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Introduction

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Part of the International Series in Operations Research & Management Science book series (ISOR,volume 315)

Abstract

It goes without saying that firms are for profit organizations whose main goal is to maximize the difference between the revenues they generate by selling goods and the cost they incur when acquiring their production factors. Firms’ management is accountable to a wide range of stakeholders, both private and public, including shareowners, workers, customers, and governments. Although firms and other organizations might have alternative complementary goals, for example, by adopting corporate socially responsible practices, in market-oriented economies, the onus is on the managers to ensure that firms perform satisfactorily and, ultimately, can survive in competitive and ever-changing environments. Under the assumption of perfectly competitive markets, including many sellers and buyers, homogenous products, free entry and exit, and perfect information, firms do not have market power and take prices as exogenously given. Consequently, when aiming at profit maximization, their only decision variables are quantities, deciding on the amount of outputs to supply and inputs to demand.

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Fig. 1.1
Fig. 1.2

Notes

  1. 1.

    Minimum cost C(yo, w) = w·xC corresponds to the inner product between the vector of input prices \( w\in {\mathrm{\mathbb{R}}}_{+}^M \) and the vector of optimal input quantities minimizing cost \( {x}^C\in {\mathrm{\mathbb{R}}}_{+}^M \). Although the formal definition of these economic and technological concepts is postponed to Chap. 2, we make use in this introduction of the general notation and terminology used throughout the book.

  2. 2.

    We reserve the term efficiency for multiplicative measures of economic efficiency whose value is bounded by one from above and the term inefficiency for additive measures which are bounded by zero from below.

  3. 3.

    Maximum revenue R(xo, p) = p·yR corresponds to the inner product between the vector of output prices \( p\in {\mathrm{\mathbb{R}}}_{+}^N \) and the vector of optimal output quantities maximizing revenue \( {y}^R\in {\mathrm{\mathbb{R}}}_{+}^N \).

  4. 4.

    As shown in Chap. 3, the approach initiated by Farrell (1957) can be equivalently expressed in terms of the input and output distance functions proposed by Shephard (1953, 1970).

  5. 5.

    These relations, known in the literature as Fenchel-Mahler inequalities, are particular applications of Minkowski’s theorem, i.e., a closed convex set is the intersection of the half-spaces that support it.

  6. 6.

    For calculating any normalized inefficiency, expressed in monetary units, we divide it by a normalizing factor that is also expressed in monetary units, ending up with an equality between pure numbers. However, if the prices change, the normalized measure of economic inefficiency also changes. Consequently, \( \tilde{p} \) shows that prices influence the value of the decomposition.

  7. 7.

    Moreover, regarding the additive decomposition of economic performance based on the directional distance function, Chambers et al. (1998) named these measures Nerlovian inefficiencies, in honor of Marc Nerlove, who first advocated their use as measures of economic performance (hence, the letter N, for Nerlovian or Normlized, preceding the abbreviation of cost and revenues inefficiencies).

  8. 8.

    Where (yΓ, xΓ) and (yΠ, xΠ) represent the optimal quantities maximizing profitability and maximizing profit, respectively.

  9. 9.

    Where, once again, \( \left(\tilde{w},\tilde{p}\right) \) denotes normalized market prices, resulting from diving profit inefficiency and its allocative component by the normalizing factor (p ⋅ gy + w ⋅ gx)

  10. 10.

    Moreover, based on the input- and output-oriented directional distance functions, the additive definitions of cost and revenue inefficiency and their decomposition into technical and allocative terms were made possible at the same time.

  11. 11.

    A mathematically equivalent measure was proposed in an independent way in the same journal 2 years later by Tone (2001), who named it “slack-based measure (SBM).” In this book, we call it ERG=SBM.

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Pastor, J.T., Aparicio, J., Zofío, J.L. (2022). Introduction. In: Benchmarking Economic Efficiency. International Series in Operations Research & Management Science, vol 315. Springer, Cham. https://doi.org/10.1007/978-3-030-84397-7_1

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