The dynamics of socially responsible product differentiation and the habit formation of socially responsible consumers

In our model of socially responsible (SR) product differentiation two duopolists (a zero profit socially concerned producer and a profit maximizing producer) compete over prices and (costly) “socially and environmentally responsible” features of their products under a given law of motion of consumer’s habits. In a continuous time model in which the location of the zero profit socially responsible entrant is fixed and the profit maximizing producer (PMP) limits himself to price competition without SR imitation, we show that the optimal dynamic PMP’s price is always lower than his optimal static price since the PMP knows that, by leaving too much market share to his competitor, he will reinforce the habit of socially responsible consumption and loose further market share in the future. We also inspect the properties of equilibria when the PMP can imitate the entrant’s SR and we find that, in this case, the threshold triggering a PMP strategy of SR imitation and minimum price differentiation is higher in the dynamic than in the static case, depending on the PMP’s shadow cost of changes in consumer social responsibility.product differentiation, social responsibility, fair trade

Optimal Social and Vaccination Control in the SVIR Epidemic Model

In this paper we introduce an approach to the management of infectious disease diffusion through the formulation of a controlled compartmental SVIR (Susceptible-Vaccinated-Infected-Recovered) model. We consider a cost functional encompassing three distinct yet interconnected dimensions: the social cost, the disease cost, and the vaccination cost. The proposed model addresses the pressing need for optimized strategies in disease containment, incorporating both social control measures and vaccination campaigns. Through the utilization of advanced control theory, we identify optimal control strategies that mitigate disease proliferation while considering the inherent trade-offs among social interventions and vaccination efforts. Finally, numerical implementation of the optimally controlled system through the Forward-Backward Sweep algorithm is presented.Comment: 22 pages, 8 figure

On The Dynamic Programming Approach To Incentive Constraint Problems

In this paper we study a class of infinite horizon optimal control problems with incentive constraints in the discrete time case. More specifically, we establish suffcient conditions under which the value function associated to such problems satisfies the Dynamic Programming Principle.In this paper we study a class of infinite horizon optimal control problems with incentive constraints in the discrete time case. More specifically, we establish suffcient conditions under which the value function associated to such problems satisfies the Dynamic Programming Principle.Non-Refereed Working Papers / of national relevance onl

A dynamic model of Gambling addiction with social costs: theory and policy solutions

We investigate the effects of gambling addiction in a dynamic model in which wellbeing crucially depends on the accumulation of relational goods which is weakened by the consumption of gambling. We outline conditions under which gambling may become addictive leading to a suboptimal equilibrium from a social point of view. We examine the relative effectiveness of different policy solutions (tax on gambling, gambling restrictions) in bridging the distance between the equilibrium without intervention and social optimum

A dynamic model of Gambling addiction with social costs: theory and policy solutions

We investigate the effects of gambling addiction in a dynamic model in which wellbeing crucially depends on the accumulation of relational goods which is weakened by the consumption of gambling. We outline conditions under which gambling may become addictive leading to a suboptimal equilibrium from a social point of view. We examine the relative effectiveness of different policy solutions (tax on gambling, gambling restrictions) in bridging the distance between the equilibrium without intervention and social optimum

The economic cost of social distancing during a pandemic: an optimal control approach in the SVIR model

We devise a theoretical model for the optimal dynamical control of an infectious disease whose diffusion is described by the SVIR compartmental model. The control is realized through implementing social rules to reduce the disease's spread, which often implies substantial economic and social costs. We model this trade-off by introducing a functional depending on three terms: a social cost function, the cost supported by the healthcare system for the infected population, and the cost of the vaccination campaign. Using Pontryagin's Maximum Principle, we are able to characterize the optimal control strategy in three instances of the social cost function, the linear, quadratic, and exponential models, respectively. Finally, we present a set of results on the numerical solution of the optimally controlled system by using Italian data from the recent COVID-19 pandemics for the model calibration

On the dynamic programming approach to incentive constraint problems

In this paper we study a class of infinite horizon optimal control problems with incentive constraints in the discrete time case. More specifically, we establish sufficient conditions under which the value function associated to such problems satisfies the Dynamic Programming Principl