Mauro Sodini

Public Security vs. Private Self-Protection: Optimal Taxation and the Social Dynamics of Fear

In this paper, we develop a simple model of social dynamics governing the evolution of strategic self-protection choices of boundedly rational potential victims facing the threat of prospective offenders in a large population with random matching. We prove that individual (and socially transmitted) fear of exposure to criminal threats may actually condition choices even in the face of objective evidence of declining crime rates, and thereby cause the eventual selection of Pareto inefficient equilibria with self-protection. We also show that a suitable strategy of provision of public security financed through discriminatory taxation of self-protective expenses may actually overcome this problem, and drive the social dynamics toward the efficient no protection equilibrium. In our model, we do not obtain, as in Cressman et al. (1998), a crowding-out result such that the net impact of public spending on the actual social dynamics is neutral and the economy keeps on cycling between phases of high and low criminal activity with varying levels of self-protection; quite to the contrary, it can be extremely effective in implementing the social optimum, in that it acts primarily on the intangible dimension, that is, on the social dynamics of fear. We claim that this kind of result calls for more interdisciplinary research on the socio-psycho-economic determinants of fear of crime, and for consequent advances in modelling approaches and techniques.

Economic Growth, Technological Progress and Social Capital: The Inverted U Hypothesis

We set up a theoretical framework to analyse the role of economic growth and technological progress in the erosion of social capital. Under certain conditions on parameters, the relationship between technological progress and social capital can take the shape of an inverted U curve. Furthermore, we show the circumstances that allow the economy to follow trajectories where the stock of social capital grows endogenously and unboundedly.

Hopf Bifurcation in a Cobweb Model with Discrete Time Delays

We develop a cobweb model with discrete time delays that characterise the length of production cycle. We assume a market comprised of homogeneous producers that operate as adapters by taking the (expected) profit-maximising quantity as a target to adjust production and consumers with a marginal willingness to pay captured by an isoelastic demand. The dynamics of the economy is characterised by a one-dimensional delay differential equation. In this context, we show that (1) if the elasticity of market demand is sufficiently high, the steady-state equilibrium is locally asymptotically stable and (2) if the elasticity of market demand is sufficiently low, quasiperiodic oscillations emerge when the time lag (that represents the length of production cycle) is high enough.

Nonlinear dynamics in a Cournot duopoly with isoelastic demand

This paper analyses the dynamics of a nonlinear Cournot duopoly with general isoelastic demand (quasi-linear preferences) and quantity-setting firms that have incomplete information about the market demand. Unlike existing papers, we propose a model where the price elasticity of demand is different from one. This causes interesting local and global dynamic events that cannot be observed in the case of unit-elastic demand and homogeneous players. In particular, the global behaviour of the map is studied through the critical curves technique, and numerical simulations show coexistence of attractors, coordination failures and complex structures of the basins of attraction.

The Fragility of Social Capital

This paper addresses two hot topics of the contemporary debate, social capital and economic growth. Our theoretical analysis sheds light on decisive but so far neglected issues: how does social capital accumulate over time? Which is the relationship between social capital, technical progress and economic growth in the long run? The analysis shows that the economy may be attracted by alternative steady states, depending on the initial social capital endowments and cultural exogenous parameters representing the relevance of social interaction and trust in well-being and production. When material consumption and relational goods are substitutable, the choice to devote more and more time to private activities may lead the economy to a “social poverty trap”, where the cooling of human relations causes a progressive destruction of the entire stock of social capital. In this case, the relationship of social capital with technical progress is described by an inverted U-shaped curve. However, the possibility exists for the economy to follow a virtuous trajectory where the stock of social capital endogenously and unboundedly grows. Such result may follow from a range of particular conditions, under which the economy behaves as if there was no substitutability between relational activities and material consumption.

Economic Growth, Technological Progress and Social Capital: The Inverted U Hypothesis (pages 401–431)

We set up a theoretical framework to analyse the role of economic growth and technological progress in the erosion of social capital. Under certain conditions on parameters, the relationship between technological progress and social capital can take the shape of an inverted U curve. Furthermore, we show the circumstances that allow the economy to follow trajectories where the stock of social capital grows endogenously and unboundedly.

Bifurcations and Chaotic Attractors in an Overlapping Generations Model with Negative Environmental Externalities

We analyze an overlapping generations model with the following features. There exists a continuum of identical individuals whose welfare depends on leisure, on the stock E of a free access environmental good and on the consumption C of a private good. The private good is produced by a continuum of identical perfectly competitive firms via a constant returns technology (represented by a Cobb–Douglas production function); the representative firm uses physical capitalK and labour L of the representative individual as productive inputs. Each economic agent considers as negligible the negative impact of his choices on the environmental good; this implies that the choices of each agent generate negative externalities on the others.

Nonlinear Dynamics in a Cournot Duopoly with Different Attitudes towards Strategic Uncertainty

This paper analyses the dynamics of a duopoly with quantity-setting firms and different attitudes towards strategic uncertainty. By following the recent literature on decision making under uncertainty, where the Choquet expected utility theory is adopted to allow firms to plan their strategies, we investigate the effects of the interaction between pessimistic and optimistic firms on economic dynamics described by a two-dimensional map. In particular, the study of the local and global behaviour of the map is performed under three assumptions: (1) both firms have complete information on the market demand and adjust production over time depending on past behaviours (static expectations—“best reply” dynamics); (2) both firms have incomplete information and production is adjusted over time by following a mechanism based on marginal profits; and (3) one firm has incomplete information on the market demand and production decisions are based on the behaviour of marginal profits, and the rival has complete information on the market demand and static expectations. In cases 2 and 3 it is shown that complex dynamics and coexistence of attractors may arise. The analysis is carried forward through numerical simulations and the critical lines technique.

Equilibrium and Disequilibrium Dynamics in Cobweb Models with Time Delays

This paper aims to study price dynamics in two different continuous time cobweb models with delays close to [Hommes, 1994]. In both cases, the stationary equilibrium may be not representative of the long-term dynamics of the model, since it is possible to observe endogenous and persistent fluctuations (supercritical Hopf bifurcations) even if a deterministic context without external shocks is considered. In the model in which markets are in equilibrium every time, we show that the existence of time delays in the expectations formation mechanism may cause chaotic dynamics similar to those obtained in [Hommes, 1994] in a discrete time context. From a mathematical point of view, we apply the Poincare–Lindstedt perturbation method to study the local dynamic properties of the models. In addition, several numerical experiments are used to investigate global properties of the systems.

Local and global bifurcations in an economic growth model with endogenous labour supply and multiplicative external habits.

This paper analyses the mathematical properties of an economic growth model with overlapping generations, endogenous labour supply, and multiplicative external habits. The dynamics of the economy is characterised by a two-dimensional map describing the time evolution of capital and labour supply. We show that if the relative importance of external habits in the utility function is sufficiently high, multiple (determinate or indeterminate) fixed points and poverty traps can exist. In addition, periodic or quasiperiodic behaviour and/or coexistence of attractors may occur.