THE MORISHIMA ELASTICITY OF SUBSTITUTION FOR THE VARIABLE PROFIT FUNCTION AND THE DEMAND FOR IMPORTS IN THE UNITED STATES*

In this article, I derive expressions for the Morishima elasticities of substitution (MES) for the variable profit function and estimate these elasticities to shed some light on the substitutability between imports, capital services, and labor services. The results reveal that capital services and imports are Morishima substitutes, irrespective of whether the price of capital services or imports changes, and imports and labor services are also Morishima substitutes, irrespective of whether the price of imports or the wage rate changes. Thus, an increase in the price of U.S. imports (through tariffs or duties) will result in substitution (in the Morishima sense) into labor and capital services.     

The Italian Automotive Industry and Economies of Scale

This article investigates scale economies in the Italian automobile industry as well as substitution possibilities between inputs and direct and cross-price elasticities of factor demand, utilizing a cost function with capital, labor, domestic, and imported intermediate goods inputs. Continuing European integration makes economies of scale an important issue. The study results are consistent with economies of scale in the Italian motor vehicle industry, a particularly interesting finding because the Italian automotive industry consists primarily of one firm, Fiat. The estimated direct price elasticities suggest that capital is most responsive to own price changes, and estimated cross elasticities imply that all inputs are substitutes. (JEL D 2, L 6, O 1)     

Dynamic factor demands and adjustment costs: An analysis of bell Canada's Technology

In this paper a dynamic model of production is estimated for Bell Canada. The dynamics arise from the costs of adjustment associated with capital expansion. Estimation results showed that there are significant adjustment costs. Thus, the hypothesis of long-run cost minimization is rejected. As Bell Canada increases its capital stock by $1, there are additional adjustment costs of $0.36. This result implies that Bell Canada minimizes the present value of production and adjustment costs which results in a short-run equilibrium position. Price, substitution and output elasticities are estimated. In the short-run the inputs are substitutes and the price effects are highly inelastic. Overshooting occurs with respect to labour and material demands in the short-run since the demand for capital responds very little to output expansion. Returns to scale are also estimated in this cost of adjustment model. Bell Canada exhibits increasing returns to scale initially and then decreasing returns such that on average there are constant returns to scale with a scale elasticity of 1.08.     

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.     

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 )     

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.     

The general equilibrium incidence of environmental taxes

We study the distributional effects of a pollution tax in general equilibrium, with general forms of substitution where pollution might be a relative complement or substitute for labor or for capital in production. We find closed form solutions for pollution, output prices, and factor prices. Various special cases help clarify the impact of differential factor intensities, substitution effects, and output effects. Intuitively, the pollution tax might place disproportionate burdens on capital if the polluting sector is capital intensive, or if labor is a better substitute for pollution than is capital; however, conditions are found where these intuitive results do not hold. We show exact conditions for the wage to rise relative to the capital return. Plausible values are then assigned to all the parameters, and we find that variations over the possible range of factor intensities have less impact than variations over the possible range of elasticities.     

Modeling technological bias and factor input behavior in China's wheat production sector

Over the past three decades, China has implemented reforms in the agricultural sector in an attempt to increase efficiency and food security. However, China now faces a number of environmental degradation problems, in part, caused by her past agricultural reforms. In this paper we estimate, using a provincial-based panel dataset, a third-order translog cost function for China's grain production sector over the period 1990–2011. Results from the estimation, including estimated elasticities of demand for and substitution of factors, suggest that labor and capital are substitutes. This arises because the increasing cost of labor, induced by urbanization and the growth of the manufacturing sector, has lead to a substitution of machinery for labor in the production of wheat. The results are consistent with current government policies to encourage via subsidies and agricultural mechanization, which we show to be technically, a substitute for labor. We further conclude this will create an additional bonus of reducing the amount of fertilizer that is needed to efficiently and securely produce wheat in China, as the new capital is more efficient at fertilizer distribution.     

A ray of hope? Another look at the Italian textile industry

Despite increasing competition from newly industrializing countries, Italy’s textile industry has continued to be an important contributor to the domestic economy. Many observers attribute this resilience to the industry’s focus on quality. Here, we take note of that view but also examine production and cost relationships to explore the existence of returns to scale and the interrelationships among inputs to gain additional insights about the future prospects for this industry. The findings are consistent with constant returns to scale and a substitute relationship between all input pairs except for domestic capital and foreign intermediate goods. The results also suggest some increasing flexibility in the labor market, perhaps including informal sector arrangements, greater responsiveness of labor demand to the price of capital, and more international production sharing arrangements. An increasing elasticity over time of the demands for domestic capital and domestic intermediate goods with respect to the price of foreign substitutes was also observed. Since further economies of scale do not exist, maintaining the Italian textile industry’s reputation for outstanding quality will likely be an important survival strategy for some products. For others, production sharing may be necessary to maintain international competitiveness.     

CHALLENGES FOR FRANCE IN THE EMERGING INTERNATIONAL ENVIRONMENT: A DYNAMIC ANALYSIS

France faces substantial challenges as the economic integration of Europe and the international economy continues. This article uses a dynamic aggregate translog cost function with inputs of capital, labor, and imports to examine the likely impact of closer world economic ties on France. This technique allows one to estimate short- as well as long-run direct price elasticities of demand for the inputs and cross-price elasticities for each respective input pair. The findings of the article include that (1) the French economy is becoming more sensitive to changes in import prices and (2) all the inputs are substitutes for one another. These results suggest that continuing international economic integration will present substantial challenges to the French economy. The short-run estimates of direct and cross-price elasticities are consistent with the Le Châtelier principle, except for the cross-price elasticities between capital and labor. Some possible reasons for the latter result are discussed in the article. (JEL F14, O10, O12)     

Factor analysis of demand growth for information technology input in Japan

The purpose of this article is to decompose demand changes for factor input and explore the factor that information technology (IT) capital stock has largely increased in Japan. The Allen partial elasticities of substitution are calculated and the variations in factor input demand are broken down into two effects—price effect and output effect, using industry-level data. From an estimation of the total cost function, the following conclusions are presented. While IT capital stock and ordinary capital stock are complementary, IT serves as a substitute for labor. The factors influencing the high growth rate in IT capital stock are the decrease in the prices of IT and ordinary capital services, and the increase in the labor price, in addition to the output effect. On the other hand, labor demand declines due to both the downward rigidity of wages and the decrease in prices of two kinds of capital services.     

The Spanish automotive industry: scale economies and input relationships

This paper investigates the existence of economies of scale in the Spanish automobile industry as well as the substitution possibilities between input pairs and the direct and cross price elasticities of demand for the various inputs by estimating a translog cost function for both a three input model involving capital, labour, and intermediate goods as well as a four input model where energy is separated from other intermediate goods. The results of this study are consistent with the hypothesis of economies of scale in the Spanish automobile industry, particularly at the low and mean levels of output. These results also are consistent with the hypothesis that capital is a substitute for the other inputs, but that labour and intermediate goods are complements. Labour and energy also appear to have a complementary relationship over most of the data points in this study. The significance of a complementary relationship between labour and intermediate goods is that any attempt by the Spanish government to restrict imports of these inputs, resulting in higher domestic prices for them, may aggravate an already serious domestic unemployment problem.     

A cost-based analysis of scale economies in the French auto industry

This paper examines cost relationships in the French automobile industry using a translog cost function with domestic capital and labor and domestic and foreign intermediate goods inputs. The findings suggest scale economies at lower output levels, but diseconomies at mean and maximum output levels. Cross price elasticity estimates implied all input pairs except capital and foreign parts and labor and domestic parts are substitutes. Except for foreign components, direct price elasticity estimates were inelastic. Thus, further integration of Europe and reduction of foreign input prices may substantially increase their quantity demanded and decrease the demand for domestic labor and parts.     

Trade liberalization and the Mexican steel industry

The impact of the North American Free Trade Agreement (NAFTA) on the competitive positions of Mexican and U.S. steel producers is investigated employing a translog cost function with four inputs (capital, labor, domestic intermediate goods, and foreign intermediate goods) to examine scale characteristics and input substitution in Mexican steel production. Results are consistent with diseconomies of scale at high levels of output and with substitute relationships between all input pairs except labor and domestic intermediate goods. Thus, output growth will likely result in cost reductions for Mexican producers only if the industry reaps significant benefits from substitution of foreign inputs for domestic. Recent increases in Mexico's imports of finished steel have much exceeded those of steel industry inputs, and it therefore does not seem likely that a Mexican cost advantage over steel producers in the United States will soon emerge as a result of economies of scale.     

Scale properties and input substitution in mexican electrical equipment manufacturing

This paper investigates the existence of scale economies in the Mexican electrical equipment industry and estimates direct and cross price input demand elasticities using a translog cost function. Although the estimated value of the cost elasticity was consistent with economies of scale, it was significantly less than 1 only at a significance level slightly greater than 5 percent. The estimated cross price elasticities indicated that all of the inputs were substitutes. Nevertheless, while lower trade barriers under the North American Free Trade Agreement, ceteris paribus, may have a short-term adverse effect on the demand for labor in this industry by increasing imports of cheaper capital and intermediate goods, the relatively low values for E_LK and E_LM also support the conclusion that the impact on employment may be relatively small.This project was supported by the Faculty Development Leave Program at the University of Texas at San Antonio.     

The structure of production of the Spanish telecommunications sector

The purpose of this paper is to provide empirical measures of the returns to scale coefficients, substitution elasticities between capital and labor, their marginal productivities, and the profitability of inputs in the Spanish telecommunications industry. The results of this study indicate that constant returns to scale can strongly be rejected and that the profitability indices of both factors have risen consistently since 1974. Furthermore, it concludes that the company is relatively overcapitalized, a result generally consistent with the Averch-Johnson effect for rate of return regulated monopolies.The author wishes to thank Dr. Boris Bravo-Ureta and Dr. Emilio Pagoulatos for thoughtful comments on an earlier draft. She is also indebted to an anonymous referee for valuable suggestions and to Telefónica de España for providing the data necessary for this study.     

The Antonelli Versus Hicks Elasticity of Complementarity and Inverse Input Demand Systems

A true measure of input substitution associated with exogenous changes in input quantities requires that the output level be held constant. To this effect, this study presents the Antonelli elasticity of complementarity characterised by the distance function. The more common Hicks elasticity of complementarity assumes that marginal cost is constant and hence does not capture pure substitution effects. The two elasticities of complementarity are related to inverse demand systems and are shown to be equivalent under constant returns to scale. A framework for estimating the Antonelli elasticity from the uncompensated demand system is presented. Estimation results reveal substantial bias of input substitutability with the use of Hicks' measure.     

RETURNS TO SCALE IN RETAIL TRADE*

This paper attempts to estimate genuine scale effects in retail trade from a cross section of retail stores in Israel. This is done by estimating a simple production function for several retail branches and employing the faithful old direct Cobb-Douglas structure with value added as output and labor and capital inputs. And indeed despite the well-known peculiarities of the retail industry, a cross section estimation produces “normal” production-function estimates with reasonable input elasticities. The estimates also identify marked increasing returns-to-scale parameters, higher in food and lower in branches less affected by consumer participation and geographical dispersion. These increasing returns may explain a good part of the increase in sales per unit of inputs observed in time series.     

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.     

The Labour Input Response to Permanent Changes in Output: An Errors-in-Variables Analysis Based on Panel Data

Using panel data for Norwegian manufacturing, we revisit 'the increasing returns to scale puzzle' for labour inputs. We consider the response of the input of white-collar workers, blue-collar workers, and blue-collar worker hours to permanent changes in output. Permanent and temporary changes in output are treated as latent variables. We compare OLS, IV, and GMM estimates of the response elasticities and conclude that the distinction between permanent and temporary changes is essential. Our GMM estimates suggest that the 'increasing returns to scale puzzle' remains for all measures of the labour input also when we consider their response to permanent changes in output. For materials, the output response indicates approximately constant returns to scale. This suggests non-homotheticity of the production technology.
JEL classification : C 23; J 23