Davide Dragone

Thinness and obesity: A model of food consumption, health concerns, and social pressure ☆

The increasing concern of the policy maker about eating behaviour has focused on the spread of obesity and on the evidence of people dieting despite being underweight. As the latter behaviour is often attributed to the social pressure to be thin, some governments have already taken actions to ban ultra-thin ideals and models. This paper proposes a theoretical framework to assess whether increasing the ideal body weight is socially desirable, both from a welfare and a health point of view. We first show that being underweight and being overweight are possible outcomes of a rational eating model. Then, assuming that people are heterogeneous in their healthy weights but exposed to the same ideal body weight, we show that increasing the thin ideal weight can be welfare improving, but may exacerbate the obesity epidemic.

A Rational Eating Model of Binges, Diets and Obesity

This paper addresses the rapid diffusion of obesity and the existence of different individual patterns of food consumption between non-dieters and chronic dieters. I propose a rational eating model where a forward-looking agent optimizes the intertemporal satisfaction from eating, taking into account the cost of changing consumption habits and the negative health consequences of having a non-optimal body weight. Consistent with the evidence, I show that the intertemporal maximization problem leads to a condition of overweightness, and that heterogeneity in the individual relevance of habits in consumption can determine the observed differences in the individual intertemporal patterns of food consumption and body weight. Sufficient conditions for determining when the convergence to the steady state implies oscillations or is monotonic are given. In the former case, the agent optimally alternates diets and binges until the steady state is reached, in the latter a regular intertemporal pattern of food consumption is optimal.

The Demand for Cigarettes as Derived from the Demand for Weight Loss: A Theoretical and Empirical Investigation

This paper offers an economic model of smoking and body weight and provides new empirical evidence on the extent to which the demand for cigarettes is derived from the demand for weight loss. In the model, smoking causes weight loss in addition to having direct utility benefits and direct health consequences. It predicts that some individuals smoke for weight loss and that the practice is more common among those who consider themselves overweight and those who experience greater disutility from excess weight. We test these hypotheses using nationally representative data in which adolescents are directly asked whether they smoke to control their weight. We find that, among teenagers who smoke frequently, 46% of girls and 30% of boys are smoking in part to control their weight. As predicted by the model, this practice is significantly more common among those who describe themselves as too fat and among groups that tend to experience greater disutility from obesity. We conclude by discussing the implications of these findings for tax policy; specifically, the demand for cigarettes is less price elastic among those who smoke for weight loss, all else being equal. Public health efforts to reduce smoking initiation and encourage cessation may wish to design campaigns to alter the derived nature of cigarette demand, especially among adolescent girls.

Hamiltonian potential functions for differential games

We introduce the concept of Hamiltonian potential functions for noncooperative open-loop differential games and we characterise sufficient conditions for their existence. We identify a class of games admitting a Hamiltonian potential and illustrate the related properties of their dynamic structure. Then, we offer a preliminary exploration of the construction of potential functions for feedback games. As an illustration, we consider an asymmetric oligopoly game with process innovation.

Static and dynamic best-response potential functions for the non-linear Cournot game

We show that the Cournot oligopoly game with non-linear market demand can be reformulated as a best-response potential game where the best-response potential function is linear-quadratic in the special case where marginal cost is normalized to zero. We also propose a new approach to show that the open-loop differential game with Ramsey dynamics admits a best-response Hamiltonian potential corresponding to the sum of the best-response potential function of the static game plus the scalar product of transition functions multiplied by the fictitious costate variables. Unlike the original differential game, its best-response representation yields the map of the instantaneous best reply functions.

The Incentive to Invest in Environmental-Friendly Technologies: Dynamics Makes a Difference

The established view on oligopolistic competition with environmental externalities has it that, since firms neglect the external effect, their incentive to invest in R&D for pollution abatement is nil unless they are subject to some form of environmental taxation. We take a dynamic approach to this issue, using a simple differential game to show that the conclusion reached by the static literature is not robust, as the introduction of dynamics shows that firms do invest in R&D for environmental-friendly technologies throughout the game. Moreover, our setup also illustrates the existence of multiple equilibria, only one of which is identified by the corresponding static game.

Regulating Environmental Externalities Through Public Firms: A Differential Game

We investigate the possibility of using public firms to regulate polluting emissions in a Cournot oligopoly where production takes place at constant returns to scale and entails a negative environmental externality. We model the problem as a differential game and investigate (i) the Cournot-Nash game among profit-seeking firms; (ii) the Markov Perfect Nash equilibrium under social planning, where the industry output is entirely controlled by a benevolent planner aiming at the maximisation of social welfare; and (iii) the Markov Perfect Nash equilibrium in a mixed setup where at least one firm is public, while the others remain profit-seeking agents. Our analysis identifies the conditions whereby having a mixed market as a regulatory instrument suffices to drive the industry to the same output, externality and social welfare as under planning, both along the optimal path and in steady state.

Tobacco Taxes and Smoking Bans Impact Differently on Obesity and Eating Habits

Policy interventions aimed at affecting a specific behavior may also indirectly affect individual choices in other domains. In this paper we study the direct effect of tobacco excise taxes and smoking bans on smoking behavior, and the indirect effect on eating behavior and body weight. Using very detailed clinical data on individual health, smoking, and dietary habits, we show that antismoking policies are effective in reducing smoking, but their consequences on eating behavior dramatically depend on the specific implemented policy. Increasing excise taxes on tobacco decreases body weight and caloric intake, and it improves the quality of eaten food. Smoking bans, instead, do not significantly affect body weight, although they impact on the diet composition. Smoking bans in restaurants induce a significant rise in the quality of food and in daily caloric intake. Conversely, smoking bans in bars negatively affect the quality of the daily diet, as individuals eat more fats and less fibers, and drink more alcohol and caffeine.

Obesity and smoking: can we catch two birds with one tax?

The debate on tobacco taxes and fat taxes often treats smoking and eating as independent behaviors. However, since there exists medical and sociological evidence about the interdependence between eating and smoking choices, antismoking policies may also affect the obesity prevalence and fat taxes could influence smoking behavior. We address this issue from a theoretical standpoint and propose a dynamic rational model where eating and smoking are simultaneous choices that jointly affect body weight and addiction to smoking. Focusing on direct and cross price effects, we compare tobacco taxes and fat taxes and we show that a single policy tool can reduce both smoking and body weight. In particular, fat taxes can be more effective than tobacco taxes at simultaneously fighting obesity and smoking.

The Leitmann-Schmitendorf advertising game with n players and time discounting

Abstract The extension of the Leitmann–Schmitendorf advertising game to n players and positive time discounting is investigated. We show that the strong time consistency of the open-loop Nash equilibrium is preserved. As to optimal controls, while the boundary solution is unaffected by the number of firms as well as discounting, the inner solution depends on industry structure. The fully symmetric version of the game allows us to identify the parameter regions wherein both solutions are sustainable.