Biodiversity, Shapley value and phylogenetic trees: some remarksJournal articleHubert Stahn, Journal of Mathematical Biology, Volume 80, Issue 3, pp. 717-741, 2020

This paper explores the main differences between the Shapley values of a set of taxa introduced by Haake et al. (J Math Biol 56:479–497, 2007. and Fuchs and Jin (J Math Biol 71:1133–1147, 2015., the latter having been found identical to the Fair Proportion index (Redding and Mooers in Conserv Biol 20:1670–1678, 2006. In line with Shapley (in: Kuhn, Tucker (eds) Contributions to to the theory of games, volume II, annals of mathematics studies 28, Princeton University Press, Princeton, 1953), we identify the cooperative game basis for each of these two classes of phylogenetic games and use them (i) to construct simple formulas for these two Shapley values and (ii) to compare these different approaches. Using the set of weights of a phylogenetic tree as a parameter space, we then discuss the conditions under which these two values coincide and, if they are not the same, revisit Hartmann’s (J Math Biol 67:1163–1170, 2013. convergence result. An example illustrates our main argument. Finally, we compare the species ranking induced by these two values. Considering the Kendall and the Spearman rank correlation coefficient, simulations show that these rankings are strongly correlated. These results are consistent with Wicke and Fischer (J Theor Biol 430:207–214, 2017., who reach similar conclusions with a different simulation method.

On Outsourced Abatement Services: Market Power and Efficient RegulationJournal articleDamien Sans, Sonia Schwartz and Hubert Stahn, Annals of Economics and Statistics, Issue 136, pp. 55-78, 2019

In this paper, we consider competitive polluting firms that outsource their abatement activity to an upstream imperfect competitive eco-industry to comply with environmental regulation. In this case, we show that an usual environmental policy based on a Pigouvian tax or a pollution permit market reaches the first-best outcome. The main intuition is based on the idea that purchasing pollution reduction services instead of pollution abatement inputs modifies for each potential tax rate (or out of the equilibrium permit price) the nature of the arbitrage between pollution and abatement. This induces a demand for abatement services which is, at least partially, strongly elastic and therefore strongly reduces upstream market power. This argument is first illustrated with an upstream monopoly selling eco-services to a representative polluting firm under a usual Pigouvian tax. We then progressively extend the result to permit markets, heterogeneous downstream polluters and heterogeneous upstream Cournot competitors.

On conjunctive management of groundwater and rainwaterJournal articleHubert Stahn and Agnès Tomini, Resource and Energy Economics, Volume 49, pp. 186-200, 2017

We consider groundwater managed by a sole owner and where a perfect substitute, rainwater harvesting, is physically connected with the primary water source. This generates a marginal opportunity cost of using rainwater, since harvested water does not infiltrate. We first discuss the conditions that lead to a switch toward rainwater harvesting, then look at long-term rainwater harvesting systems. Due to limited storage capacity, long-term use of rainwater is only possible in conjunction with groundwater. We show that this only arises if the price of water is higher than the full marginal cost of rainwater harvesting. We also provide comparative statics related to this configuration, especially concerning the long-term water table. These results are finally illustrated by numerical examples. (C) 2017 Elsevier B.V. All rights reserved.

About polluting eco-industries: optimal provision of abatement goods and Pigouvian feesJournal articleDamien Sans, Sonia Schwartz and Hubert Stahn, Environmental Economics, Volume 8, Issue 3, pp. 46-61, 2017

In this article, the authors introduce a polluting eco-industry. Depending on the level of damage, there are two optimal equilibria. If the damage is low, one generalizes the usual results of the economic literature to the polluting eco-industry: the dirty firm partially abates their emissions, only efficient eco-industry firms produce and the abatement level increases with the damage. However, very specific results are obtained if the damage is high. In this case, not all efficient eco-industry firms produce. The abatement level and the number of active eco-industry firms both decrease as the damage increases. The authors finally show that a well-designed Pigouvian tax implements these equilibria in a competitive economy.

On the Environmental Efficiency of Water Storage: the Case of a Conjunctive use of Ground and RainwaterJournal articleHubert Stahn and Agnès Tomini, Environmental Modeling & Assessment, Volume 21, Issue 6, pp. 691-706, 2016

Rainwater harvesting, consisting in collecting runoff from precipitation, has been widely developed to stop groundwater declines and even raise water tables. However, this expected environmental effect is not self-evident. We show in a simple setting that the success of this conjunctive use depends on whether the runoff rate is above a threshold value. Moreover, the bigger the storage capacity, the higher the runoff rate must be to obtain an environmentally efficient system. We also extend the model to include other hydrological parameters and ecological damages, which respectively increase and decrease the environmental efficiency of rainwater harvesting.

Rainwater Harvesting under Endogenous Capacity of Storage: a Solution to Aquifer Preservation?Journal articleHubert Stahn and Agnès Tomini, Annals of Economics and Statistics, Issue 119-120, pp. 209-234, 2015

This paper studies groundwater management in the presence of rainwater harvesting (RWH). We propose a two-state model that takes into account the dynamics of the aquifer and the standard dynamics of the storage capacity, and we assume that the collection of rainwater reduces the natural recharge. We analyze the trade-off between these two water harvesting techniques in an optimal control model. In particular, we show that, when these techniques are perfect substitutes, the development of RWH leads in the long run to a depletion of the water table, even if pumping is reduced. This result is illustrated by a numerical application for the Pecos River Basin (New Mexico, USA). JEL: Q25, C61, D61. / KEY WORDS: Rainwater Harvesting, Conjunctive Use, Groundwater Management, Optimal Control.

Competitive Permit Markets and Vertical Structures: The Relevance of Imperfectly Competitive Eco-IndustriesJournal articleSonia Schwartz and Hubert Stahn, Journal of Public Economic Theory, Volume 16, Issue 1, pp. 69-95, 2014

Permit markets lead polluting firms to purchase abatement goods from an eco-industry which is often concentrated. This paper studies the consequences of this sort of imperfectly competitive eco-industry on the equilibrium choices of the competitive polluting firms. It then characterizes the second-best pollution cap. By comparing this situation to one of perfect competition, we show that Cournot competition on the abatement good market contributes not only to a nonoptimal level of emission reduction but also to a higher permit price, which reduces the production level. These distortions increase with market power, measured by the margin taken by the noncompetitive firms, and suggest a second-best larger pollution cap.

Toward Waste Management ContractsJournal articleStéphanie Le Maitre and Hubert Stahn, Environmental Economics, Volume 5, Issue 2, pp. 32-47, 2014

This paper deals with the cost of treatment of final waste, that is waste which cannot, in the absence of recycling opportunities, be reduced by any appropriate tax scheme. The authors propose a new way to handle this waste based on Waste Management Contracts (WMC) which largely involve households in the cost reduction process. Within a set of feasible (i.e. budget budget-balancing, incentive-compatible and acceptable) contracts, the study characterizes the optimal WMC and compare this system with a more standard one based on a combination of advance and per-bag disposal fees.

Emergence of Organic Farming under Imperfect Competition: Economic Conditions and Policy InstrumentsJournal articleMélanie Jaeck, Robert Lifran and Hubert Stahn, Journal of Agricultural & Food Industrial Organization, Volume 12, Issue 1, pp. 95-108, 2014

This paper explores the economic conditions for the viability of organic farming in a context of imperfect competition. While most research dealing with this issue has adopted an empirical approach, we propose a theoretical approach. Farmers have a choice between two technologies, the conventional one using two complementary inputs, chemicals and seeds, and the organic one only requiring organic seeds. The upstream markets are oligopolistic and the firms adopt Cournot behavior. The game is solved backward. The equilibrium distribution of the farmers between both sectors is obtained by a free-entry condition. Since multiple equilibria could exist, including the non-emergence of organic farming, we spell out viability conditions for organic farming. Then, using an “infant industry” argument, we propose several public policy instruments able to support the development of organic farming and assess their relative efficiency. Results could be useful to assess the conditions of emergence and viability of agricultural innovations in analogous contexts.

Nash-implementation of competitive equilibria via a bounded mechanismJournal articleGaël Giraud and Hubert Stahn, Review of Economic Design, Volume 17, Issue 1, pp. 43-62, 2013

We deal with the problem of providing incentives for the implementation of competitive outcomes in a pure-exchange economy with finitely many households. We construct a feasible price-quantity mechanism, which fully implements Walras equilibria via Nash equilibria in fairly general environments. Traders’ preferences need neither to be ordered nor continuous. In addition, the mechanism is such that no pure strategy is weakly dominated, hence is bounded (in the sense of Jackson 1992 ). In particular it makes no use of any integer game. Copyright Springer-Verlag Berlin Heidelberg 2013