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Abstract

We devise a theoretical model to shed light on the dynamics leading to the so called toxic relationships. We want to investigate what policy interventions people could advocate to protect themselves and to reduce suffocant assuefaction so to escape to the trap of physical or psychological abuses either in family or at work. By assuming that the toxic partner's behavior is exogenous and that the main source of addiction is income or wealth, and solving a dynamical system of differential equations we find that an asympotically stable equilibrium with positive love is always possibile for enough high level of appealing unless subsides to reduces assuefaction are introduced. Also the existence of a third unconditionally reciprocating part as a benckmark (which represent not only the real presence of another partner but also the support from family, friends and overall private organizations in helping victims of domestic abuses or private organizations that offer economic and psychological support as well as legal counseling to victims of bullying at workplace and placement offices which e ectively help to find soon another job) plays an important role in reducing the toxic partner's appealing. By solving our model we outline the condition for a best mixed policy where both monetary subsides and offering alternatives are at work.
MPRA
Munich Personal RePEc Archive
Human networks and toxic relationships
Nazaria Solferino and M.Elisabetta Tessitore
University or Calabria-Unical, University of Tor Vergata in Rome
30 July 2019
Online at https://mpra.ub.uni-muenchen.de/95756/
MPRA Paper No. 95756, posted UNSPECIFIED
Human networks and toxic relationships
August 28, 2019
Abstract
We devise a theoretical model to shed light on the dynamics leading to the so
called toxic relationships. We want to investigate what policy interventions people
could advocate to protect themselves and to reduce suffocant assuefaction so to escape
to the trap of physical or psychological abuses either in family or at work. By assuming
that the toxic partner’s behavior is exogenous and that the main source of addiction is
income or wealth, and solving a dynamical system of differential equations we find that
an asympotically stable equilibrium with positive love is always possibile for enough
high level of appealing unless subsides to reduces assuefaction are introduced. Also
the existence of a third unconditionally reciprocating part as a benckmark (which
represent not only the real presence of another partner but also the support from
family, friends and overall private organizations in helping victims of domestic abuses
or private organizations that offer economic and psychological support as well as legal
counseling to victims of bullying at workplace and placement offices which e ectively
help to find soon another job) plays an important role in reducing the toxic partner’s
appealing. By solving our model we outline the condition for a best mixed policy where
both monetary subsides and offering alternatives are at work.
Keywords: Dynamical systems, stability, economics, relationships, networks
JEL Classification Numbers: C62, D11, D91
1 Introduction
Economics is a social science which analyzes the behavior of firms that maximize their
profit and individuals who maximize their utility measured as happiness within the context
of society. Therefore many interactions that are not traditionally considered economic are
often investigated. A very particular recently developed branch of economics literature
is the Economics of Love focused on the household’s well-being, marriage and long-term
relationships alongside to their effects on the economic growth (for an exhaustive survey on
this literature see Browning et al, 2014; Grossbard,2015).
The first pioneristic work in this new field of Economics appeared in the early 1970s
with the theory of marriage by Becker (1973), according to which each individual wants to
find a partner with whom they will maximise their own well-being. The equilibrium in this
marriage market is reached when no person can change her partner or become single and at
the same time to experience an higher well being (referred to the consumption of household
commodities). Beckerś empirical analysis shows that the gain from marriage is positively
dependant on income, relative difference in their wage rates, and the level of intangible
variables such as education and beauty. Moreover, individuals choose partners with similar
traits such as height, race, social background, etc. By including among the factors which can
affect marriages also love (defined as a situation where the utility of one individual depends
on the commodity consumption of their partner as well as their own), Becker (1974) finds
that it raises the likelihood of two people marrying because their well being is likely to be
higher.
After this pioneristic works, many other analyses have been mainly focused on to increase
our understanding of how households operate. Outcomes of interest concern consumption,
savings, labor supply and other uses of time, household formation and dissolution, demand
for health and other forms of human capital, fertility and children outcomes, demand for
environmental quality, migration, and household produced goods(, or a detailed survey are
Browning et al, 2014 and Grossbard, 2015.
Many papers also investigate the determinants of long-lasting relationships and their
effects on economics development. Among them, Brines and Joyner (1999) conducted an
empirical study on the stability of marriage and cohabiting couples in the United States.
They have found that inequality in employment and income among the cohabiting couple
increase the chances of separation, although the effect is not symmetric because inequality
has a larger impact when the female partner earns more than the male partner. Grossbard
(2015) studies family as a complex decision unit where partners with potentially different
objectives make decisions about consumption, work and fertility. Couples marry and divorce
partly based on their ability to coordinate these activities.
More recently Johnson et al.(2018) applied a unique longitudinal approach to study
the long-term outcomes of relationships among 3,405 couple pairs. This report’s main
questions concerned predictors of relationship longevity, from measures of conflict frequency,
types of behaviors experienced during times of conflict, satisfaction with the relationship,
and whether partners believed their relationships would last or not. The German study’s
findings show most importantly that complacency is perhaps the most significant trap to
avoid. Working to avoid falling into that same-old same- old routine, and your relationship
can be vital and fulfilling for years to come. While there is a certain number of studies
on marriage and cohabiting couples, on our knowledge there are only few papers which
theoretically study the economic dynamics of romance.
Rinaldi (1998) proposed a mathematical model based on a linear dynamical system where
three aspects of love dynamics are taken into account: the forgetting process (oblivion), the
pleasure of being loved (return), and the reaction to the appeal of the partner (instinct).
The results of the model show that the system turns out to be positive if the appeals of the
two individuals are positive. Sprott J.C. (2001), in his paper presented to the Chaos and
Complex system seminar in Madison, extends those results and discusses various models of
love and happiness, like the model of romance between Romeo and Juliet and that about
triangular relationship to analyse how a third part affects the stability of a relationship.
Wauer et.al (2007) study human romantic relationships via system dynamics methodology
where a non-linear modeling is proposed and analyzed, showing that there are short- and
long-termed fluctuations of personal feelings due to, for instance, biological cycles and vary-
2
ing stresses from the daily job. The variability is expected to be more limited for couples
of cautious individuals. In Regan (2008) individuals behave in order to optimize their net
benefit from a given relationship. The desire to maximize their rewards and minimize their
costs, where both change over time, and the inequity of the benefits to contributions among
the individuals in a relationship will cause unhappiness. This clearly also depends on the
role of expectations (Thibaut and Kelly, 1959) and on the level of investment that is given to
the relationship. This commitment then determines whether or not the relationship will be
maintained (Rusbult,1983). Satsangi and Shimano(2012) add to the initial model of Rinaldi
(1998) a crossed interactions among partners to analyse the effects and sinergies of learning
and adaptation from living toghether. According to the results of this model the system
is asymptotically stable if the ratio of appeals is greater than the reciprocal of the ratio of
mutual intensiveness coefficient.
In this paper we aim to give an additional contribution to the literature in Economics of
Love by devising a slightly modified version of the model in Rinaldi (1998) to shed light on
the dynamics leading to the so called toxic relationships. We also want to investigate what
policy interventions people could advocate to protect themselves and to reduce suffocant
assuefaction so to escape to the trap of physical or psychological abuses either in family or
at work. The dynamics of couples’ relationships are analyzed through a system of differential
equations representing the laws of motions of the amount of love that two individuals put
in a relationship which also depends on any source of partner’s appeal (financial, physical,
intellectual,coparenthood,etc.). This appeal in our work is assumed to change over time
proportionally both to the effect of the other partner’s love and to a variable representing
the main source of addiction (for instance, wealth,status,physical appearence,etc). The aim
of our analysis is to build a model that takes into account the case where toxic relationships
are at work, that is,when a partner can decide to stay in a relationship despite the low or
null love from the other, just because of the partner’s appealing that makes more difficult to
split. Therefore we focus on situations where love is transformed in a negative dependance
and the relationship produces the same effect like a drogue generating dangerous addiction.
By toxic relationship we mean a relationship disorder which can have many forms but all
are characterized by a disparity, a non-egalitarian situation in which one of the two subjects
depends on the other, triggering a mechanism of dominance and subjection. One puts in
the relationship much more affect than the other, whose contribution can even be zero.
Unlike a healthy relationship where we can still cut out our spaces, maintaining a capacity
for self-determination, benefit from reciprocity, in a toxic relationship instead the emotional
dependance enters into play that makes the partner our exclusive interlocutor, so that being
happy and enthusiastic depends exclusively on the other, just like in drug addiction. In
order to avoid the abandonment and the consequent lack of affection, the addicted-partner
cancels himself, while the counterpart, who probably has the idea of a relationship in which
love is obtained by putting aside one’s ego, exploits the relationship only to feel admired
and to exercise control. This type of relationship implies psychological violence but it can
be also physical and it can develop in tragic episodes of murders mainly against women.
Another unfortunately typical example of toxic relationship is that of bullying at a
workplace, that probably happens even more when the person engaged in mobbing is the
boss, and the silence of victims and spectators end up to favor it. The reason for this
3
behavior is obviously the fear of being involved, having retaliation of some kind or even
losing the job.
In our work we highlight the conditions for the possibility that a poisoning tight arises
and pushes for long-term relationships, relatively stable, caused by addiction. Due to the
assuefaction, the partner’s behavior still seems appealing regardless his low reciprocating
affection. In Section 2 we give an analytical definition of a toxic relationship by solving
an intertemporal dynamic model, where the toxic partner’s behaviour is assumed to be
exogenous. By assuming that the main source of addiction is income or wealth, we find that
an asympotically stable equilibrium with positive love is always possibile for enough high
level of appealing unless subsides to reduces assuefaction are introduced. In Section 3 we
compare two alternative policies that can be adopted to heal from addiction either trough a
subside that can reduce the partner’s appeal and then we introduce a third unconditionally
reciprocating part as a benckmark which represents an alternative, but less attractive, to
the partner’s love, but who plays an important role in reducing the toxic partnerś appealing.
It substantially mimics not only the real presence of another partner but also the support
from family, friends and overall private organizations in helping victims of domestic abuses
to recover their full life. It may also represent private organizations that offer economic and
psychological support as well as legal counseling to victims of bullying at workplace and
placement offices which effectively help to find soon another job. By solving our model we
outline the condition for a best mixed policy where both monetary subsides and offering
alternatives are at work. Section 4 contains our Discussions.
2 Basic Model of a toxic relationship
In this Section we devise a slightely modified version of the model by [9] where the level of
love an individual puts in a relationship varies over the time depending either on oblivion
and the partner’s love but also on her appealing which on turn follows a specific law of
motion. We assume for simplicity that the partner’s appealing decreases at the same rate of
love (i.e. the oblivion’s rate is the same) and decreases as higher it is the difference between
the amount of love he puts in the relationship and that of partner, in each period of time.
We also assume that it depends on a constant factor of appealing like income, personality,
physical appareance, etc.
If we denote by 1,2the submitted and the toxic partner respectely, so that 0< x2< x1,
therefore we have to study the stability of the following system of dynamic equations:
˙x1(t) = αx1(t) + βx2+γ1A1(t)
˙
A1(t) = αA1(t) + k(x1(t)x2) + M2
(1)
where
i) x1(t)is the love,which consists of both passion and intimacy as wellbas monetary support,
individual one has for the partner at time t.
ii) x2is the love the partner puts in the relationship and that we assume, in this first
simplified version of the model, is an exogenous variable of the system and remains
constant over time.
4
iii) A1(t)is the appeal factor. It is a subjective variable, and is dependent on the perception
of the partner at time t.
iv) M2measures the source of partner’s appealing that for simplicity we assume is constant
over time.
v) αrefers to the forgetting coefficient and measures how quickly the state of love will
decrease, exponentially, in the absence of the partner.
vi) βrefers to the response of each player’s love to their partner’s love level.
vii) kmeasures the sensitivity of an individual with respect to the excessive unreciprocated
love he gives to the partner.
viii) γ1refers to the response coefficients to the appeal of the other partner.
We assume that parameters α, β, k , γ1(0,1].
Definition 1. If there exists a minimum level of desiderered love ˆx2for individual 1 and
x2<ˆx2then the relationship between 1 and 2 is a toxic relationship.
The above Definition state a toxic relationship since individual 1 still loves 2 even if this
last doesn’t reciprocate (neither at the minimum possible level normally requested). This
happens because attraction is very high. We are going to investigate the conditions so that
system (1) has a steady state stable equilibria.
Proposition 2. Asssume 1< α < β and M2kx2, then state steady (x
1, A
1)
x
1=αβ 1
α21
x2+M2γ1
α21
A
1=α(M2kx2) + βkx2
α21
is an asympotically stable equilibrium for system (1).
Proof. Let Abe the coefficient matrix of the system
A=α γ1
kα.
since detA > 0and trA < 0the conclusion follows.
Remark that, even if x2= 0 the first individual still loves the second one since x
1=
M2γ1
α21
If individual 1 starts loving individual 2 at time t= 0, he will love 2 forever. This is true
also when x2is very low or equal to zero.
5
3 Healing
In this Section we look for conditions to help the submitted partner 1 to heal from toxicity
by reducing the toxic partner’s appeal 2 via a subsidy s > 0.
Definition 3. Individual 1 overcomes a toxic relationship, i.e. 1 is healed, if x
1= 0.
In system (1) we introduce the subsidy sin the dynamic of A1
˙x1(t) = αx1(t) + βx2+γ1A1(t)
˙
A1(t) = αA1(t) + k(x1(t)x2) + M2(1 s)(2)
Proposition 4. If kis taken such that
0< k < αβ
γ1
then the subsidy s
s=αβ 1
M2γ1
x2+ 1
is healing individual 1.
Proof. It is easy to see that in this case the steady state x
1sof system (2) is
x
1s=αβ 1
α21
x2+M2γ1(1 s)
α21
hence the result follows from the above assumpions.
Another way to heal might be the presence of a third person, denoted by 3, we want to
see if 1 can heal from the second partner. System (1) becomes
˙x1(t) = αx1(t) + β(x2x3) + γ1A1(t)
˙
A1(t) = αA1(t) + k(x1(t)x2+x3) + M2M3
(3)
where x3is the amount of love of individual 3 towards individual 1 and M3with M3< M2
is his appealing.
Proposition 5. If kis taken such that
0< k < αβ
γ1
and x3such that
x3=(M2M3)γ1
αβ 1
+x2
then 3 is healing individual 1.
6
Proof. It is enough to see that in this case the the steady state x
13of system (3) is
x
13=αβ 1
α21
(x2x3) + M2M3
α21
γ1
We remark that if in addition to the second partner 3 offering x3amount of love to
partner 1 there is also a subsidy s, then proceending as before
s=αβ 1
M2γ1
(x2x3)M3
M2
+ 1
is healing individual 1 since x
13sgiven by
x
13s=αβ 1
α21
(x2x3) + M2(1 s)M3
α21
γ1
is the steady state of system
˙x1(t) = αx1(t) + β(x2x3) + γ1A1(t)
˙
A1(t) = αA1(t) + k(x1(t)x2+x3) + M2(1 s)M3
(4)
4 Conclusions
A toxic relationship can be defined as a relationship characterized by behaviors of the toxic
partner that are emotionally and frequently physically damaging to the other. A healthy
relationship involves mutual caring, respect, compassion, a strong interest in the partner’s
happiness and in the couples both share control and decision-making. On the contrary, a
toxic relationship is characterized by insecurity, self-centeredness, dominance and control.
Anyway, when two individuals have a toxic relationship, we usually look at the behaviors
of the toxic partner, but we must look equally hard at the individual who is the recipient
of the toxic behavior. In fact, according to psychologists we should also investigate why an
adult stays in a relationship that will almost inevitably damage him or her emotionally or
physically. We think that this often happens because addiction may play a very important
role, implying that the partnerś appeal grows over time regardless to the amount of love the
other puts in that relationship.
Probably people with low self esteem are the most subjected to this kind of addiction
and often psychoterapy for couples is needed. In the worst cases when toxicity externate in
physical violence also more objective policy solutions are necessary. A typical case of violent
toxic behaviour is that of domestic abuses,which is a major issue in the US and around the
world, and many nonprofit organizations work tirelessly to provide critical support and
services to victims. Every year, more than 10 million men and women in the US are
subjected to Domestic Violence. Its impact can be felt far and wide. More than 1 in 3
women (35.6%) and more than 1 in 4 men (28.5%) in the U.S. report having experienced
rape, physical violence, and/or stalking by an intimate partner in their lifetime.
Another example of a toxic relationship, unfortunately very widespread, is that of bully-
ing at the workplace, where too often abuse and harassment are considered normal events,
7
so that the workers who suffer them prefer to be silent. This happens especially when
their work is precarious, whose duration and conditions depend on the discretion of the
employer. Istat data for Italy tell us that 9 out of 100 women during their working life have
been subjected to harassment or blackmail with a sexual background at work (1 million 403
thousand), but that only 20% talk about it with someone (usually office colleagues) and
only 0.7% complaint, for fear of retaliation, shame, or for a distorted sense of guilt, slander.
The damages are not only for the worker but also for the company, in terms of lower pro-
ductivity, increased risk of accidents and conflict. The inevitable repercussions then fall on
the health service (treatments, drugs) and on the social security system (illnesses, injuries,
etc.).
In this paper we aimed to approach to these issues from a theoretical point of view
with the purpose to devise an analytical model which can be used to highlight the main
points of this problem and investigate useful policy solutions. To this purpose we used the
model of Rinaldi (1998) where we add the possibility that the toxic partner’s appealing
evolve dynamically according to a specific law of motion. In our model we assume that this
law depends on oblivion as well as on the excess of love with respect to the partner and
a constant variable measuring the values of the source of addiction(for instance income or
wealth,etc.). Our model shows that in the most simple case where the partner’s behaviour
is given(exogenous) and hopelessly toxic, an asympotically stable equilibrium, with a sub-
mitted partner always in love even when not enough reciprocated, is always possibile for
high values of the addiction.
Neverthless an opportune measure of correction based on subsides can be introduced.
On the otherwise side, the lackness of low levels of government help is often one of the main
reasons for the low levels of immediately reported domestic abuses. For instance, in Italy
According to GROVIO( Group of Experts on Action against Violence against Women and
Domestic Violence and EstremeConseguences) of the European Council about 80% of abuse
happens at home and there not enough dormitory to host other 5000 women who have left
their house to escape from abusive partners. Public funds are not entire and a fairly used
to this purpose,only 0,02% of the available sources have been spent to support victims and
create structures to host them. Similmente to reduce dependence on boss or coworkers and
can incentivize the victim to denounce are specific laws, penalties and high compensation
for the monetary damage but also the bological and moral one, union organizations offering
cheap or free legal or help, support for finding other jobs and reintegration,etc.
To take into account this problem, we look for an alternative policy and study how the
results of our theorethical model change when an alternative third part enters the game by
competing with the toxic partner for the love of the submitted one. In this case lower or
zero subsides can be necessary as it works like a substitute to decrease the toxic dependance.
Anyway a mix of policy intervention based both in subsides and help from third part can
be realized. Therefore when a policy based only on subsides is not always sufficient other
factors can be at work to rescue from toxicity.
Into reality, often subsides are not enough high or people need also to preserve their
dignity,security,counseling,etc. and don’t want to live with free lunches all the time. In
our model for instance a high source of addiction may come from also by a very low self
esteem which can instead be raised given victims other opportunities like alternative jobs or
8
legal/counseling support. This is why on pur opinion the best solutions relies on a mix of
policies where not only the government helps with subsides but also private organizations
can offer support to the victims of abuse as well placement offices can help in finding new
jobs.
An alternative,very interesting policy solution, under this points view, for instance, is
that of the Italian government to support poor people, living under the level or substanibility
according to the Eurostat definition, or suffering from structural unemployement. This
policy implies both a granteed small income of citizenship, to subside the consumption of
the minimal necessary goods, as well as a crew of experts who help them for free with the
job search so they can find a stable position in the long run and subsides are not necessary
anymore.
With this work we aimed to give a contribution to the literature on Economics of Love
and in particular we hope to incentive more theoretical and empirical studies on relationships
which can be harmful and devise better policy solutions. In particular we think that a mix
of policies, directly or indirectly created to fight this phenomenon, like the Italian policy
about the income of citizenship(whose effects on that could be tested empirically only in
few years) based on monetary help and supportive institutions and organizations could be
very effective.
References
[1] Becker, G. S. (1973). A theory of marriage: Part i, The Journal of Political Economy,
pages 813-846.
[2] Becker, G. S. (1974). A theory of marriage. In Economics of the family: Marriage,
children, and human capital, pages 299-351. University of Chicago Press.
[3] Brines, J. and Joyner, K. (1999), The ties that bind: principles of cohesion in cohabi-
tation and marriage, American Sociological Review, pp 333-355.
[4] Browning M., Chiappori P.A., Weiss Y., Economics od the Family, Cambridge Univer-
sity Press, 2014.
[5] De Vogli R., Chandola T., Marmot M. G., (2007), Negative Aspects of Close Relation-
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[7] Shoshana Grossbard (2015), The Economics of Marriage,The International Library of
Critical Writings in Economics series, San Diego State University.
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9
[10] Rusbult, C. E. (1983), A longitudinal test of the investment model: The development
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[11] Satsangi A., Sinha K.(2012), Dynamics of Love and Happiness: A Mathematical Anal-
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[13] Thibaut, J. W. and Kelley, H. H. (1959), The social psychology of groups.
[14] J. Wauer, D. Schwarzer, G.Q. Cai, Y.K. Lin, Dynamical models of love with time-
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10
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Used a longitudinal study of heterosexual dating relationships to test investment model predictions regarding the process by which satisfaction and commitment develop (or deteriorate) over time. Initially, 17 male and 17 female undergraduates, each of whom was involved in a heterosexual relationship of 0-8 wks duration, participated. Four Ss dropped out, and 10 Ss' relationships ended. Questionnaires were completed by Ss every 17 days. Increases over time in rewards led to corresponding increases in satisfaction, whereas variations in costs did not significantly affect satisfaction. Commitment increased because of increases in satisfaction, declines in the quality of available alternatives, and increases in investment size. Greater rewards also promoted increases in commitment to maintain relationships, whereas changes in costs generally had no impact on commitment. For stayers, rewards increased, costs rose slightly, satisfaction grew, alternative quality declined, investment size increased, and commitment grew; for leavers the reverse occurred. Ss whose partners ended their relationships evidenced entrapment: They showed relatively low increases in satisfaction, but their alternatives declined in quality and they continued to invest heavily in their relationships. (39 ref) (PsycINFO Database Record (c) 2006 APA, all rights reserved).
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“The Mating Game is a comprehensive, multidisciplinary, introductory text about human mating relationships aimed specifically at a university audience. It progresses beyond a psychological or biological/physiological stance and encompasses a wide array of disciplines. The comprehensive review and up-to-date information contained in The Mating Game not only provides answers to questions about important life events but also encourages readers' interest in the field of interpersonal relationships and human mating. — The Mating Game: A Primer on Love, Sex, and Marriage, Second Edition, is the only comprehensive, multidisciplinary, introductory text about human mating relationships aimed specifically at a university audience. It progresses beyond a psychological or biological/physiological stance and encompasses a wide array of disciplines. This comprehensive review of theory and empirical research takes an integrated perspective on the fundamental human experiences of love and sex. Strongly grounded in methodology and research design, author Pamela C. Regan offers relevant examples and anecdotes along with ample pedagogy that will spark debate and discussion on these provocative and complex topics. New to the Second Edition Freshly presented material, with reorganized text that provides a smoother transition between major sections; Reviews of the most recent theoretical and empirical work in the areas of love, sexuality, mate selection, and marriage; New information on the phenomenon of “cyber-flirting” and the development of romantic relationships over the Internet; Inclusion of cutting-edge biochemistry research, including a discussion of cutting-edge research on the biochemistry of passion and affection; Discussion of emerging research on non-heterosexual relationships and cross-cultural dynamics; Expanded chapters on critical topics and an important new chapter on relationship intervention Intended AudienceThis text is ideal for upper level undergraduate or graduate students in psychology, family studies, and sociology, who will find this engaging text a valuable tool for course-related research activities, as well as for self-awareness.
Article
A vast literature addresses the correlates of marital stability, but little is known about what unites cohabiting partners over time. Although a specialized division of labor might increase the benefits of marriage and strengthen ties between husband and wife, transactional considerations make specialization unattractive for cohabitors. Drawing from work on the emergence of commitment, we argue that cohabitors are more likely to remain together under conditions of equality. Using data from the Panel Study of Income Dynamics, we test these ideas by modeling the stability of married and long-term cohabiting unions in the United States. We find that married couples who adopt a more specialized division of labor are less likely to divorce, but the effect is modest. Among cohabitors, partners whose employment and earnings are increasingly similar face sharply reduced risks of breaking up, but the effect is asymmetric: Inequality is more disruptive when the female cohabitor earns more than her partner.
Article
Human romantic relationships are studied via system dynamics methodology. Starting point is a time-invariant linear model of two individuals without interaction with environment. Specifically, time-dependent fluctuations both in the source terms and the system parameters are introduced and examined in their consequences where also more realistic nonlinear modeling is proposed and analyzed.
The Economics of Marriage,The International Library of Critical Writings in Economics series
  • Shoshana Grossbard
Shoshana Grossbard (2015), The Economics of Marriage,The International Library of Critical Writings in Economics series, San Diego State University.