Publications

(22) An $\alpha$-MaxMin utility representation for close and distant future preferences with temporal biases (with Jean-Pierre Drugeon). Journal of Mathematical Economics (2023), PDF. 

 Abstract: This paper provides a framework for understanding preferences over utility streams across different time periods. We analyze preferences for the close future, for the distant future, and a synthesis of both, establishing a representation involving weights overtime periods. Examining scenarios where two utility streams cannot be robustly compared to each other, we introduce notions in which one has more ``potential’’ to be preferred over another, which lead to MaxMin, MaxMax, and $\alpha$-MaxMin representations. Finally, we consider temporal bias in the form of violations of stationarity. For close future preferences, we obtain a generalization of quasi-hyperbolic discounting. For distant future preferences, we obtain Banach limits and discuss the relationship with exponential discounting.

(21) A multidimensional, nonconvex model of optimal growth (with Stefano Bosi). Journal of Mathematical Economics (2023), PDF.

 Abstract: In this article, we consider a multidimensional economy where the standard supermodularity property fails. We generalize the notion of net gain of investment, introduced by Kamihigashi and Roy (2007) and applied to one-sector growth models, to the case of multiple capital stocks. We prove the convergence to the set of steady states without relying on the monotonicity of the optimal path. Our approach differs from the standard dynamic programming based on convexity or supermodularity. We find that preferences are key to shaping the economy in the long run. 

(20) Balanced growth and degrowth with human capital (with Stefano Bosi and Carmen Camacho). Economics Letters (2023), PDF. 

 Abstract: We address the fundamental issue of the optimality of the Balanced Growth Path (BGP) in a discrete-time version of Lucas (1988). After proving that the value function is supermodular and that any optimal solution is monotone, we prove that the BGP is optimal and that it is the unique optimal solution. Because of human capital depreciation, we also show that the economy can experience optimal endogenous regrowth. 

(19) Long-Run Cycles in a Growth Model with Natural Externalities (with Stefano Bosi). Environmental Modeling & Assessment (2023), PDF. 

Abstract: In this paper, we consider an AK model augmented with a productive externality of nature and a process of natural capital accumulation where a reproduction force is moderated by the negative impact of productive pollution. Differently from the existing literature, more focused on the planner's solution, we consider a market economy and the effects of its imperfections. We introduce two distinct natural accumulation processes: a power law, more usual in economics, and a logistic law, more popular in ecology. In both cases, we observe the occurrence of cycles of period two, cycle of period a power of two and chaos through a flip bifurcation and perioddoubling bifurcations. In the case of the power law, dynamics are even richer because of the possibility of limit cycles through a Neimark-Sacker bifurcation. In the case of a power law, cycles occur under a larger Total Factor Productivity because the TFP amplifies the negative impact of pollution on natural regeneration. In the case of a logistic law, cycles take place when the saturation effect of nature as a larger negative impact on the reproduction process. 

(18) Recycling vs Mining: competition for market shares, collusion for market power (with Jean de Beir and Sylvain Sourisseau). Revue Economique (2023), PDF.

 Abstract: As an alternative to the production of virgin materials, recycling brings competition in a market dominated by an oligopoly of mining firms. Herein we investigate how recyclers affect the supply of materials in terms of market share and market power. An oligopoly of non-cooperative firms takes decisions about the level of extraction, knowing that this will affect the competition capacity of a fringe of competitive recyclers in the future. Hence, the mining firms are considered as leaders, and the market is completed by recyclers being considered as followers. The competition between mining firms as well as between the two sectors is described in a Cournot-Stackelberg model. We show the positive effect depending on the small number of mining firms and their aggregated market share and prove that a technology threshold is required to allow recyclers to enter the market and compete. Furthermore, we highlight that a significant switch in market shares and a decrease in the market power only arise when the levels of the recycling technology and the availability of scrap are both at a high level, while they vary a lot among countries and materials.

(17) Saving and dissaving under Ramsey-Rawls criterion (with Tuyet Mai Nguyen). Journal of Mathematical Economics (2022), PDF. 

Abstract: This article studies an inter-temporal optimization problem by using a criterion that is a combination of Ramsey's and Rawls's criteria. A detailed description of the saving behavior through time is provided. The optimization problem under the $\alpha$−maximin criterion is also considered, and the optimal solution is characterized. 

(16) A tale of two Rawlsian criteria Mathematical Social Sciences (2022), PDF.

Abstract: This article considers optimization problems under two Rawls criteria. The first one is the classical Rawls criterion in literature and the second one as a result of the maximin criteria with multiple discount factors presented in Chambers and Echenique (2018). Though these criteria are different, they have the same optimal value and solution. 

(15) Ascendant altruism and asset price bubbles (with Stefano Bosi, Cao-Tung Pham and Ngoc-Sang Pham). International Journal of Economic Theory (2022), PDF. 

Abstract: We consider an overlapping generations economy with altruism towards parents and a long-lived asset that delivers no dividends (pure bubble asset). We explore the role of ascendant altruism on the dynamic properties of equilibrium and rational bubbles in the cases of exogenous and endogenous growths. 

(14) Wheels and cycles: Sub-optimality and volatility of corrupted economies (with Stefano Bosi and David Demarchelier). International Journal of Economic Theory (2022), PDF. 

 Abstract: We consider a simple economy where production depends on labor supply and social capital. Networking increases the social capital (“greases the wheel”) but also the corruption level (“sands the wheel”). Corruption is a negative productive externality. We compare the market economy, where the negative externality is not taken into account by individuals, with a centralized economy, where the planner internalizes the negative effect. We highlight the possible existence of cycles in the market economy and optimal cycles in the planned economy. We compare the centralized and the decentralized solutions in the short and long run. 

(13)  A Not so Myopic Axiomatization of Discounting (with Jean-Pierre Drugeon). Economic Theory (2022), PDF.

 Abstract: This article builds an axiomatization of inter-temporal trade-offs that takes an explicit account of the distant future. The focus is on separable representations and the approach is completed following a decision-theory index based approach that is applied to utility streams understood as the well-being of future generations. The introduction of some new axioms is herein shown to lead to the emergence of two distinct orders that respectively relate to the distant future and close future components of some utility stream. This enlightens the limits of the commonly used fat tail intensity requisites for the evaluation of utility streams. These are replaced by an axiomatic approach to myopia degrees. 

(12) A simple characterization for sustained growth (with Nhat-Thien Tran). Journal of Mathematical Economics (2020), PDF.

 Abstract: This article considers an inter-temporal optimization problem in a general form and gives conditions ensuring the convergence to infinity of the economy. These conditions can be easily verified and applied to a large class of problems in the literature. Some applications for different economies are given as illustrative examples. 

(11) Economic dynamics with renewable resources and pollution (with My Dam, Cuong Le Van and Thi Tuyet Mai Nguyen). Mathematical Social Sciences (2020), PDF.

 Abstract: This article considers a two-sector economy with externalities. In particular, the analysis involves an industrial sector whose polluting production activities have negative effects on the regeneration of a natural resource in the other sector. Without convexity or supermodularity, we prove that the economy evolves to increase the net gain of stock (a similar notion to the net gain of investment in Kamihigashi and Roy (2007)), and establish the conditions ensuring the convergence of the economy in the long run. 

(10) Optimal growth when consumption takes time (with Cuong Le Van and Thi Do Hanh Nguyen). Journal of Public Economic Theory (2020), PDF.

 Abstract: This article analyzes a one-sector growth model where the consumption takes time. When the consumption takes time, the consumption set is compact and we meet satiety. However, we prove that dynamic constraints are binding. This result is crucial to prove that, under well-known assumptions in macroeconomic dynamic programming, the optimal path is monotonic and always converges to a unique nontrivial steady state as in the case where consumption is timeless. 

 (9) Heterogeneous human capital, inequality and growth: the role of patience and skills (with Stefano Bosi, Kirill Borisov and Leonor Modesto). International Journal of Economic Theory (2020), PDF.

 Abstract: We extend the Lucas (1988) model, introducing two classes of agents with heterogeneous skills, discount factors and initial human capital endowments. We consider two regimes according to the planner's political constraints. In the meritocratic regime, the planner faces individual constraints. In the redistributive regime, the planner faces an aggregate constraint. We find that heterogeneity matters, particularly with redistribution. In the meritocratic regime, the optimal solution coincides with the balanced growth path (BGP) found by Lucas (1988) for the representative agent's case. In contrast, in the case of redistribution, the solution for time devoted to capital accumulation is never interior for both agents. Either the less talented agents do not accumulate human capital or the more skilled agents do not work. Moreover, social welfare under the redistributive regime is always higher than under meritocracy, and it is optimal to exploit existing differences. Finally, we find that inequality in human capital distribution increases in time and that, in the long run, inequality always promotes growth. 

 (8) On dynamic programming with optimal rates of discount (with Jean-Pierre Drugeon and Thi Do Hanh Nguyen). Economic Theory (2020), PDF.

 Abstract: This article establishes a dynamic programming argument for a maximin optimization problem where the agent completes a minimization over a set of discount rates. Even though the consideration of a maximin criterion results in a program that is not convex and not stationary over time, it is proved that a careful reference to extended dynamic programming principles and a maxmin functional equation however allows for circumventing these difficulties and recovering an optimal sequence that is time consistent. 

 (7) Rational bubbles in altruistic economies: when Tirole meets Ramsey (with Stefano Bosi, Cao-Tung Pham and Ngoc Sang Pham). Economic Bulletins (2019), PDF.

 Abstract: We consider an overlapping generations model a la Tirole (1985) augmented with altruism from parents to children as in Barro (1974). We compute the global dynamics and we show that, in the case of low altruism, bequests are zero and our model works exactly as the Tirole's model (1985) where rational bubbles can arise, while, in the case of high altruism, bequests are positive and bubbles are ruled out. This result holds whatever the share of altruistic agents in total population. Our contribution raises the question of the robustness of Tirole's conclusion about the existence of rational bubbles under a large degree of altruism. 

 (6) Financial bubbles and capital accumulation in altruistic economies (with Stefano Bosi, Cuong Le Van, Cao-Tung Pham and Ngoc Sang Pham). Journal of Mathematical Economics (2018), PDF.

 Abstract: We consider an overlapping generations model à la Diamond (1965) with two additional ingredients: altruism and an asset (or land) bringing non-stationary positive dividends (or fruits). We study the global dynamics of capital stocks and asset values as well as the interplay between them. Asset price bubbles are also investigated. 

 (5) Arbitrage and equilibrium in economies with short-selling and ambiguity (with Cuong Le Van and Cuong Tran-Viet). Journal of Mathematical Economics (2018), PDF.

 Abstract: We consider a model with a finite number of states of nature where short sells are allowed. We present a notion of no-arbitrage price weaker than the one of Werner (1987) that we call weak no-arbitrage price. We prove that in the case of maximin expected utility functions, the existence of one common weak no-arbitrage price is equivalent to the existence of an equilibrium. 

 (4) Existence of equilibrium on asset markets with a countably infinite number of states (with Cuong Le Van). Journal of Mathematical Economics (2017), PDF.

 Abstract: We consider a model with a countably infinite number of states of nature. The agents have equivalent probability beliefs and von Neumann–Morgenstern utilities. The No-Arbitrage Prices in this paper are, up to a scalar, the marginal utilities. We introduce the Beliefs Strong Equivalence and the No Half Line Condition of the same type conditions. Under these conditions, the No Arbitrage price condition is sufficient for the existence of an equilibrium when the commodity space is $\ell_\infty$. This No Arbitrage condition is necessary and sufficient for the existence of equilibrium when the total endowment is in $\ell_\infty$. Moreover, it is equivalent to the compactness of the individually rational utility set. 

 (3) No arbitrage condition and existence of equilibrium in infinite dimension with expected very risk averse utilities. (with Cuong Le Van and Manh-Hung Nguyen). Mathematical Social Sciences (2016), PDF.

 Abstract: We consider a model with an infinite number of states of nature, von Neumann–Morgenstern utilities, where agents have different probability beliefs and where short sells are allowed. We show that no-arbitrage conditions, defined for finite dimensional asset markets models, are not sufficient to ensure existence of equilibrium in presence of an infinite number of states of nature. However, if the individually rational utility set $\mathlcal U$ is compact, we obtain an equilibrium. We give conditions which imply the compactness of $\mathcal U$. We give examples of non-existence of equilibrium when these conditions do not hold. 

 (2) A Never decisive and Anonymous Criterion for Optimal Growth Models (with Alain Ayong le Kama, Cuong Le Van and Katheline Schubert). Economic Theory (2013), PDF. 

 Abstract: We address in this paper the question of the existence of a Social Welfare Function that would be sustainable and would allow us to obtain solutions to optimal growth models. We define sustainability by two new axioms called Never-decisiveness of the present and Never-decisiveness of the future. We first show that a SWF which has Never-decisiveness properties cannot be defined on a ball of $\ell_\infty$. We must (i) restrict to the set of utility streams for which the value of the SWF is finite and (ii) introduce additional assumptions in order to obtain the Never-decisiveness properties. Our main result in this paper is therefore to show that the undiscounted utilitarian criterion is an anonymous and never-decisive criterion for optimal growth models. We consider the set of utilities of consumptions which are generated by a specific technology, namely a technology with decreasing returns for high levels of capital, and restrict ourselves to good programs, i.e., any program for which intertemporal utility is well defined. 

 (1) No unbounded arbitrage, weak no market arbitrage and no arbitrage price system condition: The circular result (avec Manh-Hung Nguyen). Journal of Mathematical Economics (2010).

 Abstract: Page and Wooders (1996) prove that the no unbounded arbitrage (NUBA), a special case of a condition in Page (1987), is equivalent to the existence of a no-arbitrage price system (NAPS) when no agent has non-null useless vectors. Allouch et al. (2002) extend the NAPS introduced by Werner (1987) and show that this condition is equivalent to the weak no market arbitrage (WNMA) of Hart  (1974). They mention that this result implies the one given by Page and Wooders (1996). In this note, we show that all these conditions are equivalent.