Publications des chercheurs de PSE

We revisit the classical Ramsey (1928) model with time discounting and a linear production function, explicitly accounting for the inevitable limitations of tangible production factors, which must remain both finite and positive. By employing Pontryagin's (1962) maximum principle, we transform state constraints into control constraints and provide a complete solution for all impatience rates under the linear production framework. While we classify the levels of impatience as established in the existing literature, we show that the behaviors associated with this threshold fundamentally differ when input limitations are considered -a factor previously overlooked. Our analysis extends beyond the literature's traditional focus on agents with mild impatience, encompassing the entire spectrum of impatience. For highly patient agents, the policymaker prioritizes investment over consumption, ensuring the economy reaches its maximum capital level in finite time. Once this level is attained, consumption stabilizes indefinitely, achieving the golden rule trajectory -an outcome previously deemed unattainable under time discounting. Conversely, beyond the classical impatience threshold, capital and consumption decline over time. For agents with extreme impatience, we identify a second threshold where investment ceases entirely, leading to rapid depletion of capital and output.

Acknowledging the economic role of knowledge, education, training and health, can preserve and make them thrive without assuming that preferences depend on any of them. In this paper we will define living capital as the aggregate of all these factors, and then, total capital as the sum of physical and living capital. In a planned economy, we find that the optimal sequence of total capital is always monotonic. Depending on the productivity of total capital, three different regimes hold: bounded growth; asymptotically balanced unbounded growth or unbalanced unbounded growth. At the early stages of development the economy optimally devotes all its investment effort to increase the stock of physical capital and only physical capital. As the economy develops, it will start involving living capital in production. In the first regime, total capital converges to a steady state with a positive stock of total capital, which is larger than the one without living capital. In the second regime, growth becomes unbounded, and consumption grows at a constant rate. Total capital grows at the same rate but only asymptotically. In the third case, living capital is used increasingly from the beginning. Once the economy is sufficiently rich, physical capital starts growing faster than living capital. To close, we consider a market economy with externalities from the living. In this scenario, if the government levies taxes to finance the accumulation of living capital and implements exactly the optimal sequence of living capital as in the planner’s program, then the equilibrium market prices exactly decentralize the planner’s solution.

We construct a Susceptible–Infected–Vaccinated Economic two‐sector growth model to explore the dynamics of inequality in an economy with distinct groups of workers exposed to a transmissible disease. Our analysis reveals a spectrum of outcomes in the long term, ranging from a disease‐free economic environment to a scenario where only the most susceptible group suffers from the disease. Long‐term outcomes are influenced by the reproduction rates both of the overall economy and those of the two groups of workers. If one group remains infected over time, the other will surely follow, leading to a perpetual disease burden for both. Additionally, because long‐term equilibria may not be unique, there is a possibility of long‐term uncertainty, posing additional challenges for policymakers. Notably, our calibrated model suggests that if the vaccination rate exceeds 24%, the relationship between disease exposure and inequality in capital assets becomes nonmonotonic.

Under the threat of a rapid expanding virus like the 2020 COVID-19, policy-makers need to decide relatively fast whether and under which conditions to invest in a vaccine, and eventually adopt other protective measures like social distancing or lockdowns, or to wait for natural herd immunity. Taking into account that vaccines take time to be fully developed and effective, this paper considers a unified framework at the crossroad between economics and epidemiology to study optimal public spending in medical research to obtain a vaccine against an infectious disease evolving according to a SIR dynamics. We prove that developed economies always invest in the search of a vaccine. The more individuals care about consumption, the more they actually reduce their current consumption and the more they invest in the vaccine research program to recover their consumption potential at the earliest. Our model would only recommend economies with very poor technology to restrain from investment and wait for herd immunity.

Food waste constitutes a significant economic inefficiency and should therefore be a central policy issue. While in low-income countries food waste is often associated with poor harvesting, storage and transportation conditions, in middle-and high-income countries consumers' behavior is considered to be the main driver of this problem. The general aim of our paper is to contribute to the understanding of food waste. We focus on household food waste and the economic mechanisms behind it. We propose a stylized model in which food waste appears as an economic decision of households. Our framework of "rational food waste" relies primarily on consumer behavioural biases, which could be further encouraged by aggressive pricing strategies such as quantity discounts.

In this paper we propose a time-space economic model to control the evolution and the spread of a disease. The underlying epidemiological model is formulated as a reaction-diffusion integro-differential partial differential equation. This specific model formulation, supported by empirical data, contains three different terms: a pure diffusion term, a linear growth term, and an integral term. These three terms capture different diffusion channels of a transmissible disease: a local diffusion effect, a temporal effect, and a global diffusion effect. The decision maker aims at deciding the optimal effort to be implemented in order to control the number of infections and, at the same time, minimize the cost of treatment. We analyze the finite horizon case in detail and we provide the closed-form expression of the optimal policy to be implemented to control the epidemic while sustaining economic growth. We also propose two different extensions: The first one considers an infinite horizon model while, the second one, is related to a multi-period framework.

We use Ekeland’s variational principle together with Pontryagin’s maximum principle to solve an optimal spatiotemporal economic growth model with a state constraint (no-negative capital stock) where capital law of motion follows a diffusion equation. We obtain the set of necessary optimal conditions for the solution to meet the state constraints for all time and locations. The maximum principle allows to reduce the infinite-horizon optimal control problem into a finite-horizon one ultimately leading to prove the uniqueness of the optimal solution with positive capital, and non-existence of the optimal solution with eventually strictly positive capital when the time discount rate is too large or too small.

We develop a spatial growth model for an agricultural economy where pollution diffuses in the soil. At each location, the only production factor is fertile soil, which is at the same time naturally bounded by the amount of available land, and eventually exposed to pollution diffused from neighboring locations. We develop a novel technique to obtain the policy maker’s optimal solution, which is analytical in the case of an homogeneous economy and covers all cases, for impatience rates ranging from almost zero to extremely high. When agents are very patient, the policy maker starts by making fully fertile all land before allowing for positive consumption. For slightly more impatient agents, the policy maker will allow for some consumption from the beginning, in the cleaning-up stage. With time, abatement stops, consumption raises and land becomes fully polluted in the long-term. We provide with some general results for the general spatially heterogeneous economy and its long-run, completing our study with some numerical exercises. Worth noting, simulations reveal that also in the non-homogeneous economy optimal consumption may transit through four different stages in time, responding to changes in fertile land and not necessarily in a smooth manner.

In a simple discrete-time version of Lucas (1988) we find that the Balanced Growth Path (BGP) is always the unique optimal planner’s solution: with linear or strictly concave production functions, with unbounded utility functions, with or without human capital depreciation. When the ”speed” of human capital accumulation is high, the optimal working time is constant and below its upper bound. Capital grows at a constant factor, but degrowth is also possible when this factor is less one (under positive capital depreciation). When this speed is low, optimal working time is at its boundary and capital declines at its depreciation factor (degrowth).

In a simple discrete-time version of the Lucas (1988) model, we prove, first, that the Balanced Growth Path (BGP) is optimal and, second, that the optimal solution is unique. After briefly discussing the results obtained in some of the continuous-time versions of the Lucas model, we address the issues of existence and uniqueness of the optimal solution in discrete time. Making use of the supermodularity of the value function, we prove that the optimal solution must be monotonically increasing. This feature does indeed suit the BGP, although nothing can ensure yet its optimality. After providing the exact expression of the BGP, we do prove both its optimality and its uniqueness.

We study here whether and when a social movement can turn into a successful revolution and modify the production system. To do so, the dynamics of social unrest is de_ned as a function of the number of discriminated workers, and their organizational skills, wage inequalities, and retaliation. Then, taking the evolution of social unrest into account, we obtain the optimal time for a revolution as the moment which maximizes discriminated workers' lifetime welfare. It is proven that if unrest increases with time and if a revolution does improve the discriminated's welfare, then a revolution arises independently of the initial state and the characteristics of the economy. Whenever the gains are high enough, then a revolution arises immediately. Worth noting, we show that even if social movement loses momentum, a revolution arises if the initial mass of discontent is sizeable or the system is so repressive that it becomes necessary to revolt.

This paper aims to fill the methodological gap in development economics that until now there exists no quantitative tool that allows to prioritize reforms in a systematic nor optimal way. Following the recent debate on the issues Randomized Control Trials (RCTs) have with establishing external validity and general equilibrium effects, this paper proposes a micro-founded Growth Diagnostics framework to consider general equilibrium effects and prioritize policy prescriptions. Contrarily to Hausmann et al. (2005), we set up two continous-time Overlapping Generations (OLG) models to account for the different net-marginal valuations of various economic activities rigorously. We solve the household and planner problem to respectively obtain the private and social net-marginal valuations of economic activities via the corresponding Lagrange multipliers. With these in hand, we define the wedges in the net-marginal private and social valuations to set up a new planner problem (we call super policy maker problem), where the planner minimizes the sum of wedges. This final wrapping optimization problem allows to prioritize optimally economic reforms in a second-best framework, thus, to put it in the words of Rodrik (2010), to first diagnose before one prescribes the remedy.