The CES‐‐Translog Production Function, Returns to Scale and AES

The translog functional form imposes no a priori restrictions on the substitution possibilities between the factor inputs, by relaxing the assumption of strong separability, and the CES–translog cost function specification allows for testing homothetic technology with Hicks‐neutral technical change. In this paper an n ‐factor CES–translog production function is presented which develops the parameters to directly assess scale effects from those due to technology in the production structure. In addition, by applying Shephard's lemma it was possible to derive the input demand functions, as well as the partial elasticities of substitution and the cross‐partial price elasticities of demand for a generalized CES–translog production structure.     

Are sports teams multiproduct firms?

The appropriate conception of team outputs is investigated by estimating a two-output factor demand system for baseball teams, relative to which single-output models are rejected. This finding is robust to alternative approaches to testing and model choice. The factor demands are those of the symmetric generalized McFadden cost function, which has several advantages in this context. The team factor inputs are the skill characteristics of players, the prices of which are obtained hedonically. In addition to investigating one- versus two-output models, the estimation results are used to obtain demand and substitution elasticities, factor input elasticities with respect to output, cost elasticities, and measures of economies of scale and scope. Although the results support a multiproduct conception of team production, output separability is not rejected, suggesting that team outputs may sometimes be adequately treated as a production aggregate.     

Intertemporal production and intertemporal substitution in output supply and input demand

This article presents an intertemporal model of production with multiple inputs to investigate substitution opportunities facing firms over time. The firm’s intertemporal profit maximization problem is characterized with the familiar cost function, and various intertemporal substitution elasticities are delineated for output supply and input demand. The absence of intertemporal substitution in production can imply production smoothing, and allowance for intertemporal substitution in labour demand reinforces the prediction of the real business cycle model. For aggregate US manufacturing, we find substantial substitution in output supply and labour demand over time due to intertemporal changes in output price and wage rates.     

Indeterminacy and multiple steady states with sector-specific externalities

This paper studies a two-sector model with aggregate and sector-specific external effects in production and inelastic labor supply. We first characterize the existence, uniqueness and multiplicity of the steady states as well as their welfare properties. We particularly focus on the CES production functions and show that the steady state is generically either unique or there are exactly two. A simple geometrical methodology enables us to characterize the local dynamics of the steady state. We show that in order to get indeterminacy, the presence of both aggregate and sector-specific external effects is needed, along with low capital–labor elasticities of substitution and high, but bounded from above, elasticities in intertemporal consumption. We perform a sensitivity analysis and show that indeterminacy emerges for parameter values in line with those used in calibrations of standard RBC models, that is for unitary elasticities of input substitution and of intertemporal substitution in consumption.     

An investigation of issues relating to where energy should enter the production function

This paper examines the impact of imposing different separability assumptions in the specifications of the standard hierarchical KLEM production function in a computable general equilibrium (CGE) model. The appropriate means of introducing energy to production functions has been a source of debate for a number of years. However, while modellers often subject results to parametric sensitivy analysis regarding the values associated with elasticities of substitution between inputs, it is rarely the case that the structure of the production function is subjected to testing. However, the chosen structure reflects the modeller's view about elasticity between different inputs and will have implications for model results wherever there are changes in relative prices. We illustrate our argument by introducing a simple demand shock to a CGE model of the Scottish economy (targeted at the energy supply sector) under different assumptions regarding the structure of the KLEM production function and separability assumptions therein.     

Production and costs in the South African motor vehicle industry

This study investigates the existence of economies of scale in the South African motor vehicle industry as well as the substitution possibilities between input pairs and the direct and cross-price elasticities of demand for the various inputs. Because of data limitations, a translog cost function was estimated for only a three input model corresponding to a homogeneous production function involving capital, labour and intermediate goods. The issue of the existence of economies of scale in the South African motor vehicle industry is a particularly important one because South Africa once again is a member of GATT and a full participant in the international trade arena. The null hypothesis of constant returns to scale was rejected at the 0.5% level of significance. Thus, the results of this model are certainly consistent with economies of scale in the South African motor vehicle industry. The estimated direct price elasticities were consistent with the hypothesis that, during the past two decades, capital was the productive factor with the most elastic demand, and the estimated cross-elasticities between input pairs generally supported the hypothesis that all inputs are substitutes.     

Adjustment costs and threshold effects in factor demand relationships

It has been recently argued that producers may not respond to every input price change in the way that a linear factor demand model would predict. This lumpy response is due to adjustment costs that are inherent in the act of adjusting the mix of inputs applied in the underlying production technologies. This study aims to provide a solid conceptual framework for these nonlinearities in factor demand relationships. Industry-specific implications of convex and non-convex adjustment costs for the linearity of the factor demand relationships as well as price and substitution elasticities are explored. A two-regime threshold system of factor demand equations is estimated for several manufacturing industries in the United States. Empirical results suggest significant threshold effects in the factor demand relationships in most nondurable goods sectors. The size and the nature of thresholds depend upon industry characteristics, including input composition and (non)convexity of underlying adjustment costs. Complete matrices of price and substitution elasticities for each industry are derived using estimates of threshold factor demand systems. Discussion of two contrasting cases in greater detail sheds light on how the effect of price shocks on factor demand relationships varies across industries with different adjustment cost structures.     

A model of income distribution in a revenue-sharing firm

Income distribution within a fixed-membership firm is modeled assuming that all net revenue is distributed to workers. The payment system used is a generalization, for heterogeneous workers, of an income equation first adopted by Sen. We introduce the assumption that payment rates for different workers are chosen to maximize an individualistic welfare function for the firm. A general result for a maximin welfare function is obtained and, using a simulation, we explore the effects of different elasticities of substitution in individual utility functions and different weights put on egalitarianism in the welfare function.     

The role of labour demand elasticities in tax incidence analysis with heterogeneous labour

Whether labour bears full burden of household level income and consumption taxes ultimately depends on the degree of substitutability among different types of labour in production. We find more variation in incidence patterns across households with less than perfectly substitutable heterogeneous labour than with perfectly substitutable homogeneous labour in production. This finding is based on results obtained from homogeneous and heterogeneous labour general equilibrium tax models calibrated to decile level income and consumption distribution data of UK households for the year 1994. We use labour supply elasticities implied by the substitution elasticity in households' utility functions and derive labour demand elasticities from the substitution elasticity in the production function. First version received: March 1998/Final version received: April 1999     

Elasticities of substitution between energy and non-energy inputs in China power sector

Energy substitution is considered as a key process to determine the economic outcome of decisions related to energy and environment policies. The sign and magnitude of energy substitution have been widely debated, and the results are divergent. This paper applies the translog cost function specification to estimate factor share equations based on the energy and non-energy inputs, whose coefficients are used to observe the energy degree of substitutability with the other traditional inputs for power industry in China. The results suggest that energy is the least price sensitive among three production factors. The four types of input elasticities (cross-price, Morishima's, Allen and McFadden's shadow elasticity of substitution) show that there are substantial substitution possibilities between energy and capital, while energy and labor have weak substitution. The findings imply that for power industry in China, to reduce energy consumption, more capital should be invested. With respect to labor, though, it appears less energy-saving potential.     

A short and intuitive proof of Marshall's Rule

Summary. When the price of an input factor to a production process increases, then the optimal output level declines and the input is substituted by other factors. Marshall's rule is a formula that determines the own-price elasticity for one factor as a weighted sum of the elasticities of output market demand and factor substitution. This note offers a proof for Marshall's rule that is significantly shorter and somewhat more intuitive than existing derivations. Received: February 19, 2001; revised version: April 3, 2002 RID="*" ID="*" I thank Charalambos Aliprantis, John Moore, Patrick Schmitz, and the anonymous referee for helpful suggestions. Support by the German Academic Exchange Service is gratefully acknowledged.     

Nachfragefunktionen für die Produktionsfaktoren Arbeit und Kapital

Summary In this paper we present dynamic factor demand functions for labour and capital, and the underlying production function for the Austrian economy. Our approach is neoclassical. By definition, the production function is of the Cobb-Douglas type; experiments with a CES production function were not successful. Our empirical results look very plausible. The adjustement speeds, the output and price elasticities of both factor demand functions, as well as the parameters of the underlying production function are of a order of magnitude highly compatible with neoclassical theory.     

European Integration and Production in the French Economy

Effects of greater European integration on the French economy are explored with an aggregate cost function. Input direct price elasticities are inelastic, but greatest (absolute value) for capital and lowest for imports. Cross-price elasticities suggest inputs are substitutes and are higher for domestic inputs than domestic input and imports pairs. As trade restrictions fall, effects on domestic input demand may increase as substitution elasticities rise. Inverse output supply price elasticities indicate domestic input prices are relatively important factors affecting consumption goods prices and import prices more important for investment goods. Thus, import price decreases may stimulate investment and growth. (JEL F14 , O10 , O12 )     

General equilibrium models with Morishima elasticities of substitution in production

Analytical general equilibrium (AGE) models are important tools that economists use to answer questions about theory and policy. When a production function has three or more inputs, the traditional modeling technique employs Allen elasticities of substitution to represent general functional forms. This paper builds an analytical general equilibrium model using the Morishima elasticity of substitution (MES). Specifically, an existing model using Allen elasticities is reformulated to employ the MES and the new, closed-form solutions are interpreted with additional insights from the reformulation. Importantly, the special case of constant elasticity of substitution (CES) production follows directly when using Morishima elasticities, but not Allen elasticities. This paper also provides a general technique for switching from Allen to Morishima elasticities in any existing AGE model and demonstrates a one-to-one numerical equivalence regardless of the elasticity measure employed. Replicating prior results, plausible parameter values are applied to the reformulated model to analyze the source-side, distributional effects of a pollution tax and highlight how the Allen and Morishima elasticities differ.     

The aggregate elasticity of factor substitution with middle products

The elasticity of substitution between factors in production relates the change in the ratio of factors used in a production process to a given change in the factor price ratio. An aggregate concept of such an elasticity relates a change in overall factor endowments to the resulting change in factor prices. For a closed economy the behavior of consumers is an important part of such an aggregate elasticity, since endowment changes can bring about changes in commodity prices and resulting adjustments to factor prices. For a small open economy, commodity prices in typical models are exogenous. In the model with middle products, all final consumer goods are non-traded, so that local consumer behavior can affect factor prices. The aggregate elasticity of substitution is shown to be an average of production elasticities and demand elasticity even for a small open economy.     

Global restrictions on the parameters of the CDES indirect utility function

This paper extends the analytical and empirical application of the basic indirect utility function of Houthakker–Hanoch—called the CDES specification (constant differences of elasticities of substitution). The non-homothetic CDES preferences are the natural parametric extension on the global domain of the homothetic CES preferences with many commodities, and CDES can conveniently be used in specifying CGE multisector models with a demand side satisfying observable Engel curve patterns. Moreover, all Marshallian own-price elasticities are no longer restricted to exceed one, and positive and negative cross-price effects are allowed for in empirical demand analyses. Explicit calculations of the Allen elasticities of substitution are instrumental in demonstrating the economic implications of the parameters of indirect utility functions with global regularity properties and flexibility of the derived demand systems.     

The structure of production in South Korea's manufacturing sector

This paper estimates a model of producer behavior for South Korean manufacturing that simultaneously identifies substitution elasticities and scale economies. A non-homothetic translog function is employed which takes on various other functional forms (i.e., Cobb–Douglas, Homothetic, Homogeneous) as special or limiting cases. Four significant conclusions are: (a) there is potential scale economies in each subsector of South Korean manufacturing, (b) the substitutabilities between factor inputs are relatively low, (c) factor demands are price elastic, (d) the scale economies are correlated with the factor intensity.     

How substitutable is natural capital?

One of the recurring themes in the sustainability literature has been the extent to which a loss of natural capital can be made up for in welfare terms by an increase in other forms of capital. This issue was raised early on in the debate on sustainability by Pearce and has never really been resolved. This paper is an empirical attempt to measure the degree of substitutability between different forms of capital. A nested CES production function is used to allow flexibility in the estimated elasticities of substitution. Also, within this specification, natural resources and other inputs are combined in different levels of the function, thus allowing for different levels of substitutability. Institutional and economic indicators are also incorporated in the production function estimated. Results show that the elasticities derived from functions involving land resources were generally around one or greater, implying a fairly high degree of substitutability. Furthermore, changes in trade openness and private sector investment have a statistically significant and direct relationship on the efficiency of production and hence on income generation. No statistically significant relationship between income and any of the institutional indicators was found.      

Coca Substitution and Free Trade in Bolivia: The Pending Crisis

This paper uses the factors proportion model of production and trade with ten inputs to analyze the potential impact of the Free Trade Agreement of the Americas (FTAA) on the coca substitution program in Bolivia. With six crops including coca, the model produces comparative statics elasticities of changing prices on factor prices and output. Results show that the coca substitution program with free trade will result in large income redistribution in the coca‐producing region as a result of increased competition from larger and more efficient economies. Increased subsidies and institutional changes will be needed to sustain the coca substitution program in the long run.     

Variable output elasticities and technique-specific technical progress: A method of measurement

The possibility of accounting for technique specific technical progress in an econometric production function is raised. In addition the validity of the assumption of constant output elasticities over input combinations is questionned and tested using aggregate U.S. industrial data. There appears to be considerable variation in output elasticities over different techniques of production.