In management contexts, mathematical programming is usually used to evaluate a collection of possible alternative courses of action en route to selecting one which is best. In this capacity, mathematical programming serves as a planning aid to management. Data Envelopment Analysis reverses this role and employs mathematical programming to obtain ex post facto evaluations of the relative efficiency of management accomplishments, however they may have been planned or executed. Mathematical programming is thereby extended for use as a tool for control and evaluation of past accomplishments as well as a tool to aid in planning future activities. The CCR ratio form introduced by Charnes, Cooper and Rhodes, as part of their Data Envelopment Analysis approach, comprehends both technical and scale inefficiencies via the optimal value of the ratio form, as obtained directly from the data without requiring a priori specification of weights and/or explicit delineation of assumed functional forms of relations between inputs and outputs. A separation into technical and scale efficiencies is accomplished by the methods developed in this paper without altering the latter conditions for use of DEA directly on observational data. Technical inefficiencies are identified with failures to achieve best possible output levels and/or usage of excessive amounts of inputs. Methods for identifying and correcting the magnitudes of these inefficiencies, as supplied in prior work, are illustrated. In the present paper, a new separate variable is introduced which makes it possible to determine whether operations were conducted in regions of increasing, constant or decreasing returns to scale in multiple input and multiple output situations. The results are discussed and related not only to classical single output economics but also to more modern versions of economics which are identified with "contestable market theories."

http://www.utdallas.edu/~ryoung/phdseminar/BCC1984.pdf

Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis

Monopoly and product quality

This literature review of decision making (how people make choices among desirable alternatives), culled from the disciplines of psychology, economics, and mathematics, covers the theory of riskless choices, the application of the theory of riskless choices to welfare economics, the theory of risky choices, transitivity of choices, and the theory of games and statistical decision functions The theories surveyed assume rational behavior: individuals have transitive preferences (“… if A is preferred to B, and B is preferred to C, then A is preferred to C”), choosing from among alternatives in order to “… maximize utility or expected utility” 209-item bibliography (PsycINFO Database Record (c) 2006 APA, all rights reserved)

https://psycnet.apa.org/doi/10.1037/h0053870

The theory of decision making.

Обсуждаются следующие темы: чистая теория производства, функциональное распределение дохода, технический прогресс, источники международных конкурентных преимуществ. Анализируются эластичность замещения между трудом и капиталом в обрабатывающей промышленности; производственные функции различного типа.

Capital-labor substitution and economic efficiency

In this paper we demonstrate how certain very ordinary economic principles lead maximizing individuals to choose consumption-production plans that display many of the characteristics commonly associated with business cycles. Our explanation is entirely consistent with (i) rational expectations, (ii) complete current information, (iii) stable preferences, (iv) no technological change, (v) no long-lived commodities, (vi) no frictions or adjustment costs, (vii) no government, (viii) no money, and (ix) no serial dependence in the stochastic elements of the environment. We also provide a completely worked out example of the type of artificial economy we have in mind. The time-series properties of the example exhibit some major features of observed business cycles. Although this type of model may not be capable of explaining all of the regularities in actual business cycles, we believe that it provides a useful, well-defined benchmark for assessing the relative importance of factors (e.g., monetary disturbances...

R. G. D. Allen

Papers

Mathematical Analysis for Economists

Mathematical Analysis for Economists.

Macro-Economic Theory

Index numbers in theory and practice

Index Numbers in Theory and Practice.