather than the theoretically required averages.     

The premiss-based approach to judgment aggregation

In the framework of judgment aggregation, we assume that some formulas of the agenda are singled out as premisses, and that both Independence (formula-wise aggregation) and Unanimity Preservation hold for them. Whether premiss-based aggregation thus defined is compatible with conclusion-based aggregation, as defined by Unanimity Preservation on the non-premisses, depends on how the premisses are logically connected, both among themselves and with other formulas. We state necessary and sufficient conditions under which the combination of both approaches leads to dictatorship (resp. oligarchy), either just on the premisses or on the whole agenda. Our analysis is inspired by the doctrinal paradox of legal theory and is arguably relevant to this field as well as political science and political economy. When the set of premisses coincides with the whole agenda, a limiting case of our assumptions, we obtain several existing results in judgment aggregation theory.     

The probability approach to general equilibrium with production

We develop an alternative approach to the general equilibrium analysis of a stochastic production economy when firms’ choices of investment influence the probability distributions of their output. Using a normative approach we derive the criterion that a firm should maximize to obtain a Pareto optimal equilibrium: the criterion expresses the firm’s contribution to the expected social utility of output, and is not the linear criterion of market value. If firms do not know agents utility functions, and are restricted to using the information conveyed by prices then they can construct an approximate criterion which leads to a second-best choice of investment which, in examples, is found to be close to the first best. We are grateful to participants in the 2006 Public Economic Theory Conference, Hanoi, the 2007 CARESS/COWLES workshop on General Equilibrium at Yale University, the 2007 SAET Conference at Kos, Greece, the NSF/NBER 2007 Conference on General Equilibrium at Northwestern University, and seminars at Rice University, the University of Southern California, Indiana University, and U.C. Davis for helpful comments. We particularly thank Jacques Drèze and David Cass for stimulating discussions, and a referee for helpful suggestions for improving the paper.     

Differentiability of the cost functions is equivalent to strict quasiconcavity of the production functions

The assumption that cost functions are differentiable with respect to input prices is equivalent to the assumption that production functions are strictly quasiconcave.     

Structural change in Finnish manufacturing: The theory of the aggregation of production functions and an empirical analysis with a plant-level panel

In this paper, structural change in the Finnish manufacturing industries is studied using the theory of the aggregation of production functions and longitudinal plant-level data for the period from 1980 to 2005. To characterise the nature of structural change in 12 industries, we examine the invariance of aggregate production functions over time. Aggregate production functions need not be estimated because, according to the theory of the aggregation of production functions, the invariance can be analysed by investigating the stability of capacity density functions, which describe the distribution of value added in these industries. Even though the shapes of aggregate production functions alter over time in most industries, there are differences in timing and in the degree of turbulence across industries. The analysis confirms that in some industries (e.g., the paper industry) the late 1980s marked the beginning of a period of relatively strong structural change. The food and communications equipment manufacturing industries are examples of industries for which the 1990s was a period of turbulence.     

试论按劳分配与按生产要素分配

长期以来,对于分配制度原则的选择,我国经历了从单纯的按劳分配,到按劳分配为主、其他分配形式为辅,再到按劳分配与按生产要素分配相结合这样一个较长的过程。按劳分配是以马克思主义理论为依据的。社会主义初级阶段的基本经济制度决定了我们必须把按劳分配和按要素分配两种不同的分配方式结合起来。按劳分配与按生产要素分配两种分配方式的结合是我国建立社会主义市场经济体制的客观要求。     

The production of functionality by the elderly: a household production function approach

This paper extends Becker's model of the household production function of human capital to the production of elderly functionality. In this model, elderly functionality is produced with the direct inputs of assistive devices, personal assistance, and nutritional intake. Education, endowment variables (like genetic endowment and sex) and health conditions (like stroke) determine the production function environment. Data from the Survey of Asset and Health Dynamics Among the Oldest-Old (AHEAD) are used to estimate a production function of bathing functionality, using a two-stage estimation procedure. In the first stage, input demands for the endogenous functionality inputs are estimated, recognizing health heterogeneity. The results suggest that reverses in functionality caused by age and health conditions can be partially compensated for by the use of assistive devices (like grab bars and bathing equipment), secure nutritional intake, and moderate alcohol consumption. However, non-inputs like chronic health conditions, age, sex and genetic endowment exert a strong influence on the level of functionality.     

Rational functions: an alternative approach to asset pricing

This paper shows that asset prices are linear polynomials of various underlying explanatory factors and asset returns being ratios of these polynomials, are rational functions that do not add linearly when averaging. Hence, average returns should be modeled based on stock prices. However, continuous returns may be treated as approximately linear across time and modeled directly. Our new Rational Function (RF) models, empirically outperform the traditional asset pricing models like the Capital Asset Pricing Model (CAPM) and the Fama–French three and five-factor models for both average and continuous returns. Moreover, the RF theory also provides a model to estimate the asset volumes. The average change in asset volumes together with average returns provide the estimates for average change in market values of assets. Thus, the RF model approach can be used to select assets that provide either highest returns for profit maximization or highest change in market values for wealth maximization for given levels of risk.     

Market behavior and the types of production functions

The paper presents a unified approach to theory and estimation of production functions based on a simple observation that any production function has a unique representation of its isoquants in terms of the differential equation which may be observable in market. Expressing the marginal rate of substitution between two inputs as the differential equation in these two inputs, various classes of production functions are obtained by integrating this differential equation. Not only does this general approach yield a systematic framework for all known forms but it also generates new types of production functions. Empirical application is also indicated.     

The amenity value of the climate: the household production function approach

A basic assumption of the hedonic technique is that there are no barriers to mobility that prevent prices changing to reflect the net benefits of a given location. But climate variables are undeviating over relatively large distances and the absence of a common language coupled with the existence of political boundaries may prevent the net advantages associated with a particular region from being eliminated. Apart from in a handful of countries, methods alternative to the hedonic approach may therefore be required to estimate the amenity value of climate. Adopting the household production function approach this paper undertakes a systematic examination of the role played by climate in determining consumption patters using data from 88 different countries. Given certain assumptions the paper then proceeds to calculate the constant utility change in the cost of living for a 2.5 °C increase in globally averaged mean temperature. It is determined that high latitude countries benefit from limited climate change whereas low latitude countries suffer significant losses.     

Some comments on the Sraffian Supermultiplier approach to growth and distribution

Abstract

The article discusses the Sraffian Supermultiplier (SSM) approach to growth and distribution. It makes 5 points. First, in the short run, the role of autonomous expenditure can be appreciated within a standard post Keynesian framework (Kaleckian, Kaldorian, Robinsonian, etc.). Second, and related to the first, the SSM model is a model of the long run and has to be evaluated as such. Third, in the long run, one way that capacity adjusts to demand is through an endogenous adjustment of the rate of utilization. Fourth, the SSM model is a peculiar way to reach what Garegnani called the “second Keynesian position.” Although, it respects the letter of the “Keynesian hypothesis,” it makes investment quasi-endogenous and subjects it to the growth of autonomous expenditure. Fifth, in the long run it is unlikely that “autonomous expenditure” is really autonomous. From a stock-flow consistent point of view this implies unrealistic adjustments after periods of changes in stock-flow ratios. Moreover, if we were to take this kind of adjustment at face value, there would be no space for Minskyan financial cycles. This also creates serious problems for the empirical validation of the model.     

The macro production function uniquely determines the capacity distribution of the micro units

A wellknown approach to the theory of production obtains the macro production function from an integration over a distribution of capacities of micro units. An elementary proof is given for the fact that the macro production function uniquely determines the capacity distribution.