Stochastic Scale Elasticity

In recent years, the notion of scale elasticity—the relative changes of outputs with respect to relative changes of inputs—has received a lot of ink in the literature. However, all prior studies, except a few of them, assume that changes are equi-proportional. This simplifying assumption makes scale elasticity measure to preserve the throughput mix and implicitly ignores both input independencies and decision-maker preferences. This paper seeks to investigate two main objectives. It initially proposes the notion of directional scale elasticity to allow evaluation of elasticity in any direction which may naturally alter the mix. Subsequently, by providing a tangible geometric interpretation, it attempts to clarify the measure. Relevant computations are used to construct cross sections of frontier in a given direction by enlisting the advantages of parametric optimization algorithm.

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Unique Equivalence Scales: Estimation and Implications for Distributional Analysis

Journal of Income Distribution ◽

10.25071/1874-6322.700 ◽

1995 ◽

Author(s):

David S. Johnson ◽

Thesia I. Garner

Keyword(s):

Consumer Price Index ◽

Equivalence Scales ◽

Consumer Expenditure ◽

Constant Elasticity ◽

Scale Elasticity ◽

Inequality Measures ◽

Base Level ◽

Expenditure Data ◽

Family Types ◽

The Us

Equivalence sales are used to adjust income by family size to obtain income distribution measures. Recently, the concept of equivalence scale elasticity has been introduced to characterize the effect that scales have on distribution measures. We produce utility-based equivalence scales that have the property of constant elasticity. By assuming a particular functional form for the scales and that the scales are independent of the base level of utility, we obtain unique equivalence scales. In contrast to previous estimates of utility-based scales, we do not restrict our sample to particular family types. We determine price-dependant scales by estimating a characteristic-dependent almost ideal demand system using quarterly expenditure data from the US Consumer Expenditure Survey and price indices from the US Consumer Price Index. We use our scales and those implicit in the US official poverty thresholds to adjust expenditures and show that these scales have similar effects on inequality measures.

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Returns to Scale and Scale Elasticity in Two-Stage Dea

Mathematical and Computational Applications ◽

10.3390/mca17030193 ◽

2012 ◽

Vol 17 (3) ◽

pp. 193-202 ◽

Cited By ~ 1

Author(s):

Maryamsadat Khaleghi ◽

Gholamreza Jahanshahloo ◽

Majid Zohrehbandian ◽

Farhad Lotfi

Keyword(s):

Returns To Scale ◽

Two Stage ◽

Scale Elasticity

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Scale elasticity in the presence of integer data: An application to electricity distribution companies

Studies of Applied Economics ◽

10.25115/eea.v39i2.3155 ◽

2021 ◽

Vol 39 (2) ◽

Author(s):

Homeira Amirmohammadi ◽

Alireza Amir Amirteimoori ◽

Sohrab Kordrostami ◽

Mohsen Vaez-Ghasemi

Keyword(s):

Operations Research ◽

Returns To Scale ◽

Mixed Integer ◽

Data Envelopment ◽

Electricity Distribution ◽

Scale Elasticity ◽

Frontier Point ◽

Integer Linear Programming Problem ◽

Lagrangian Dual ◽

Scale Properties

Returns to scale and scale elasticity are two important issues in the field of economics and operations research. Recently, estimating returns to scale and scale elasticity using tools such as data envelopment analysis (DEA) has attracted considerable attention among researchers. The existing approaches to calculate scale elasticity in DEA context, assume all inputs and outputs are real-valued and in this sense, the underlying technology is a continuous set. In many real cases, however, we face input/output measures that are restricted to be integer-valued. Scale properties of frontier points in such cases are interesting and important. In this paper, this problem in integer-valued DEA is studied. The Lagrangian dual formulation of a mixed integer linear programming problem is used to calculate the scale elasticity of a frontier point. To illustrate the real applicability of the theoretical framework, a real case on electricity distribution companies is given.

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