Carmen Camacho-Perez

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.

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.

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.

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.

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 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 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.

Purpose – The authors characterize the conditions under which a country may eventually split and when it splits within an infinite horizon multi-stage differential game. Design/methodology/approach – In contrast to the existing literature, the authors do not assume that after splitting, players will adopt Markovian strategies. Instead, the authors assume that while the splitting country plays Markovian, the remaining coalition remains committed to the collective control of pollution and plays open-loop. Findings – Within a full linear-quadratic model, the authors characterize the optimal strategies. The authors later compare with the outcomes of the case where the splitting country and the remaining coalition play both Markovian. The authors highlight several interesting results in terms of the implications for long-term pollution levels and the duration of coalitions under heterogenous strategies as compared to Markovian behavior. Originality/value – In this paper, the authors have illustrated the richness of the simplications of enlarging the set of strategies in terms of the emergence of coalitions, their duration and the implied welfare levels per player. Varying only three parameters (the technological gap, pollution damage and coalition payoff share distribution across players), the authors have been able to generate, among other findings, quite different rankings of welfare per player depending on whether the remaining coalitions after split play Markovian or stay precommited to the pre-splitting period decisions