Controlling complex dynamics in a protected-area discrete-time model

This paper investigates how the introduction of user fees and defensive expenditures change the complex dynamics of a discrete-time model, which represents the interaction between visitors and environmental quality in a Open-Access Protected-Area (OAPA). To investigate this issue more deeply, we begin by studying in great detail the OAPA model and then we introduce the user fee () and the defensive expenditures () specifically directed towards at the protection of the environmental resource. We observed that some values of can generate a chaotic regime from a stable dynamic of the OAPA model. Finally, to eliminate the chaotic regime, we design a controller by OGY method, assuming the user fee as a controller parameter.sustainable tourism; controlling chaos;

Mathematical analysis of an economic growth model with perfect-substitution technologies

The purpose of this paper is to highlight certain features of a dynamic optimisation problem in an economic growth model with environmental negative externalities that gives rise to a two-dimensional dynamical system. In particular, it is demonstrated that the dynamics of the model, which is based on a production function with perfect substitutability (perfect substitution technologies), admits a locally attracting equilibrium with a basin of attraction that may be considerably large, as it can extend up to the boundary of the system phase plane. Moreover, this model exhibits global indeterminacy because either equilibrium of the system can be selected according to agent expectation. Formulas for the calculation of the bifurcation coefficients of the system are derived, and a result on the existence of limit cycles is obtained. A numerical example is given to illustrate the results

Consumption of private goods as substitutes for environmental goods in an economic growth model

We analyze growth dynamics in an economy where a private good can be consumed as a substitute for a free access environmental good. In this context we show that environmental deterioration may be an engine of economic growth. To protect themselves against environmental deterioration, economic agents are forced to increase their labour supply to increase the production and consumption of the private good. This, in turn, further depletes the environmental good, leading economic agents to further increase their labour supply and private consumption and so on. This substitution process may give rise to self-enforcing growth dynamics characterized by a lack of correlation between capital accumulation and private consumption levels, on one side, and economic agents’ welfare, on the other. Furthermore, we show that agents’ self-protection consumption choices can generate indeterminacy; that is, they can give rise to the existence of a continuum of (Nash) equilibrium orbits leading to the same attracting fixed point or periodic orbit.Self-protection choices; indeterminacy; undesirable economic growth; negative externalities

Free riders and strong reciprocators coexist in public goods experiments: evolutionary foundations

Experimental evidence indicates that free riders and strongly reciprocal papers coexist in the public goods game framework. By means of an evolutionary analysis, we provide an endogenization of this behavioral regularity.Free Riding, Cooperation, Strong Reciprocity, Public Goods Game, Evolutionary Game Theory.

Free Riders and Cooperators in Public Goods Experiments: Can Evolutionary Dynamics Explain their Coexistence?

An oft-cited and robust result from Public Goods Game experiments is that, when subjects start playing, the aggregate level of contributions is significantly different from zero. At the same time, a sizeable proportion of players free ride from the outset. Behavioural economics has persuasively shown that these laboratory findings are compatible with the presence of motivationally heterogeneous agents, displaying both standard, self-centred preferences and non-standard, interdependent preferences. However, at the theoretical level, economists would prefer to account for motivational heterogeneity endogenously, instead of simply assuming it from the outset. Our work provides such endogenisation, by assuming that social evolution is driven by material payoffs only. By separately focusing on different types of ‘experimentally salient’ pro-social players (such as Reciprocators, Strong Reciprocators and Altruists), we are able to shed light – to our knowledge, for the first time, within the public good framework – on the evolutionary stability of two-type populations consisting of positive proportions of both ‘nice’ and ‘mean’ guys.Free Riding, Strong Reciprocity, Altruism, Nonstrategic Punishment, Public Goods Game, Evolutionary Game Theory

Biodiversity and Economic Growth: Stabilization Versus Preservation of the Ecological Dynamics

This work examines the impact that economic growth can have on biodiversity and on the ecological dynamics that would naturally emerge in the absence of human activity. The loss of biodiversity may induce policy-makers to implement defensive actions that prevent single species from extinction. These defensive actions, however, may deeply alter the natural dynamics of interaction between species, leading to an ecological equilibrium that is completely different from the one that would exist in the absence of human intervention. This suggests that there might exist a conflict between preserving biodiversity (through stabilization of the ecological system) and preserving the intrinsic features of the ecological dynamics. To investigate this issue more deeply, we analyze the impact that different objective functions and defensive technologies can have on the natural ecological dynamics, and show that human action can modify the stability of the ecological fixed points. From the simple analytical formulations adopted in the paper, it emerges that it is possible to stabilize the ecological fixed point and consequently to avoid the extinction of a species, even in the absence of defensive expenditures specifically finalized at the protection of that species. The stabilizing. effect of human intervention, however, turns out to be enhanced when specific defensive expenditures are implemented. Finally, numerical simulations suggest that human activity can have an even deeper impact on the ecological dynamics, substantially modifying not only the stability of the fixed points, but also their number.Biodiversity, Growth, Defensive actions, Ecological dynamics

Structural change, economic growth and environmental dynamics with heterogeneous agents

This paper presents a model which takes into account two main factors that have been partially neglected by the economic development literature: the environmental externalities of human activities and agents' heterogeneity in terms of asset endowment and, consequently, in terms of income source and vulnerability to depletion of natural resources. This approach permits to shed light on agents' differences in feed-back mechanisms and interactions between their choices and environmental dynamics and allow us to propose a taxonomy of structural changes on the basis of distributive, environmental and economic impact. In such context, we identify under which conditions each structural change can occur. In par ticular, we identify new requirements for prompting positive structural changes, i.e. a movement of labour to capitalistic activities associated with poverty reduction and the alleviation of environmental pressures.Structural change; environmental externalities; eco- nomic development; poverty alleviation

On the Optimality of Limit Cycles in Nature Based-Tourism

Virgin nature, as well as historical and cultural monuments located in National Parks, all form part of our national heritage. Tourism and recre- ation allow visitors to National Parks to enjoy nature, to reinstate, recover and broaden their personal outlook, to experience local history, culture, ora and fauna and to interact with the environment harmoniously. One of the ob- jectives of the administration of a Governmental Institution 'National Park' is to maximize prots from tourism and recreation, where prot is dened as the difference between the revenues from visitors and the sum of expenditures on recreation investments and defensive expenditures for ensuring the preserva- tion of natural and cultural heritage. This paper is an attempt to model some relevant aspects of these prey-predator relations. The model is formulated in terms of optimal control theory, and then is transformed into an `augmented' dynamic system by meas of the optimal choice of control variables resulting form the application of Pontryagin's Maximum Principle. It turns out that, for reasonable parameter values, the optimal trajectory exhibits a cyclical behavior.bioeconomic model; tourism; optimal dynamic control model; optimal policy mix; financing and protected areas

Structural Change, Environment and Well-being: Interactions Between Production and Consumption Choices of the Rich and the Poor in Developing Countries

Vulnerability to scarcity or to reduction of natural capital depends on defensive substitution possibilities that, in turn, are affected by the availability of other productive factors. However, in several developing countries asset distribution tends to be highly skewed. Taking into ac- count these elements, this paper argues that environmental degradation may represent a push factor of economic development in an economy polarized into two main classes (the Rich and the Poor) and characterized by the following stylized facts: a) the main income source of the rural poor is self-employment in traditional activities highly depending on natural resources; b) labor remuneration in rural sector represents the basic opportunity cost for (unskilled) labor in the economy. Thus, given that environmental degradation reduces labor productivity of the rural poor, it may depress wages; c) production of the modern sector managed by the rich is less affected by depletion of natural resources because they can adopt defensive strategies that the poor cannot. They are able to defend themselves by partially substituting natural resources with physical capital accumulation and wage labor employment. We will show that, in this context, environmental depletion may benefit the modern sector through an increase in low cost labor supply and, in turn, it may stimulate economic transition. However the structural change is likely to result in an increase in inequality.Production, Consumption Choices, Welfare

Free riders and strong reciprocators coexist in public goods experiments: evolutionary foundations

Experimental evidence indicates that free riders and strongly reciprocal papers coexist in the public goods game framework. By means of an evolutionary analysis, we provide an endogenization of this behavioral regularity.Free Riding, Cooperation, Strong Reciprocity, Public Goods Game, Evolutionary Game Theory