Estimation of Returns to Scale and the Elasticity of Substitution

Econometrica ◽  
1967 ◽  
Vol 35 (3/4) ◽  
pp. 419 ◽  
Author(s):  
G. S. Maddala ◽  
J. B. Kadane

2009 ◽  
Vol 54 (2) ◽  
pp. 176-206 ◽  
Author(s):  
Vittorio Corbo ◽  
Jean-Marie Dufour

The purpose of this paper is to study the characteristics of the production process in the Quebec economy. We devote particular attention to two features of the technology: the returns to scale and the substitution possibilities. Two forms of production functions, the Cobb-Douglas and an homothetic translog production function, are estimated for six branches of economic activity. These are: Agriculture; Fishing and Forestry; Mining; Quarying and Oil Wells; Manufacturing; Utilities; Services. Two main conclusions are derived from this work. First, there is strong evidence of constant returns to scale in all branches of the Quebec economy but services. Second, when comparing the Cobb-Douglas model with an homothetic translog model, the hypothesis that the true model is the Cobb-Douglas one cannot be rejected for five of our six sectors. Therefore, there is evidence that the elasticity of substitution is around one. Finally a byproduct of our work has been the construction of capital stock series for the Quebec economy (1960-73) disaggregated into 14 sectors, and two types of capital: construction and machinery and equipment.



2011 ◽  
Vol 3 (2) ◽  
pp. 112
Author(s):  
Martin Williams ◽  
Tuan Ton-That

A nonhomogeneous production is used to study the features of the production technology across U.S. cities. We compute marginal productivities and scale elasticities for different levels of inputs and outputs. The form of the production function allows variable returns to scale. We can also test the Cobb-Douglas and constant elasticity of substitution forms within the nonhomogeneous specification. Conclusions are drawn concerning returns to scale across cities of different sizes.





1989 ◽  
Vol 28 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Ashfaque H. Khan

Production functions have been widely studied in the relevant literature. In this paper, apart from labour and capital, we have used energy as a factor input and calculated the elasticity of substitution between these inputs, measured technical progress, and determined the returns to scale in the manufacturing sector of Pakistan. Since we have more than two factors of production, the standard Cobb· Douglas and CES production functions do not provide satisfactory results. Hence, two·level (nested) CES production function becomes the natural choice for the appropriate technology. Using this technology, we have found low elasticity of substitution between the three factors of production. Furthermore, the manufacturing sector is found to exhibit decreasing returns to scale, having experienced disembodied technical progress at the rate of 3.7 percent per annum.



2021 ◽  
Author(s):  
Françoise Larbre

Depending on the workers qualification, the use of robots is perceived either as a helpful tool or as a competitor. We analyze the substitution of capital for labor, including the case where the product is entirely made by robots. We use CES production functions and their derived cost functions (the later being surprisingly missing in the literature). We focus on short-run and the case of an elasticity of substitution greater than 1. We highlight a level of product for which the cost is identical regardless of the factor used. As a joint product, we provide a foundation to cost functions exhibiting first increasing and then decreasing returns to scale (a so far missing justification to the usually assumed shape of cost functions).



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