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We introduce well-known microeconomics productivity measures in Solow models in discrete time or continuous time by adopting a Luenberger-type approach. In each framework, we derive the productivity indicators and the dynamical paths. Firstly, we show that the expression of the productivity indicators are similar to the well-known Solow residuals, allowing us to make ananalogy between a firm's behaviour in a microeconomic setting and a country's behaviour in a macroeconomic setting. Secondly, we demonstrate that the properties of the paths are similar in both frameworks Postprint

B -convexity is defined as a suitable Peano-Kuratowski limit of linear convexities. An alternative idempotent convex structure called inverse B -convexity was recently proposed in the literature. This paper continues and extends some investigation started in these papers. In particular we focus on the Ky-Fan inequality and prove the existence of a Nash equilibrium for inverse B -convex games. This we do by considering a suitable “harmonic” topological structure which allows to establish a KKM theorem as well as some important related properties. Among other things a coincidence theorem is established. The paper also establishes fixed point results and Nash equilibriums properties in the case where two different convex topological structures are merged. It follows that one can consider a large class of games where the players may optimize their payoff subject to different forms of convexity. Among other things an inverse B -convex version of the Debreu-Gale-Nikaido theorem is proposed.

International audience; The purpose of this contribution is to provide an overview of developments in nonconvex production technologies and economic value functions, with special attention to the cost function. Apart from a somewhat selective review of theoretical issues, the emphasis is on whether the assumption of convexity makes a difference in practice. Anticipating our conclusion, we argue that traditional convex empirical results differ on average rather markedly from alternative nonconvex ones. This should make the discipline reconsider its traditional relationship with convexity in both theoretical and applied production analysis.

In the article “Input Efficiency Measures: A Generalized, Encompassing Formulation” we develop a generalized, encompassing formulation unifying four traditional input efficiency measures: radial, Färe-Lovell, asymmetric Färe, and multiplicative Färe-Lovell. This is basically motivated by the fact that observations on production need not be situated near the efficient subset, but could also be positioned close to the isoquant or even the boundary of the technology. This new generalized Färe-Lovell input efficiency measure shares its axiomatic properties with the original Färe-Lovell input efficiency measure. In addition, we can derive new dual interpretations for this generalized Färe-Lovell input efficiency measure. Finally, we derive mathematical programming formulations, with a special focus on cases where linear programming applies.

This paper investigates the economics of uncertainty using a state‐contingent approach with a focus on the role of non‐convexity. Under efficiency, the slopes of a separating hypersurface measures state‐contingent prices. As argued by Yaari, normalized state‐contingent prices provide a measure of subjective probabilities. But efficiency under non‐convexity can require non‐linear pricing. The analysis identifies non‐convexity conditions under which probability assessments are not appropriate. Implications for economic and welfare analysis under uncertainty are discussed.

Boussemart et al. (2009, 2010, 2018) propose to identify a global α-returns to scale that allows to minimise the inefficiency of the production set. This paper extends this notion to the concept of specific α-returns to scale. In such case, it is possible to identify the impact of each input component on each output component.

This paper considers an idempotent and symmetrical algebraic structure as well as some closely related concept. A special notion of determinant is introduced and a Cramer formula is derived for a class of limit systems derived from the Hadamard matrix product and we give the algebraic form of a sequence of hyperplanes passing through a finite number of points. Thereby, some standard results arising for Max-Times systems with nonnegative entries appear as a special case. The case of two sided systems is also analyzed. In addition, a notion of eigenvalue in limit is considered. It is shown that one can construct a special semi-continuous regularized polynomial to find the eigenvalues of a matrix with nonnegative entries.

This paper is devoted to non-cooperative games in idempotent measures. We consider two kinds of such games. Firstly, players are allowed to play their mixed idempotent strategies. We also consider games where belief of each player about a choice of the strategy by the other players is an idempotent measure. We prove existence of equilibria in both cases and discuss the difference between them.

We present what the title says with an emphasis on separation and topological properties as they relate to some of the fundamental principles of nonlinear analysis.

In marine science, it is usually assumed that there is a functional relationship between the parental population size and subsequent offsprings. The function is referred to as the Stock Recruitment Function (SRF). Determining the SRF translates to the optimization problem of estimating a set of parameters using past and sparse observation, which are usually of modest accuracy. The problem is challenging because several candidate functions exist in the literature, and the choice of best function is non-trivial, due to data sparsity and uncertainty. This paper formulates the problem as a constrained optimization task, and uses B-spline basis functions to represent the functional family to which the SRF belongs. Regularized solutions are obtained by requiring that the derived functions are both monotone and convex. The approach presents two major contributions to the existing computational challenges: • It avoids the non-trivial problem of choosing the functional form a priori. • Regularization of the problem using constraints ensures that parameter estimates are realistic. Numerical examples are presented to compare ℓ1 and ℓ2-norm solutions.

In this paper we study the exact null-controllability property for a class of controlled PDMP of switch type with switch-dependent, piecewise linear dynamics and multiplicative jumps. First, we show that exact null-controllability induces a con-trollability metric. This metric is linked to a class of backward stochastic Riccati equations. Using arguments similar to the euclidian-valued BSDE in [4], the equation is shown to be equivalent to an iterative family of deterministic Riccati equations that are solvable. Second, we give an example showing that, for switch-dependent coefficients, exact null-controllability is strictly stronger than approximate null-controllability. Finally, we show by convenient examples that no hierarchy holds between approximate (full) controllability and exact null-controllability. The paper is intended as a complement to [15] and [14]., Comment: arXiv admin note: text overlap with arXiv:1602.00920

International audience; This paper extends to production theory some notions of compensated and equivalent variation analyzed in Luenberger (Econ Theory 7:445-462, 1996) in a consumer context. Along this line the Luenberger-Hicks-Moorsteen productivity indicator introduced in Briec and Kerstens (Econ Theory 23:925-939, 2004) is derived from these concepts for multi-output production technologies. The dual properties of this productivity indicator are analyzed and an aggregate indicator is introduced inspired from the resource function proposed in Luenberger (1996). A connection to a suitable Slutsky matrix is established.

International audience; From a theoretical point of view, -returns to scale is a relevant alternative to traditional DEA models for estimating production technologies under global returns to scale assumptions such as strictly increasing or strictly decreasing returns to scale. However, from a methodological and empirical point of view, a remaining question is the estimation of . This contribution proposes an effective methodology to estimate an optimal value of based upon a goodness-of-fit strategy. A global method using a grid search is presented first. Second, for generalised FDH technologies, a minimum extrapolation principle is developed to estimate directly the optimal -returns from a linear program. An illustration on 63 US industries over the period 1987-2012 shows the relevancy of our approach.

This empirical contribution reviews the rather limited existing literature measuring congestion in production. It first compares current ways to measure congestion using nonparametric specifications of technologies. In particular, it focuses on the magnitude and incidence of the congestion detected in empirical studies using traditional radial efficiency measures. Thereafter, it shows the limitations of this radial measurement and how alternative measurement schemes may reveal higher amounts of congestion. Then, the new, more general methodology of measuring S-congestion is presented. In particular, we first present a numerical example to illustrate the way the S-disposable technologies allow to capture more extreme forms of congestion by setting empirically determined upper bounds to the wasting of inputs. Then, an empirical illustration is presented based on an existing sample of data. A final section concludes. ispartof: Applied Economics vol:50 issue:27 pages:2938-2956 status: published

International audience; The purpose of this paper is to establish a topological relation between several known production models, precisely a link between -convex and Cobb–Douglas production models. The framework is based on the algebraic structures of the technology sets, issued from data envelopment, respecting either the assumption of constant elasticity of substitution and transformation (CES–CET) or -returns to scale. It is shown that the Painlevé–Kuratowski limit of the CES–CET technology provides either -convex or inverse -convex technologies. Also, -returns to scale models have topological limits relevant with constant return to scale -convex (or inverse -convex) technologies.

The paper is devoted to some new results concerning the topology of hyperspaces of max-plus convex subsets in Euclidean spaces and some other spaces.

This contribution aims to detect and measure more severe forms of congestion than the ones that could hitherto be evaluated in axiomatic production theory. To this end, we define a new S-disposal axiom, a kind of limited strong disposability. This S-disposal assumption leads to a duality result between a general input directional distance function and the cost function that is weaker than the ones established in the literature. Finally, we indicate how finite data sets can or cannot be rationalized by a minimal technology compatible with S-disposal, thereby generalizing the nonparametric weak axiom of cost minimization test. ispartof: Journal of Economics vol:119 issue:1 pages:65-90 status: published

This paper exams the concept of Pollution-generating Technologies (PgT). The main goal of this methodological contribution is to reveal any PgT in production processes compatible with a minimal set of assumptions. We model PgT using a congestion approach of the output set relaxing strong disposability assumption. To this end, we define the B-disposal assumption, that is a kind of limited strong disposability. The B-disposal assumption reflects cost disposability assumption with respect to the undesirable outputs. This disposability assumption leads to a new duality result between an output distance function and the revenue function with possibly negative shadow prices. A sample of 13 representative French airports is considered over the period 2007-2011, in order to implement the new B-disposal assumption on convex non-parametric technologies.

Cooperation between firms can never improve the technical efficiency of any coalition of firms. This standard result of the productivity measurement literature is based on the directional distance function computed on firm groups. Directional distance functions are usually defined on the standard sum of input/output vectors.In this paper, the aggregation of input/output vectors is generalized thanks to an isomorphism in order to capture three results: the cooperation improves technical efficiency ; the cooperation reduces technical efficiency ; and finally the cooperation between firms yields no variation of technical efficiency, i.e. , the distance function is quasi linear.The improvement of technical efficiency is shown to be compatible with semilattice technologies. In this case, the firms merge according to their inputs only because constraints are imposed on outputs, and conversely, they may merge according to the outputs they can produce because some limitations are imposed on the use of inputs.

Determining the allocation and the distribution of scarce resources is fundamental in economics. Thus, decision theory is the cornerstone of economic theory. In this thesis, we first provide a state of the art insisting on the fact that information, that is a central element of decision-making, is imperfect. Secondly, using fuzzy set theory, which aims to capture imprecision, we construct a fuzzy number, so-called C-Shape that captures the sensitivity of the decision-maker. Thirdly, we study decision theory through two key concepts of operation research: (1) game theory and (2) multi-criteria decision making. We provide an analogy between the gauge functions of convex sets and the membership functions arising in fuzzy set theory. Coupling a suitable notion of -convexity with the C-Shape function, we introduce a class of games for which the players can be optimistic, pessimistic or neutral. In addition the existence of Nash equilibrium is proved for such a class of games. Finally, concerning multi-criteria decision analysis, we use the C-Shape functions to characterize a new type of criteria called C-Shape pseudo-criterion, which makes possible to consider the alternatives as substitutable. This should be of interest to take into account, for example, the institutional context in which decision-making is taken., En sciences économiques, l'une des questions centrales concerne l'allocation des ressources rares et plus particulièrement leur répartition. La décision apparait ainsi au cœur des thématiques économiques, que ce soit en micro-économie ou en macro-économie. Dans un premier temps, nous revenons sur le fait que l’information, élément central de la prise de décision, est imparfaite. En utilisant la théorie des ensembles flous, qui a pour objet de capturer l’imprécision, nous construisons un nombre flou nommé nombre flou C-Shape qui permet de capter la sensibilité du preneur de décision. Nous étudions ensuite la théorie de la décision au travers de deux axes de recherche à savoir (1) la recherche opérationnelle couplée à la théorie des jeux et (2) l’aide à la décision. En premier lieu, Nous faisons une analogie entre la fonction distance et la fonction d’appartenance. Grâce à l’hypothèse de B-convexité et à la fonction C-Shape nous construisons des classes de jeux pour lesquels les joueurs peuvent être optimistes, pessimistes ou neutres, et pour lesquels l’existence d’équilibre de Nash est avérée. Enfin, concernant l’aide à la décision, nous utilisons la fonction C-Shape pour caractériser un nouveau type de critère nommé pseudo critère C-Shape qui permet de considérer les alternatives comme substituables. Ceci permet de prendre en compte, par exemple le contexte institutionnel dans lequel la prise de décision est prise.

This thesis aims to present two efficiency measures. First, a log-additive distance function is introduced. It is dual to non-linear pseudo cost, revenue and profit functions. This structure means that the relation between factors and products is not constant. Moreover, exponential Luenberger (Chambers, Färe and Grosskopf (1996)) and Luenberger-Hicks-Moorsteen (Briec and Kerstens (2004)) indicators are proposed. Second, a non-linear distance function is defined. It inherits thestructure of CES (Solow (1956)) and CET (Powell and Gruen (1968))functions. The duality theory allows to present non-linear cost, revenue and profit functions. In this sense, non-linear adjusted price functions are deduced. Non-linear prices occur when the production unit faces internal and/or non-linear tariffs. The alpha-returns to scale model (Boussemart, Briec, Peypoch and Tavéra (2009)) is applied to this new non-linear efficiency measure. Indeed, it is shown that returns-to-scale impact efficiency of production units.; Ces travaux proposent deux nouvelles mesures de l’efficience. La première est une fonction de distance log-additive qui peut être orientée soit en input, soit en output, soit dans le graphe. Celle-ci est duale à des pseudo fonctions de coût, de revenu et de profit non-linéaires. Cette structure des fonctions, indique une relation non-constante entre les intrants et les extrants. Cet outil de mesure de l’efficacité peut servir à estimer la variation de la productivité dans le temps. A cet effet,nous proposons des indicateurs de productivité, de type Luenberger (Chambers, Färe et Grosskopf (1996)) et Luenberger-Hicks-Moorsteen (Briec et Kerstens (2004)), exponentiels. La seconde mesure, est une fonction de distance non-linéaire structurellement inspiré des fonctions CES (Solow (1956)) et CET (Powell et Gruen (1968)). La théorie de la dualité amène à présenter des fonctions de coût, de revenu et de profit non-linéaires. De ce fait, des fonctions de prix ajustés non-linéairesen sont déduites. Une telle structure des prix peut être rencontrée lorsque les unités productives font face à des tarifications non-linéaires en interne et, en externe. Nous appliquons cette nouvelle mesure de l’efficacité au modèle de rendements d’échelle alpha (Boussemart, Briec, Peypoch et Tavéra)(2009)). En effet, ce modèle permet d’estimer l’influence des rendements d’échelle sur l’efficacité.

The exposition of this thesis is based on three parts. First, production technologies are analysed with respect toseveral axiomatic approaches. The B-disposability property is introduced in order to give a more general definition ofthe pollution-generating technologies. This methodological innovation aims to reveal pollution-generating technologiescompatible with a minimal set of assumptions. Then, a more general class of pollution-generating technologiessatisfying both convex and non-convex axioms, can be defined. Furthermore, this axiomatic contribution allows toconsider inputs and outputs partitions, which is of particular interest in empirical studies. The second part of thiswork concerns the measurement of technical efficiency. Then, generalised distance functions are introduced in B-disposable production sets. Following these results, several tests are suggested in order to characterize the structure ofB-disposable production technologies. Moreover, innovative duality results are proposed based on the B-disposabilityproperty. This considerably weakens classical duality results based upon usual disposal assumptions. In the thirdpart, productivity change is studied. Generalisation of additive and multiplicative complete eco-productivity measures,are introduced. Following non-parametric technologies, a procedure to implement the generalised eco-productivitymeasures is exposed. This process is based on the non-parametric estimation of the generalised distance functionssuggested in this work.; Ces travaux structurés en trois parties, mettent à jour différents apports théoriques et empiriques. La premièrepartie est consacrée à l’étude des technologies de production selon différentes approches axiomatiques. L’axiome deB-disponibilité est introduit afin d’apporter une définition générale aux technologies de production polluante. Seloncette propriété, il est possible de définir ces technologies productives grâce à un ensemble réduit d’hypothèses. Ainsi,des technologies de production polluante convexes, non-convexes et hybrides, peuvent être définies. De plus, cetteapproche peut être appréhendée suivant plusieurs stratégies de partitionnement qui présentent un intérêt particulierpour la mise en oeuvre des études empiriques. La deuxième partie est vouée à l’analyse des fonctions de distance. Ainsi,des mesures d’efficience technique généralisées sont proposées. Ces dernières sont présentées dans des ensembles deproduction B-disponibles. Partant de ces résultats, plusieurs tests permettant d’apprécier la structure des ensemblesproductifs B-disponibles, sont proposés. De plus, de nouveaux résultats de dualité sont introduits. Ces derniers sontconstruits sous l’hypothèse de B-disponibilité, ce qui atténue l’importance des axiomes usuels de disponibilité dansl’élaboration de ces résultats. La troisième partie est dédiée aux mesures de productivité. Une généralisation desmesures d’éco-productivité possédant des structures additives et multiplicatives complètes, est introduite. De plus,une spécification non-paramétrique permettant d’implémenter ces nouvelles mesures d’éco-productivité est proposée.Celle-ci repose sur l’estimation non-paramétrique des fonctions de distance additives et multiplicatives généralisées relatées dans ces travaux.

The exposition of this thesis is based on three parts. First, production technologies are analysed with respect toseveral axiomatic approaches. The B-disposability property is introduced in order to give a more general definition ofthe pollution-generating technologies. This methodological innovation aims to reveal pollution-generating technologiescompatible with a minimal set of assumptions. Then, a more general class of pollution-generating technologiessatisfying both convex and non-convex axioms, can be defined. Furthermore, this axiomatic contribution allows toconsider inputs and outputs partitions, which is of particular interest in empirical studies. The second part of thiswork concerns the measurement of technical efficiency. Then, generalised distance functions are introduced in B-disposable production sets. Following these results, several tests are suggested in order to characterize the structure ofB-disposable production technologies. Moreover, innovative duality results are proposed based on the B-disposabilityproperty. This considerably weakens classical duality results based upon usual disposal assumptions. In the thirdpart, productivity change is studied. Generalisation of additive and multiplicative complete eco-productivity measures,are introduced. Following non-parametric technologies, a procedure to implement the generalised eco-productivitymeasures is exposed. This process is based on the non-parametric estimation of the generalised distance functionssuggested in this work.; Ces travaux structurés en trois parties, mettent à jour différents apports théoriques et empiriques. La premièrepartie est consacrée à l’étude des technologies de production selon différentes approches axiomatiques. L’axiome deB-disponibilité est introduit afin d’apporter une définition générale aux technologies de production polluante. Seloncette propriété, il est possible de définir ces technologies productives grâce à un ensemble réduit d’hypothèses. Ainsi,des technologies de production polluante convexes, non-convexes et hybrides, peuvent être définies. De plus, cetteapproche peut être appréhendée suivant plusieurs stratégies de partitionnement qui présentent un intérêt particulierpour la mise en oeuvre des études empiriques. La deuxième partie est vouée à l’analyse des fonctions de distance. Ainsi,des mesures d’efficience technique généralisées sont proposées. Ces dernières sont présentées dans des ensembles deproduction B-disponibles. Partant de ces résultats, plusieurs tests permettant d’apprécier la structure des ensemblesproductifs B-disponibles, sont proposés. De plus, de nouveaux résultats de dualité sont introduits. Ces derniers sontconstruits sous l’hypothèse de B-disponibilité, ce qui atténue l’importance des axiomes usuels de disponibilité dansl’élaboration de ces résultats. La troisième partie est dédiée aux mesures de productivité. Une généralisation desmesures d’éco-productivité possédant des structures additives et multiplicatives complètes, est introduite. De plus,une spécification non-paramétrique permettant d’implémenter ces nouvelles mesures d’éco-productivité est proposée.Celle-ci repose sur l’estimation non-paramétrique des fonctions de distance additives et multiplicatives généralisées relatées dans ces travaux.

This phd contributes to the definition of efficiency measures and productivity indicator, in the microeconomic theory. It presents theoretical and empirical contributions. Firstly, this phd develops a review on standard measures of efficiency and productivity. It is shown that the directional measure, under the assumption of constant returns to scale, raises some problems in the assessment of productivity changes. Moreover, it is established that the "slacks-based" and directional "slack-based" measures (or Färe-Lovell measures) do not allow to characterize technology. It follows that such measures do not allow to evaluate efficiency and productivity changes. An alternative approach is proposed which overcomes this difficulty. Then, this phd introduces two new indicators: a social Luenberger-Hicks-Moorsteen indicator and a generalized indicator of productivity. The first mesure the impact of publics policies in the line of the capability theory introduce by A. Sen. This indicator consists on a transposition of the Hicks-Moorsteen indicator by considering a sub-vector of social factors. The second indicator generalizes standards productivity indicators. It allows to find the Luenberger and the Luenberger Hicks-Moortsteen as special cases of this general indicator. Considering the multiplicative version of the generalized indicator, on can find the Malmquist and Hicks-Moorsteen indicators, as special cases. Finally, this phd presents some empirical applications to illustrate the methodology. These studies evaluate and compare the performance of the tourist destination, and specifically for the Languedoc-Roussillon, which involves a cross-border analysis framework, Ce travail contribue à la définition des mesures de l'efficacité et de la productivité dans la théorie microéconomique. Il présente des apports théoriques et empiriques. En premier lieu, cette thèse élabore une critique sur certaines mesures classiques de l’efficacité et de la productivité. Il est montré que la mesure directionnelle, sous l'hypothèse de rendements d'échelle constants, pose un certain nombre de problèmes quant à l’évaluation des variations de la productivité. De plus, il est établi que la « slacks-based » et la directionnelle « slack-based » mesures (ou mesures de Färe-Lovell) ne permettent pas de caractériser la technologie de production. Il résulte que ce type de mesure ne permet pas d’évaluer l'efficacité et les variations de productivité. Une approche alternative est proposée qui permet de contourner cette difficulté. Ensuite, cette thèse introduit deux nouveaux indicateurs: un indicateur social de Luenberger-Hicks-Moorsteen et un indicateur de productivité généralisé. Le premier permet d'évaluer l'effet des politiques sur les capabilités au sens d'A. Sen. Il consiste en une transposition des indicateurs de Hicks-Moorsteen en considérant le rôle spécifique d’un sous-vecteur prenant en compte les facteurs sociaux. Le second indicateur généralise les indicateurs standards de productivité. Il permet de retrouver à la fois les indicateurs de Luenberger et le Luenberger Hicks-Moortsteen comme cas spéciaux de cet indicateur généralisé. En considérant la version multiplicative de l’indicateur généralisé, on retrouve comme cas particuliers, les indicateurs de Malmquist et le Hicks-Moorsteen. Enfin, cette thèse présente des applications empiriques qui illustrent la méthodologie. Ces études évaluent et comparent la performance des régions touristiques et plus précisément celle du Languedoc-Roussillon, qui mobilise un cadre d'analyse transfrontalier.