20174 "Sustainability of an economy relying on two reproducible assets"
Robert D. Cairns, Stellio Del campo, Vincent Martinet
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 Résumé
 Evaluating the sustainability of a society requires a system of shadow or accounting values derived from the sustainability objective. As a first step toward the derivation of such shadow values for a maximin objective, this paper studies an economy composed of two reproducible assets, each producing one of two consumption goods. The effect of the substitutability between goods in utility is studied by postulating, in turn, neoclassical diminishing marginal substitutability, perfect substitutability and perfect complementarity. The degree of substitutability has strong effects on the maximin solution, affecting the regularity or nonregularity of the program, and on the accounting values. This has important consequences for the computation of genuine savings and the sustainability prospects of future generations.
 ClassificationJEL
 O44; Q56.
 Mot(s) clé(s)
 sustainable development; maximin; sustainability accounting; substitutability.
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201214 "Combining Rights and Welfarism: a new approach to intertemporal evaluation of social alternatives"
Ngo Van Long, Vincent Martinet
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 Résumé
 We propose a new criterion which reflects both the concern for welfare (utility) and the concern for rights in the evaluation of economic development paths. The concern for rights is captured by a preordering over combinations of thresholds (floors or ceilings on various quantitative indicators) that serve as constraints on actions and on levels of state variables. These thresholds are interpreted as minimal rights to be guaranteed to all generations. They are endogenously chosen within the set of all feasible thresholds, accounting for the "cost in terms of welfare" of achieving these rights. We apply the criterion to several examples, including the standard DasguptaHealSolow model of resource extraction and capital accumulation. We show that if the weight given to rights in the criterion is sufficiently high, the optimal solution may be on the threshold possibility frontier. The development path is then "driven" by the rights. In particular, if a minimal consumption is considered as a right, constant consumption can be optimal even with a positive utility discount rate. The shadow prices of thresholds play an important role in the determination of the rate of discount to be applied to social investment projects.
 ClassificationJEL
 Mot(s) clé(s)
 D63, H43, Q01
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201213 "Effect of soil heterogeneity on the welfare economics of biofuel policies"
Vincent Martinet
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 Résumé
 Biofuel policies (blend mandate or tax credit) have impacts on food and energy prices, and on landuse. The magnitude of these effects depends on the market response to price, and thus on the agricultural supply curve, which, in turn, depends on the land availability (quantity and agronomic quality). To understand these relationships, we develop a theoretical framework with an explicit representation of land heterogeneity. The elasticity of the supply curve is shown to be nonconstant, depending on land heterogeneity and the availability of land for agricultural expansion. This influences the welfare economics of biofuels policies, and the possible carbon leakage in land and fuel markets. We emphasize that the impacts of biofuel policies on welfare and landuse change depend strongly on the potential development of the agricultural sector in terms of expansion and intensification, and not only on its current size.
 ClassificationJEL
 Mot(s) clé(s)
 Agricultural and energy market, Biofuels, Land use, Soil heterogeneity, Welfare
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201211 "Risk and Sustainability: Assessing Fisheries Management Strategies"
Michel De Lara, Vincent Martinet, Julio PeñaTorres, Héctor Ramírez Cabrera
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 Résumé
 We develop a theoretical framework to assess sheries management strategies from a sustainability perspective, when the bioeconomic dynamics are marked by uncertainty. Using stochastic viability, management strategies are ranked according to their probability to satisfy economic and ecological constraints over time. The proposed framework is useful when it is not possible to dene a multiattribute utility function to represent the tradeoffs between the several sustainability objectives. This framework is applied to a Chilean shery casestudy, faced with El Niño uncertainty. We study the viability of effort and quota strategies, when a minimal catch level and a minimal biomass are required. For realistic sustainability objectives, effortbased management results in a better viability probability than quotabased management.
 ClassificationJEL
 Mot(s) clé(s)
 sustainability, risk, shery economics and management, viability, stochastic
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20122 "An EnvironmentalEconomic Measure of Sustainable Development"
Robert D. Cairns, Vincent Martinet
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 Résumé
 A central issue in the study of sustainable development is the interplay of growth and sacrifice in a dynamic economy. This paper investigates the relationship among current consumption, growth, and sustained consumption in two canonical, stylized economies and in a more general context. It is found that the maximin value measures what is sustainable and provides the limit to growth. Maximin value is interpreted as an environmentaleconomic carrying capacity and current consumption or utility as an environmentaleconomic footprint. The time derivative of maximin value is interpreted as net investment in sustainability improvement. It is called durable savings to distinguish it from genuine savings, usually computed with discounted utilitarian prices.
 ClassificationJEL
 Mot(s) clé(s)
 sustained development; growth; maximin; sustainability indicator
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20117 "Bargaining with intertemporal maximin payoffs"
Michel De Lara, Pedro Gajardo, Vincent Martinet, Héctor Ramírez Cabrera
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 Résumé
 We present a new class of dynamic bargaining problems, called "bargaining problems with intertemporal maximin payoffs," that may reflect sustainability problems having to encompass conflicting issues in the longrun. Each bargainer (or stakeholder) has a representative indicator, namely a function of the state and decisions, and aims at maximizing its minimal value over time. Bargaining on sustainability issues consists in defining the vector of stakeholder's payoffs. We are interested in defining the set of feasible outcomes of such problems. This set is interpreted as a support for a social choice of sustainability objectives. We introduce a MONDAI condition – Monotonicity of Dynamics And Indicators – consistent with many economic problems and, in particular, "environmental economic" sustainability issues. We characterize the set of feasible outcomes for problems satisfying these monotonicity properties, and the bargaining solutions under the axioms of Pareto efficiency and Independence of Irrelevant Alternatives. We also provide a "satisficing" common decision rule to achieve any given solution. We then examine the timeconsistency of the solution under the axioms of Veto Power and Individual Rationality.
 ClassificationJEL
 Mot(s) clé(s)
 bargaining theory; dynamics; maximin; monotonicity; feasibility set; sustainability
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201019 "Maximin, Viability and Sustainability"
Luc Doyen, Vincent Martinet
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 Résumé
 The maximin criterion defines the highest utility level which can be sustained in an intergenerational equity perspective. The viability approach characterizes all the economic trajectories sustaining a given, not necessarily maximal, utility level. In this paper, we exhibit the strong links between maximin and viability: We show that the value function of the maximin problem can be obtained in the viability framework via a static optimization problem under constraints. This result allows us to extend the maximin approach beyond optimality and characterize the sustainability of other economic trajectories. In particular, we show how the maximin value and viability kernel can be combined as sustainability indicators along any economic trajectory. Attention is especially paid to positive net investment at maximin prices, which is shown to be necessary to maintain the productive capacities of the economy. The DasguptaHealSolow model illustrates the assertions.
 ClassificationJEL
 Mot(s) clé(s)
 Sustainability; Maximin; Viability; Dynamics; Optimality
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20107 "Risk and Sustainability: Is Viability that far from Optimality?"
Michel De Lara, Luc Doyen, Vincent Martinet
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 Résumé
 Economic analysis addresses risk and longterm issues with discounted expected utility, focusing on optimality. Viability theory is based on sustainability constraints to be satis ed over time, focusing on feasibility. We make a bridge between these two approaches by showing that viability is equivalent to an array of degenerate intertemporal optimization problems. This makes the approach more interpretable in economic terms, and especially regarding efficiency. First,the deterministic case is examined. A particular emphasis is put on the connections between the viability kernel and the minimal time of crisis function. Then, we present stochastic viability with the notions of viable scenario and maximal viability probability. We show that the maximal viability probability shares dynamic programming properties with optimal discounted expected utility. Thus, both exhibit timeconsistency, which may be a basis for an axiomatization of criteria under risk and long run for public decisionmaking.
 ClassificationJEL
 Q01 D81 D63
 Mot(s) clé(s)
 Sustainability; uncertainty; multicriteria; viability
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200918 "Agricultural landuse and biological conservation"
Frédéric Barraquand, Vincent Martinet
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 Résumé
 Land use change is a main driver of biodiversity erosion, especially in agricultural landscapes. Incentivebased landuse policies aim at influence landuse pattern, and are usually evaluated with habitat suitability scores, without accounting explicitly for the ecology of the studied population. In this paper, we propose a methodology to define and evaluate agricultural landuse policies with respect to their ecological outcomes directly. We use an ecologicaleconomic model to link the regional abundance of a bird species to the economic context. Policies based on such ecological economics approaches appear to be more efficient than that based on landscape evaluation, from both economic and ecological viewpoints.
 ClassificationJEL
 Mot(s) clé(s)
 Ecologicaleconomic model, agriculture, landuse, landscape, conservation
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20097 "Defining sustainability objectives"
Vincent Martinet
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 Résumé
 Two of the challenges of thinking sustainability are how to deal with potentially conicting issues and how to ensure intergenerational equity. In practice, policymakers define sustainability objectives by setting thresholds that act as constraints on indicators. When defining a specific objective, they usually do not take into account either potential conflicts with other objectives or the diffculty to achieve all of them over time. In this paper, we propose an approach that defines sustainability objectives represented by a set of constraints on indicators and their associated thresholds. This approach meets the challenges of sustainability because objectives are defined such that all the constraints can be satisfied at all times. The thresholds are interpreted as minimal rights to be guaranteed to all generations, in a Rawlsian equity perspective. To define them, we have developed a criterion, which is, from a mathematical point of view, a "generalized" maximin. Applying the criterion is a twostep process. Firstly, the set of achievable objectives, given the endowment of the economy, is defined, revealing the necessary tradeoffs between them. Secondly, a static optimization of sustainability preferences on that set results in the proposed definition of sustainability objectives. We illustrate this approach by applying it to a canonical model often used to investigate sustainability issues (DasguptaHealSolow model; Review of Economic Studies 1974). We emphasize the relevance of this approach because it rationalizes the practice of using indicators to deal with sustainability in terms of the given challenge. We also discuss how to apply our approach to real sustainability issues.
 ClassificationJEL
 Q01, Q32, O13, C61
 Mot(s) clé(s)
 sustainability, indicators, intergenerational equity, criterion, minimal rights, viability
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200720 "Maximizing minimal rights for sustainability: a viability approach"
Vincent Martinet
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 Résumé
 This paper examines how the viability approach can be used to define
sustainability goals. In an economic model with a non renewable natural resource,
we define minimal rights to be guaranteed for all generations. These
rights can include a minimal consumption (economic goal) and the preservation
of natural resources (environmental goal). From a given economic
state, it is possible to define the set of minimal rights that can be provided
for all generation. To address the intergenerational equity issue, we propose
to use a criterion that define the set of minimal rights that provide the
maximal utility, in a Rawlsian perspective (Rawls, 1971). We describe how
this criterion can be applied and computed, and discuss it with respect to
usual criteria, including the maximin criterion, the Green Golden Rule, the
Chichilnisky approach and the Mixed BenthamRawls criterion.
 ClassificationJEL
 Q01, Q32, O13, C61
 Mot(s) clé(s)
 sustainability, intergenerational equity, minimal rights, viability.
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20065 "Recovering viable fisheries"
Luc Doyen, Vincent Martinet, Olivier Thebaud
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 Résumé
 This paper develops a formal analysis of the recovery processes for a fishery, from undesired to desired levels of sustainable exploitation, using the theoretical framework of viability control. We define sustainability in terms of biological, economic and social constraints which need to be met for a viable fishery to exist. Biological constraints are based on the definition of a minimal resource stock to be preserved. Economic constraints relate to the existence of a minimum profit per vessel. Social constraints refer to the maintenance of a minimum size of the fleet, and to the maximum speed at which fleet adjustment can take place. Using fleet size and fishing effort per vessel as control variables, we identify the states of this bioeconomic system for which sustainable exploitation is possible, i.e. for which all constraints are dynamically met. Such favorable states are called viable states. We then examine possible transition phases, from nonviable to viable states. We characterize recovery paths, wih respect to the economic and social costs of limiting catches during the recovery period, and to the duration of this transition period. Sensitivity of each of the constraints to transition costs and time are analyzed. The analysis is applied to a single stock fishery; preliminary results of an empirical application to the bay of Biscay nephrops fishery are presented.
 ClassificationJEL
 Q22, C61
 Mot(s) clé(s)
 sustainable fishing, recovery, fishery policies, bioeconomic modeling
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