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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

We introduce the special issue in memory of our late colleague Bernard Philippe of the University of Perpignan. We would like to acknowledge Bernard for the many things he gave us before leaving: scientific rigor, the importance of teaching, open-mindedness, and generosity.

In a recent paper Ramos and Silber (2005) used techniques developed in efficiency analysis to obtain estimates of human development obtained on the basis of Sen (1985) and Narayan et al. (2000) capability approach. In particular they propose to measure standard achievement and well being indexes using a distance function approach. In this paper, it is shown that the ratio based of well-being and standard achievement indexes form the Hicks–Moorsteen index introduced by Bjurek (1996). Along this line, an additive form of the standard achievement and well-being indexes is proposed. In particular, the paper focusses on the case of social inputs. Axiomatic and dual properties are established and some parametric and nonparametric models are proposed.

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

The renormalization procedure facilitates the detection of periodic and chaotic patterns of many two-dimensional systems of nonlinear equations. We first give a comprehensive presentation of this procedure. We then generalize it to make it more applicable to economic frameworks.

Two linear maps are usually needed to separate disjoint convex subsets of an idempotent semimodule. In the context of Max-Plus convexity separation can be achieved by a single map if one considers linear maps with values in a linearly ordered semimodule, whose construction is given here, which is not the Max-Plus semiring R ∪ { - ∞ } .

This paper analyses productivity growth and the nature of technical change in a sample of Portuguese hydroelectric generating plants over the period 2001 to 2008. In a first step, we employ the Luenberger productivity indicator to estimate and decompose productivity change. A Malmquist productivity index is also used for a comparative purpose. The results paint a picture of mixed productivity performance in the Portuguese energy sector. The first decomposition underlines that, in average, the productivity variation is explained by the technological change. Then, in a second step, we analyse the nature of this technical change by using the recent concept of parallel neutrality (Briec et al., 2006). We observe a global shift in the best practice frontier as well as in the evidence of input bias in technical change.

Morey and Morey [1] have developed an approach for gauging portfolio efficiencies in the context of the Markowitz model. Following some recent contributions [2,3], this paper analyzes the axiomatic properties of distance functions extending an earlier approach proposed by Morey and Morey. The paper also focusses on the hyperbolic measure and the McFadden gauge function [4]. Among other things, overall, allocative and portfolio improvements possibilities (in term of return expansion or/and risk contraction) based upon the indirect mean-variance utility function are analyzed. Along this line, duality results are established in each case. This enables us to calculate the degree of risk aversion maximizing the investor indirect mean-variance utility function in either return expansion or risk contraction. An empirical illustration is provided and reveal ranking of preferred risks aversion for some “CAC40” assets.

There are two total factor productivity indices available in the literature based on a primal notion of the technology. In a ratio tradition, these are the Malmquist and the Hicks-Moorsteen productivity indices. In a difierence perspective, the Luenberger and LuenbergerHicks-Moorsteen productivity indicators are based upon a sightly different concept. The purpose of this note is to establish that -in contrast to the Malmquist index- the Hicks-Moorsteen type of productivity index (as well as its difierence-based counterpart) is well-deflned and satisfles the determinateness property, since the underlying distance functions are always feasible.

This contribution provides a way to define and compute a tangency notion of economic capacity based upon the relation between the various directional distance functions and the profit and cost functions using non-parametric technologies. A new result relating profit and cost function-based tangency capacity notions is established. ispartof: Economic Modelling vol:27 issue:5 pages:1156-1166 nrpages: 31 status: published

This paper proposes a procedure for analysing tourism productivity. The procedure is based on the Luenberger productivity indicator for estimating and decomposing productivity change into efficiency change and technological change. The authors expand the procedure and further decompose the process of technological change to study the sources of bias within it. Therefore, a clearer and more enlightening view emerges of the productivity of travel agencies. The Portuguese travel agency sector is used as an application. Some managerial implications are developed.

This paper develops a general approach for the single period portfolio optimization problem in a multidimensional general and partial moment space. A shortage function is defined that looks for possible increases in odd moments and decreases in even moments. A main result is that this shortage function ensures sufficient conditions for global optimality. It also forms a natural basis for developing tests on the influence of additional moments. Furthermore, a link is made with an approximation of an arbitrary order of a general indirect utility function. This non-parametric efficiency measurement framework permits to differentiate mainly between portfolio efficiency and allocative efficiency. Finally, information can, in principle, be inferred about the revealed risk aversion, prudence, temperance and other higher-order risk characteristics of investors.