First, a comparison of alternative models of an economy reveals that the information content is so sparse in Sraffa’s 1960 model that the concept of **constant** **returns** to **scale** in production simply cannot be defined in it. It is therefore impossible to impose the requirement of **constant** **returns** to **scale** on the economic structure investigated by Sraffa. Nor indeed can **constant** **returns** to **scale** be entailed in a model in which the concept is impossible to define. A second point to note is that, from an information analytic perspective, conclusions deduced on the basis of strictly more restrictive assumptions, as from models that assume CRS, cannot legitimately be used to refute any claims of another theory that is based on strictly less restrictive (or strictly more general) assumptions, as in Sraffa, as shown in the Venn diagram below.

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In DEA (Data Envelopment Analysis), the Full Dimensional Efficient Facets (FDEFs) of PPS (Pro- duction Possibility Set) play a significant role and have many useful applications. In this research, we, first, provide a detailed characterization of the structure of FDEFs of the PPS with **constant** **returns** to **scale** technology, using basic concepts of the polyhedral sets theory. Then, using the mentioned characterization together with a mixed integer linear programming, we propose an effective algorithm for finding all of the FDEFs of the PPS. We will elaborate on our algorithm by an illustrative example.

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This article discusses the effect of uncontrollable factors on **constant** **returns**-to-**scale** production technologies in data envelopment analysis(DEA). First we show that the Banker and Morey CRS technology is not convex and it is nevertheless a suitable reference technology for the assessment of **scale** efficiency and achieves model by the incorporation of variant inputs and outputs in data envelopment analysis. Second, we propose that if changes axiom **returns** to **scale** of production possibility set, model will secure variant another model with uncontrollable factors. Therefore **returns** to **scale** properties very depending on the manner in which uncontrollable factors are treated and approaches can be compared both theoretically and empirically.

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The Efficiency Analysis based on **Constant** **Returns** to **Scale** reveals that five Engineering Institutions (IIT MADRAS, NIT Trichy, PSG, SRI SIVA SUBRAMANIYA, and THANTHAI PERIYAR) stand first and the analysis based on Variable Return to **Scale** Communicates that seven Engineering Institutions (IIT MADRAS, NIT Trichy, SRM, PSG, R.M.K, SRI SIVA SUBRAMANIYA and THANTHAI PERIYAR) takes the first place. Comparing both the analysis one can conclude that IIT MADRAS, NIT Trichy, PSG, SRI SIVA SUBRAMANIYA &THANTHAI PERIYAR is doing exceedingly well.

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Charnes et al. [1] established data envelopment analysis (DEA) on the basis of the calculation of decision-making units (DMUs) efficiency. If we calculate the efficiency of a DMU by DEA models on the assumption that it is **constant** **returns** to **scale** in different times, we reach the conclusion that the amounts of efficiency for given DMU is a number which is greater than zero and smaller or equal to one; but if one uses interpolation the resulted interpolant may not be restricted to this region, i.e. it may have values greater than one or less than zero.

The efficiency scores obtained in CCR and BCC models reveal that 31.25% of the ports are relatively effi- cient and experience **constant** **returns** to **scale** while the other ports (68.75%) are operating under variable **returns** to **scale**. Further, the analysis of the nature of **returns** to **scale** indicates that about 18.75% of the ports exhibit decreasing **returns** to **scale** while 50% shows increasing **returns** to **scale**. It is suggested that the ports observed in the decreasing **returns** to **scale** zone should reduce their **scale** of operation whereas the others ports showing in- creasing **returns** to **scale** should increase their production **scale**. On the whole, the inefficient ports being as- sessed suffer from the effect of inappropriate operational **scale**. Consequently, for container ports to survive in the competitive environment, port authorities should examine their operational **scale** to identify whether the production size is appropriate or not before making investment decision in terms of inputs resources enhance- ment or capacity expansion. Finally, the results given by super-efficiency indicate that among the sample ports Mombasa has the best management practices while Maputo is the most inefficient one suffering from **scale** inef- ficiency.

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nonlinearity is strong and highly significant (away from the gradient peak near S = 12). The estimated change in the rate of return per year of schooling (away from S = 12) is huge relative to the estimates of the rate of return. Thus, **constant** **returns** to **scale** are decisively rejected at low levels of education in favor of increasing **returns**, and **constant** **returns** to **scale** are decisively rejected at high levels of education in favor of decreasing **returns**. Evidently the production function for human capital has the cubic shape of the sort that we typically argue is ubiquitous for firms' production functions in ECON 101.

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Constant returns to scale mean that the firm’s long-run average cost curve remains flat... 25 of 33[r]

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in the real sense of it. The neoclassical economists also attacked the model on the bases that the productivity theory is more of an abstraction than a quantifiable. Douglass while responding to the criticisms noted that the critics were so hostile even to the extent of recommending for the work to be thrown into the waste basket and further research in it stopped. In the defence of the model, From criticism, Cobb-Douglass model started receiving research interest with positive comments and positive empirical result. Miller (2008) accepts that Cobb-Douglass model is very simple to use and can fit many data sets very well for empirical forecasting. Many studies have equally been done in developing as well as developed countries, trying to validate the Cobb-Douglass model. Results of such studies have differed, making it difficult to make a definite conclusion about the Cobb-Douglass postulation. Hence, up to this point, the applicability of **constant** **returns** to **scale** production as postulated by Cobb-Douglass is still at the centre of research interest around the globe.

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Table 7.2 Results of Tariff Liberalisation under Imperfect Competition and Constant Returns to Scale Percentage changes Sectors Subsistence Agriculture Commercial Agriculture Forestry Fo[r]

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This paper examines the extent to and the conditions under which re- source misallocation negatively affects aggregate productivity in a model of heterogeneous firms to the highest degree. I analytically derive the minimum aggregate total factor productivity (TFP) under resource mis- allocation, when frictions are modeled as the taxes levied on a firm’s output, and the range of these taxes is provided. I find that the lower limit of the minimum aggregate TFP is the TFP under perfect substitute goods and **constant** **returns** to **scale** technology. Further, with the excep- tion of particular parameter values in which the misallocation effect on aggregate TFP is small, the minimum aggregate TFP is achieved when the proportion of firms in the lowest tax level is small or when the TFP level of these firms is low.

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Labour productivity is defined as output per unit of labour input. Economists acknowledge that technical progress as well as growth in capital inputs increases labour productivity. However, little attention has been paid to the fact that changes in labour input alone could also impact labour productivity. Since this effect disappears for the **constant** **returns** to **scale** short-run production frontier, we call it the **returns** to **scale** effect. We decompose the growth in labour productivity into two components: 1) the joint effect of technical progress and capital input growth, and 2) the **returns** to **scale** effect. We propose theoretical measures for these two components and show that they coincide with the index number formulae consisting of prices and quantities of inputs and outputs. We then apply the results of our decomposition to U.S. industry data for 1987 – 2007. It is acknowledged that labour productivity in the services industries grows much more slowly than in the goods industries. We conclude that the **returns** to **scale** effect can explain a large part of the gap in labour productivity growth between the two industry groups.

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safety and the quality of life within prison. We include this proxy as an additional variable for the incarceration output and repeat the analysis as a robustness check for our conclusions with respect to the optimal **scale** size of prisons. We dropped one observation due to a missing value for the number of prisoner-on-officer assaults and consequently performed the robustness check for 101 observations. The average order-m efficiency for incarceration equals 1,08 under variable **returns** to **scale** and 1,31 under **constant** **returns** to **scale**. These efficiency scores are slightly lower than the scores in the original model, due to the inclusion of an additional output. Figure 4 plots the **returns** to **scale** and **scale** efficiency for the incarceration output, taking prisoner-on- officer assaults into account. The general pattern remains similar to Figure 3(a). On average, the **scale** efficiency equals 1,21. When including assaults, 12 observations are characterized by **constant** **returns** to **scale**. Remarkably, 3 of those observations correspond to smaller **scale** prisons. However, most smaller **scale** prisons remain **scale** inefficient.

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Table 2 shows the full set of calibrated parameter values. Table 3 shows the results for our targeted moments, compared to the values in the data. We do well on all targeted moments. Particularly, all four simulation-based slopes have the correct sign and magnitude. Even though there are **constant** **returns** to **scale** in the R&D cost function, the spillover eﬀect in advertising, which is set to target the decreasing advertising intensity with size observed in the data, is also able to correctly predict both the decreasing R&D intensity and the deviation from **constant** ﬁrm growth. This implies that the observed decreasing R&D intensity in ﬁrm size observed in the data is not necessarily evidence for the existence of decreasing **returns** to **scale** in R&D. Our calibration shows that it could simply be the result of the interaction between R&D and advertising even when there exist **constant** **returns** to **scale** in R&D. As we will argue in Section 7, this aspect can have important policy implications regarding the optimal design of R&D subsidies.

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Results indicated that 50% of the hospitals were Constant Returns to Scale technically efficient with a mean efficiency score of 80.6% while 66.6% of the hospitals were Variable Returns [r]

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The study uses the DEA approach to investigate the determinants of performance efficiency of 19 selected banks in Nigeria for the year 2009. In order to have a robust empirical analysis, three DEA performance efficiency measure are employed to include the **constant** **returns** to **scale** (CRS), variable **returns** to **scale** (VRS) and **scale**. The independent variables (determinants) of bank efficiency used in the study include Bank size, Bank age, Board independence and Bank ownership structure. The measurement of the variables is demonstrated below in the table below.

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This article sought to evaluate the efficiency of the countries presented in the GII regarding their performance in competitivity and technological innovation. To analyze the results, Data Envelopment Analysis (DEA) is utilized through input oriented BCC (Variable **Returns** to **Scale**) and CCR (**Constant** **Returns** to **Scale**).The variable dispersion analysis shows that the data is not equally distributed for presenting a variation coefficient superior to 25% and through Pearson’s coefficient correlations have been found and it’s being verified that there is a strong positive correlation between variables in the study.

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Data envelopment analysis (DEA) is the model of the study which measures the efficiencies of various organizations with not one input and output but with multiple inputs and outputs. This chapter explains the results which wrangled after the implementation of the DEA (data envelopment analysis technique) to the data of the ten Islamic banks taken from Pakistan and Malaysia for the study period 2013-2018. This model refers to the Islamic banks to inspect the performance of the Islamic banking system in Pakistan as well as in Malaysia for a comparison. In the study of the DEA technique our focus is on CRS (**Constant** **returns** to **scale**) output based, VRS (Variable **returns** to **scale**) output based and Malmquist DEA which are employed to measure the efficiency of Meezan Bank, Burj Bank, Dubai Islamic Bank, Albaraka Bank, and bank Islamic from Pakistan, and Bank Islam, Alliance Islamic bank, Public Islamic bank, standard Chartered Saddiq, and am bank Islamic are from Malaysia. Malmquist total factor productivity index is used to compute the distance and the change concomitant with productivity. For this reason, there is the decomposition in the total factor productivity, change as there is the change of technology, efficiency change, pure efficiency change, and the **scale** efficiency change. In this study Malmquist, CRS and VRS approaches are concentrated on the evaluation of the performance and the efficiency.

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(Faliva and Zoia 2000): In this paper a novel partitioned inversion formula is obtained in terms of the orthogonal complements of off-diagonal blocks, with the emblematic matrix of unit-root econometrics springing up as the leading diagonal block of the inverse. On the one hand, the result paves the way to a stimulating reinterpretation of restricted least-squares estimation and, on the other, to a straightforward derivation of a key-result of time-series econometrics. (Elias, 1992) in (Gujarati and Sangeetha, 2007) used Restricted Least Squares to observe Mexican Economy from 1955 – 1974. Using data on the country’s Gross Domestic Product, Employment (labour), and Fixed capital, they found that Mexican economy was probably characterized by **constant** **returns** to **scale** over the sampled period and concluded that using Restricted Least Squares obtained for the data set could not be harmful. They also observed that increasing capital/employment ratio by 1 percent, on the average will increase the labour productivity by about 1 percent.

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Entry creates two effects. First, as in Mankiw and Whinston (1986), it creates a “business-stealing effect” by lowering the outputs of the incumbent final goods producers. On the other hand, as observed by Ghosh and Morita (2007a, b), entry creates a “business-creation effect” in the input sector by raising the total input demand. We find that the latter effect dominates the former effect for social welfare and makes entry less attractive than the socially optimum level. This result affirms the finding of Ghosh and Morita (2007a, b), suggesting that entry is insufficient in a vertically related industry with **constant** **returns** to **scale** technologies.

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