In this paper, I propose an economic theory of anorexia nervosa (henceforth anorexia) and its impact on health and longevity. Anorexia is a severe and potentially life-threatening eating disorder, which affects about 0.1 percent of the U.S. population, with similar prevalence rates in other Western countries (GBD, 2016). In order to be diagnosed with anorexia, a person must meet the following DSM-5 criteria: (i) restriction of energy intake leading to significantly low body weight (ii) intense fear of gaining weight or becoming fat, (iii) distorted body image perception, i.e. perceiving oneself as too fat when being underweight (APA, 2013). A significantly low body weight is commonly conceptualized as 15% or more below the expected weight for one’s age, gender, and height and expressed in a body mass index (bmi) below 17.5 kg/m2. In the brain, anorexia is associated with increased activity of the nucleus accumbens, a region of the ventral striatum that controls reward and motivation. The cause of the disease is basically unknown and treatment remains ineffective for most patients (Nestler, 2013). But long-term studies also showed that more than 50 percent of individuals diagnosed with anorexia recover from the disease with advancing age (Zipfel et al., 2000, Dobrescu et al., 2020). It has been estimated that more than half the risk of developing anorexia is due to genetic factors (Bulik et al., 2000). Anorexia is about ten times more prevalent among women than men. Other risk factors are being an adolescent, having an obsessional style, and the exposure to thin peers and role models.

Anorexia exhibits the highest mortality rate of any psychiatric illness. Up to 10 percent of anorexia patients are estimated to die from suicide (Pompili et al., 2006). Here, I focus on the long-run consequences that are caused by the inadequate supply of energy and nutrients and lead to faster health deficit accumulation, frail bodies, and premature death by ‘natural causes’ such as cardiac diseases and organ failure. Among the long-term effects of anorexia are osteoporosis, cardiovascular disturbances, diabetes mellitus, thyroid disorders, and gastrointestinal disorders. About 80 percent of anorexic patients have cardiac complications, and most sudden cardiac death in anorexic patients is due to abnormal heartbeat (Meczekalski et al., 2013, Casiero and Frishman, 2006). The mortality rate for all causes of death is estimated to be up to six times higher than that of the general population (Meczekalski et al., 2013, Arcelus et al., 2011).1

It has been shown that the trait of high self-control is predictive for restrained eating, exercise and weight loss (Crescioni et al., 2011, Cobb-Clark et al., 2014, Stutzer and Meier, 2016). Since anorexia patients are particularly “successful” in weight loss, it has been argued that individuals with anorexia are characterized by high levels of self-control (Fairburn et al., 1999, Steinglass et al., 2012, Butler and Montgomery, 2005).2 Walsh (2013) argues that anorexia is initiated in young women by initial successes in weight control, which then ‘takes on a life of its own and evolves into an unrelenting pursuit that becomes the individual’s primary focus.’ Reinforcement mechanisms make restrained eating and exercise a habit and anchored in neural mechanisms that underlie the formation and persistence of habits. This way, anorexia resembles the neural mechanisms underlying addiction to substance abuse.

The similarity of anorexia to addiction and substance dependence has been highlighted in a series of studies (e.g. (Barbarich-Marsteller et al., 2011, Kaye et al., 2013, Godier and Park, 2014, Godier and Park, 2015, Compan et al., 2015)). The onset of anorexia, characterized by an initial success in weight loss is experienced as rewarding and pleasurable (resembling the initial phase of an addiction). The positive experiences motivate anorexic individuals to continue setting increasingly more ambitious weight goals (resembling the tolerance effect in addiction). As the disease continues, individuals find it increasingly more difficult to give up restrained eating and to return to healthy behavior and healthy body weight (resembling the withdrawal effect in addictions). The initially positive feelings associated with weight loss, however, cannot be maintained and are replaced by negative feelings associated with not being able to reach the increasingly ambitious target weight. The target weight adjustment implies that, despite increasing emaciation, individuals perceive themselves as to fat (distorted body image) such that the relentless pursuit of weight loss turns into a joyless and painful activity. It is thus understandable that anorexia patients perceive their behavior as an illness and want to be cured from the disease (resembling substance addicts).

In the health-economic theory of anorexia proposed below, I take these features into account. I set up a life cycle model of endogenous health deficit accumulation (based on Dalgaard and Strulik, 2014) in which individuals consume food and non-food goods and invest in their health and exercise. Body size increases with food consumption and declines with exercise. Deviations from a healthy bmi accelerate the speed of health deficits accumulation and, at any age, survival depends on the level of health deficits. While eating behavior and exercise have previously been studied in the obesity-related health deficit model (Strulik, 2019), here I extend the model to include the following features. Individuals derive positive or negative utility from body image, depending on the relative deviation of actual bmi from target bmi. Target bmi may deviate from the healthy bmi because it is socially constructed. In non-anorexic individuals target bmi is constant or changes only occasionally and exogenously. Anorexia is characterized by a habituation process (addiction) that leads to a continuous reduction of target bmi. It is initiated by weight loss successes in individuals who are (genetically) susceptible to target weight updating and for whom body image is an important factor of experienced utility, a feature which implies a high level of self-control in terms of body weight. Individuals are assumed to be perfectly rational except for the fact that they cannot plan their target weight updating. I model this as an imperfectly controlled addiction as proposed in Strulik, 2018, Strulik, 2021. Anorexia is conceptualized as a disease because addiction is unplanned and involuntary. This feature deviates from the standard economic theory of rational addiction built on Becker and Murphy (1988) where addiction is an optimally planned process and therefore cannot be understood as a disease.

While there exists a rich economic literature on overweight and obesity, relatively little attention has been paid to the phenomenon of underweight. The paper is broadly related to theories of rational eating (e.g. (Levy, 2002, Levy, 2009, Caputo and Dragone, 2022)). In this literature, individuals achieve their individually optimal weight (which may be unhealthy). The feature that actual weight maximizes utility makes it difficult to understand severe underweight as a pathological condition. Here, in contrast, anorexia is explained by an element of bounded rationality in form of unplanned addiction such that anorexic individuals, according to their own preferences, would be better off without the disease. Moreover, theories of rational eating usually exhibit one or more steady states of constant, weight-influenced survival probability. Therefore, in contrast to the present model, they cannot be conceptualized as life-cycle models of human aging, since aging is a non-steady-state phenomenon of continuously deteriorating health and declining probability of survival (e.g. (Arking, 2006, Gavrilov and Gavrilova, 1991)). The cited theories of rational eating also focus on food consumption and ignore alternative uses of income.

A couple of economic studies have addressed the problem of unhealthy underweight. Ham et al. (2013) show that bulimia nervosa is to a large extent driven by path dependence and argue that it shares many characteristics with common addictions (substance abuse). Costa-Font and Jofre-Bonet (2013) show that European women are more likely to be anorexic when they are exposed to low peer-group bmi. Arduini et al. (2019) show that eating disorders (purging) of female adolescents are influenced by peers’ body size through interpersonal comparisons. Dragone and Savorelli (2011) develop a theory of body size evolution where food consumption causes utility, deviations from healthy body weight as well as deviations from socially desirable weight cause utility losses, and eating increases body weight. They show that one of several steady states to which rational individuals converge is characterized by underweight and underconsumption of food. In a society in which individuals are heterogenous with respect to healthy weight and face the same exogenously determined desirable weight, a higher desirable weight reduces the prevalence of unhealthy thinness but may exacerbate the prevalence of obesity. Goldfarb et al. (2009) propose a static model of anorexia as a utility maximizing choice. Since individuals ‘choose to become anorexic’ (p. 13), severe underweight is explained by ‘wrong preferences’ such that, for given preferences, anorexic individuals would not seek and benefit from treatment. In the present study, in contrast, anorexia is initiated by a rational choice to lose weight, which then starts an addiction-like compulsive eating behavior that is not under control of the otherwise fully rational individual. Anorexia is conceptualized as an illness such that, for given preferences, individuals suffering from anorexia benefit from treatment. The static model of Goldfarb et al. (2009) differs also fundamentally from the current life-cycle approach in that it does neither consider the consequence of being underweight on health deficit accumulation and longevity nor the possibility of spending income on purposes other than food consumption.

Other studies focussed on the social determination of body image. Strulik (2014) proposed a theory in which social approval of physical appearance is endogenous and shows how this feature explains the obesity epidemic. The theory focuses on obesity but also takes into account the overall distribution of body weight in society. Further developments of this approach were presented by Mathieu-Bolh (2020) and Mathieu-Bolh and Wendner (2020). Acknowledging the importance of social determination of body image, the present paper applies Occam’s razor and takes social influence as exogenous in order to focus on anorexia as a pathological condition that develops as an uncontrolled addiction. The theory explains why in a group of otherwise similar individuals, exposed to the same socially determined ideal of thinness, anorexia as a health-threatening and potentially fatal illness occurs only in few individuals and why these individuals would be better off without the illness, not only in terms of health, but also in terms of lifetime utility.

The paper is organized as follows. In the next section, I set up the theoretical model, derive the implied dynamics for life cycle behavior, and obtain analytical solutions for optimal food consumption and optimal exercise. In Section 3, I calibrate a benchmark version of the model to an average 16-year-old American female such that predicted health behavior supports a bmi of 28.6 and a life expectancy at 20 of 61 years. An otherwise identical woman endowed with a greater importance of body image is predicted to achieve a bmi of 19 and a 3.2 years higher life expectancy. In Section 4, I show that if a high importance of body image occurs in conjunction with susceptibility to weight loss addiction, a process sets in such that target bmi decreases continuously and actual bmi reaches a trough at 15. The entailed acceleration of health deficits reduces life expectancy by about 15 years. I show how a mechanism of endogenous recovery explains why anorexia is primarily a disease of adolescents and young adults. With advancing age and accumulating health deficits, physical exercise becomes increasingly painful and the ambitious weight goals set in youth can no longer be met. If individuals respond by gradually upgrading their target bmi, a healthy weight is regained in middle age. I also use the model to evaluate two stylized therapies. I show that resetting the target weight has no long-run success since the mechanism of weight loss addiction remains operative and is re-triggered by subsequent weight loss. In contrast, a body image reset, can be effective in inducing a sustained return to healthy eating and exercise behaviors.

I then turn to a calibration for a young man and try to give an explanation of why the disease is much more common in women than in men. Finally, I consider the phenomenon of anorexia athletica. The paper was partly inspired by the fate of Bahne Rabe, a 2 meter tall German rower who won the Olympic gold medal with the eights in 1988 when he had a bmi of 23.7 and who died of a lung infection in 2001 shortly before his 38th birthday with a bmi of 14.6 (Kurbjuweit, 2001). I develop a variant of the model that shows how anorexia athletica can be triggered by an individual’s propensity to exercise excessively. Section 5 concludes the paper.