TENACITY OF SOCIAL NORMS: HOW ECONOMIC MODELS EXPLAIN
PERPETUATION OF GENDER-BASED DISCRIMINATION
Mavzuna Turaeva
May 2, 2015
ABSTRACT
This paper investigates how social norms emerge and can survive through millennia. I apply
Ramsey economic growth and overlapping generations models as a theoretical framework to
explain the tenacity of social norms and female-driven perpetuation of gender-based
discrimination in developing countries. I argue that, similar to any goods that are produced and
consumed, social norms that guide decision making of individuals can be thought of as an output
of a production process. Norms are “produced” through human practices and “reproduced” through
repetition that transcends generations, with the main factors of production being the collective
memory and dense networks. In the context of social norms “consumption” represents a range food
and non-food, norm-enforcing activities while “saving” is a range of norm-maintaining behavior.
The paper’s particular focus is norms that marginalize women with a special attention to the Queen
Bee Syndrome. Understanding the process of emergence and tenacity of gender oriented social
norms may provide insight into why many attempts to empower women in patriarchal societies
fail.
Introduction
North Sentinel Island located in the Bay of Bengal between India and Myanmar is famous for its
unique inhabitants. Sentineli islanders are one of the few known groups in the world who preserved
the life style of the humanity’s Stone Age ancestors. They sustain themselves through hunting and
gathering. “Known” is probably an overstatement when it comes to Sentinelese. They are the only
survived hunter-gatherer society which fervently resists contact with the outside world (The
Economist, 2007). Whatever is known about Sentinelese people is mostly inferred from what
scientists know about the hunter-gatherer societies at large.
One distinguishing feature of the pre-agrarian societies is their egalitarian culture. Gender
inequality, in particular, is believed to become a phenomenon of the human society later, beginning
with the emergence of agriculture and persisting to the modern age. In this paper I apply
neoclassical growth model to show how some of the ways people live their lives may be preserved
through centuries and millennia. Although Sentinel inhabitants are a remarkable example of
endurance of human experience, gender inequality and gender based discrimination is certainly an
enduring vestige of the distant past practiced in both developing and developed countries. I further
apply overlapping generations model (OLG) to explain how women themselves could be
perpetrators of gender discrimination in both developing and advanced societies. Famously known
as the Queen Bee syndrome (The Wall Street Journal, 2013) in the workplace, alpha female
behavior is observed across patriarchal societies of the developing world as well.
A vast body of literature documents oppressive cultural practices around the world where elder
women often play a leading role perpetuating oppression against women. Some examples include:
bridal kidnapping (Central Asia, Caucasus), “enslaving” of daughter-in-law’s (most of CentralAsia with varying severity across countries), genital mutilation (some counties in Africa and the
Middle East), Shim-pua marriages (existed in China and Taiwan) and as such.
Customs and beliefs emerge and evolve over time. They are passed down from generation to
generation and can date decades, centuries, or even thousand years back. The Persian New Year
Nowruz, for example, celebrated by peoples of Central Asia, Iran, Afghanistan, parts of Middle
East, Russia and Caucasia is linked to the Zoroastrian religion that dates back around 2,500 years.
Traditions shape preferences, tastes, form identities and norms of behavior in a society, thereby
often guiding the very decision-making process of individuals affecting their utilities.
Conventional utility functions in economics can express a wide array of non-pecuniary tastes and
preferences with the presumption that theses tastes and preferences are independent of individuals’
identity shaped by the social context. However, Akerlof and Kranton (Akerlof & Kranton, 2010)
argue that people derive utility from making choices that align with the norms and ideals that shape
identity of the group they want to belong to and derive disutility from making nonconforming
choices. The utility function proposed by A&K includes individual’s identity and norms, and ideals
that that shape the identity, although no specific formal utility function has been proposed.
The Model
Production of Norms
Social norms are often referred to as a form of social capital and are increasingly recognized for
their impact on the development of societies. Keefer and Knack (Keefer & Knack, 2003) view
social norms in terms of trust and trustworthiness and find that social norms that prescribe
cooperative behavior have significant impact on people’s abilities to collective action and
cooperation that induces development. In this paper I use a more general definition given by
Coleman (1990), quoted by Keefer and Knack, of social norms as specifying “what actions are
regarded as proper or correct, or improper and incorrect”. I apply this definition to those norms
that concern women’s behavior.
In all the economic literature I have reviewed thus far, I have not come across the discussion on
the emergence of social norms. Simply put, how do social norms come to existence and why some
of them persist regardless of the harm they may cause to a good half of the population, women?
Like any form of goods and services that are produced and consumed, norms guiding decision
making of individuals can be thought of as capital good that, although intangible, is an output of a
production process. Norms are “produced” through human practices and “reproduced” through
repetition that transcends generations. They are produced by households (norms of behavior
imposed by parents), groups of people (fraternities, Girl Scouts of USA), communities (Duke
University standards) or societies at large (Sentineli Islanders).
The production function framework is utilized beyond the conventional realm of goods and
services in health economics, for instance, where health, as a form of human capital itself is
considered as an output generated through such factors of production as “medical services” and a
combination of “environmental variables” including urbanization, industrialization, education,
income, and as such (Auster, Leveson, & Saracheck, 1972). In the context of norm production I
specify the factors of production as follows:
The production function for norms at time 𝑡 takes the general CES form:
𝑌𝑡 = 𝐹(𝑀𝑡 , 𝐷𝑡 𝑁𝑡 )
Time enters the production function indirectly, i.e. more norms (or stricter norms) are produced
over time only if the factors of norm production increase over time. One of the main ingredients
necessary to produce, maintain or transform the norm is collective memory, 𝑀𝑡 , that I ascribe to
the category of intangible cultural capital defined by Throsby (Cultural Capital, p.6) as “stock of
cultural value embodied in an asset”. Throsby distinguishes between tangible cultural capital
assets, or “cultural heritage” that includes buildings, or sites endowed with cultural significance,
as well as artworks and artefacts. Intangible cultural capital, on the other hand, “comprises the set
of ideas, practices, beliefs, traditions, and values which serve to identify and bind together a given
group of people, however a group may be determined… which may form part of private final
consumption and/or may contribute to the production of future cultural goods”. Throsby mentions
“collective memory” (p.7), the loss of which leads to the deterioration of the intangible Spanish
cultural stock that the works of the musician Manuel de Falla represent. I argue that collective
memory itself is a form of cultural capital that assigns cultural value to an intangible asset. 9 th of
May, for instance, may be just a day in the calendar, but for people born in the Soviet Union, it is
widely celebrated as Victory Day commemorating the Red Army’s victory over Nazi army in the
Second World War. The collective memory of the war and victory has been actively maintained
through film, music, literature, annual parades, celebration of the war veterans; this day invokes
the feelings of pride and patriotism and in a way, a sense of power and superiority (among ethnic
Russians at least).
The second necessary ingredient in the production of norms is 𝐷𝑡 𝑁𝑡 , which stands for “dense
networks”, or how people in society are connected to one another, which constitute a form of social
capital. Keefer and Knack (Keefer & Knack, 2003) speak of dense horizontal relationships among
people that emerge from participation in civic activities, sports clubs, neighborhood associations,
and as such. Small rural communities as well as tight-knot diaspora communities can be
conceptualized as dense horizontal networks. High density networks are those where all members
of the network are directly linked to each other without an intermediary through exchange of
information (Bloch, Genicot, & Ray, 2004).
I further assume that the production function takes Cobb-Douglass form which is often used in
conventional contexts as this form is easy to manipulate and I do not have any sense of higher
order terms:
𝐹 (𝑀𝑡 , 𝐷𝑡 𝑁𝑡 ) = 𝑀𝑡𝛼 (𝐷𝑡 𝑁𝑡 )1−𝛼 , 0 < 𝛼 < 1
𝐹(
(1𝑎)
𝑀𝑡
1
, 1) =
𝐹 (𝑀𝑡 , 𝐷𝑡 𝑁𝑡 )
𝐷𝑡 𝑁𝑡
𝐷𝑡 𝑁𝑡
(1𝑏)
𝑀𝑡
, 1)
𝐷𝑡 𝑁𝑡
(1𝑐)
𝑓(𝑚𝑡 ) ≡ 𝐹 (
𝑓(𝑚𝑡 ) ≡ (
𝑀𝑡 𝛼
)
𝐷𝑡 𝑁𝑡
𝑓(𝑚𝑡 ) ≡ 𝑚𝑡𝛼 , where 𝑚𝑡𝛼 reflects the tenacity of social norms
(1𝑑)
(1𝑒)
The conventional properties of the Cobb-Douglas production function, where 𝑓: [0, ∞) → [0, ∞)
and 𝑚0 ≠ 0, is given, hold in the context of norm production as well. 𝑓 (0) = 0 is satisfied. Norms
are born out of past behaviors and experiences, the memory of which is stored in people’s minds,
thus norms exist because of the existence of such memory, otherwise there are no norms to speak
of. Important aspect to note is that the collective memory emerges out of people’s interaction with
each other, thus, it exists if and only if the interaction is maintained. If interaction ceases, the
shared memory depreciates and goes to zero over time.
I assume that Inada conditions are satisfied as well. 𝑓 is continuous and twice differentiable on
(0, ∞). I assume that there are no “jumps” in my function and it makes sense in the context of
norm production. People do not change their ways overnight. Having said that I recognize the
cases of exogenous shocks, for example, the Iranian Revolution of 1979 overthrowing the
monarchy rule of the Pahlavi dynasty. People replaced lax secular norms and customs by the ones
based on strict Sharia Law precipitously, which on the scale of the duration of existence of
monarchy is an “overnight” change. But even in the case of such exogenous shocks it takes time
for individuals to internalize change. Thus, the production function converges to the higher level
of norm production asymptotically.
𝑓 ′(𝑚𝑡 ) > 0, 𝑓 ′′(𝑚𝑡 ) < 0, for each 0 < 𝑚𝑡 < 0, i.e. the production of norms exhibits positive
and diminishing marginal returns. As shared memories per densely connected unity of network
increase additional norms emerge, but creation of new norms slows down as memories continue
to be created. Think of a newly established organization. A formal Code of Conduct outlining rules
and responsibilities of the organization is devised from the start and their fulfillment over time
create a collective memory of the organization. With maturing of the organization the Code of
Conduct may be revisited and new items may be added but the core norms that defined the
organization from the start will be revered for the time conceivable. In this example,
lim 𝑓 ′ (𝑚𝑡 ) = ∞ and lim 𝑓 ′ (𝑚𝑡 ) = 0 make sense as well. As the Inada condition holds the
𝑚𝑡 →0
𝑚𝑡 →∞
production function becomes asymptotically Cobb-Douglas, which further justifies my choice of
the functional form of the production function for norms.
𝑀
𝑚𝑡 (≡ 𝐷 𝑁𝑡 ), or the tenacity of social norms may reduce in two cases: either 𝐷𝑡 , density, reduces
𝑡 𝑡
or 𝑁𝑡 , networks, weaken, or both, without collective memory created or maintained. This happens
when 𝑁𝑡 increase at the expense of the density of the networks (𝐷𝑡 remains constant) Think of how
migration “disrupts” or dilutes the established norms of the recipient community. Only if the norms
of the recipient community are effectively assimilated by the immigrants and new collective
memory is created, i.e. 𝑀𝑡 increases, the existing norms can be maintained. Otherwise the old
norms become obsolete and the new norms emerge, thus moving the process of norm production
forward. The tradition of celebrating a Persian holiday Nowruz by a sizable proportion of the
world’s population can be explained by exactly by the process of vast migration but lack of
interaction leading to the depreciation of existing shared memory with no new created: increasing
𝑁𝑡 and depreciating 𝐷𝑡 resulting in preserving one ancient tradition shared by so many people.
The preservation of the hunter-gatherer lifestyle by the Sentineli Islanders is the result of the exact
opposite trend: maintaining 𝐷𝑡 𝑁𝑡 constant while creating more and more collective memory.
Non-pecuniary Returns
Production and reproduction of certain norms in the society implies that they are viewed as
beneficial by a part or the entire society, otherwise, they would be abolished. Thus, we can think
of the society as a profit or benefit maximizing “firm” that produces norms in the following
maximization problem:
max
𝑀𝑡 >0,𝐷𝑡 𝑁𝑡 >0
Π = 𝐹 (𝑀𝑡 , 𝐷𝑡 𝑁𝑡 ) − (𝑟𝑡 + 𝛿) ∗ 𝑀𝑡 − 𝑤𝑡 ∗ 𝐷𝑡 𝑁𝑡
(𝟐𝒂)
Where 𝛿 −constant rate of depreciation of memory.
The type of return that an individual receives from the shared memory, 𝑀𝑡 , is obvious if we think
in the context of Shame and Honor societies and in terms of women. Reputation and a certain
social status attained based on reputation is a direct outcome of a collective memory of the
community. I borrow the definition of social status from (Glaeser, Laibson, & Sacerdote, 2002) as
a “measure of social influence that enables its possessors to reward and punish others”. In many
patriarchal societies where women are largely marginalized, by attaining a certain social status,
albeit later in the woman’s lifetime, the woman gains a significant power over junior men and
women in her immediate and extended family. The matriarchal power may still fall short of the
power of the head of the household but the benefits associated with such power are tempting. For
instance, newly-wed women in Tajikistan customarily live with and serve the in-law parents for
life, where the mother-in-law is the main beneficiary of the custom: as she can retire from carrying
the brunt of the household chores. By attaining the status of the mother-in-law, the woman enjoys
many associated perks, such as “free labor”, preferential treatment from the relatives of the bride,
or respectable position among neighbors. For older women to gain status (and younger women to
serve them), they must bear sons in Tajik culture. Therefore, older women have a vested interest
in maintaining the patriarchy even if their daughters do not. It is easy to see why such women
would oppose any change to the status quo.
Reputation is “sticky” because of the existence of memory, otherwise someone involved in a
reputation- damaging behavior could start over with a clean slate every day. I allow for a small
depreciation rate 𝛿. Even though the memory of the past behavior will persist the details may still
be lost in time due to human nature. As for the returns to 𝐷𝑡 𝑁𝑡 , we may think in terms of many
forms of informal risk sharing in developing countries associated with how people are connected
in networks, such as quasi-credit, labor pooling, child fostering, funeral cost sharing, job search,
and as such (Fafchamps, 2008). An individual gains access to such risk sharing arrangement by
being part and actively participating in such horizontally dense networks, through becoming and
the “insurer”, or “earning” 𝑤𝑡 , for example, by making monetary contribution to the funeral costs
of the neighbor and getting a “payback” when in need.
Using conventional notation for the returns to collective memory, as “capital” and to dense
networks, as “labor”, we have 𝑟𝑡 and 𝑤𝑡 , respectively:
∂Π
= 𝐹 ′ (𝑀𝑡 , 𝐷𝑡 𝑁𝑡 ) − (𝑟𝑡 + 𝛿) = 0 => 𝑟𝑡 = 𝐹𝑀 (𝑀𝑡 , 𝐷𝑡 𝑁𝑡 ) − 𝛿
𝜕𝑀 𝑡
(2𝑏)
∂Π
= 𝐹𝐷𝑁 (𝑀𝑡 , 𝐷𝑡 𝑁𝑡 ) − 𝑤𝑡 = 0 => 𝑤𝑡 = 𝐹𝐷𝑁 (𝑀𝑡 , 𝐷𝑡 𝑁𝑡 )
𝜕𝐷𝑡 𝑁 𝑡
(2𝑐)
Utility function
I assume an individual has CRRA lifetime utility from “consumption” of norms:
∞
𝑈(𝑐, 𝑦) = ∫ 𝑒 −𝜌𝑡 [(𝑒 −(𝜎𝜑)𝑡 𝑢 (
0
𝑐 1−𝜃
𝑦 1−𝜃
)) + 𝑢 (
)] 𝑑𝑡
1−𝜃
1−𝜃
(3)
In this model 𝑐 is consumption related to enforcing of norms and 𝑦 is all other consumption
(including the norm-violating consumption). For the purpose of this exercise I omit 𝑦 from the
utility function in further calculations.
By consumption I assume a range of food and non-food, norm-enforcing activities, beginning from
avoiding certain foods, making choices of clothing, conduct, life choices, choices of work and
leisure and etc. It really encompasses a wide range of human activities, just like norms guiding an
individual’s behavior penetrates many spheres of her life. For example, avoiding pork is a norm
among Muslim and Jewish people; giving gifts to people in the position of authority is dubbed as
“bribing” in some societies but may be a norm, although unwritten, of professional conduct in
many others. In this exercise I differentiate between consuming and saving behavior of individuals.
The consuming side is the fact of receiving bribes, not eating pork, wearing Islamic clothing, or
accepting arranged marriage. When an individual acts upon the norms of the society he or she
enters into a tacit agreement with the society to further reciprocate or to further perform norm
reinforcing acts. For example, when receiving a bribe an individual is expected to give something
in exchange, in the form of favor, whatever form it takes, thus further reinforcing corruption, which
is the norm of the society. By accepting an arranged marriage, i.e. the act of “consuming” the
norm, woman, again, agrees to the norms of the society and is expected to follow other norms of
behavior prescribed to the newly wed bride and wife. For example, the woman will also have to
be submissive to the will of her husband and the family-in-law, the requirements that usually go
hand-in-hand in the societies with arranged marriage customs. In other words, the young woman
cannot easily get out of the agreement that she made with the society by accepting the arranged
marriage in first place.
As in actual agreements enforced by laws, breach of the tacit agreement with the society is subject
to punishment as well, which may take quite serious emotional and physical form. It is interesting
to note, (from my own extensive life observations) that a woman who initially goes against norms
by rejecting arranged marriage and marrying someone of her own choosing will further undermine
other accompanying norms but does not bear consequences as harsh as a conservative woman
would. Thus, the consumption here also includes the acts of reciprocation. The “saving”, however,
is all norm - “maintaining” behavior. For example, a young woman in patriarchal societies is
expected to perform a range (a really wide range indeed) of small and big acts of conduct in order
to be viewed as marriageable: beginning from dressing certain way, speaking certain way in public,
learning how to cook and so forth. Likewise, an ambitious person who wants to get to the position
of power will have to bribe his/her way up the career ladder is certain societies. As in case of real
financial savings which benefit the individual later in life, for example, in retirement; the savings
in this case, too, benefit people later in life.
The consumption of norms, however, can cause either net utility or disutility, depending on many
factors. For instance, in patriarchal societies norms are often beneficial to men and marginalize
women, thus 𝜎 → 0 for men and 𝜎 → ∞ for women, or likewise they are more beneficial to old
versus young people; in Apartheid (and post-apartheid) society of South Africa, 𝜎 → 0 for the
white and 𝜎 → ∞ for black population; or a person engages in corrupt behavior out of necessity
but still has a moral remorse. The level of 𝜎, however, does not determine whether or not an agent
1
𝑐 1−𝜃
will choose to consume, because often the choice is not really a free choice. Thus, (1+𝜎) 1−𝜃 will
measure the net utility of consuming norms, where 𝜎 ∈ (0, ∞).
𝜑 ∈ (0, ∞), is a measure of individual’s tolerance to the status quo. If an individual has no
tolerance (𝜑 → ∞ ) with the way things are done in his or her community he or she will not
engage in the norm consuming behavior but will engage in a norm-violating behavior instead. (In
this exercise I will not discuss the utility function of a deviant). On the other end of the spectrum
𝜑 → 0 means that an individual really appreciates the status quo beyond the immediate
benefit/inconvenience that consumption of norms brings. For instance, a woman may have some
disutility from accepting an arranged marriage but in general agrees with the norms guiding
woman behavior and will certainly teach the same norms to her children. Thus for her 𝜑 < 1. Thus
the net utility derived from the arranged marriage will be amplified by her overall attitude to the
norms. 𝜑 = 1 is the point of indifference.
𝜑 should be viewed distinctly from 𝜎, because there are distinct factors determining its degree.
For instances, 𝜎 is not affected by an individual’s level of education, while 𝜑 is, although with
reservations. I link 𝜑 to education with caution. For example, there are many known cases of
American corporations engaging in corruption overseas. Recently, Wal-Mart has been caught
“greasing the wheels” in Mexico to circumvent local laws (Gandel, 2012) and it is only one
example. It is obvious that WalMart’s executives’ undoubtedly high level of education did not
make them less tolerant to the corrupt practices of the Mexican officials. In another example, high
educational attainment of the Queen Bee does not prevent her from engaging in marginalizing
women in workplace. Regardless, of these cases, education affects 𝜑 in that exposes an individual
to other practices by expanding his or her worldview. Another distinct feature is that the lack of
tolerance usually erupts in an action (a norm-violating behavior), while low 𝜎 is a passive
indicator. It is common to see marginalized segments of society to remain apathetic with the status
quo (𝜑 = 1, 𝜎 → ∞).
Ramsey Growth Model or Persistence of Norms
The total utility of the population is 𝑛 ∗ 𝑢(𝑐 (𝑡)). I normalize it to 1. So an agent’s problem is the
following:
𝑐 1−𝜃
∞
max 𝑈(𝑐) = ∫0 𝑒 −𝜌𝑡 [𝑒 −(𝜎𝜑)𝑡 (
)] 𝑑𝑡
1−𝜃
(4𝑎)
s.t
𝑎̇ = 𝑤(𝑡)𝐿 + 𝑟𝑎(𝑡) − (1 − 𝜑)𝑐(𝑡)
(4𝑏)
𝑎(0) = 𝑎0 > 0
(4𝑐)
lim 𝑒 −𝜌𝑡 𝑎(𝑡) ≥ 0
(4𝑑)
𝑡 →∞
In this model an individual’s asset, 𝑎(𝑡) is the aggregate social credits that she earns through living
by norms of the society that is reduced by the amount of norm violating behavior. The condition
that the initial level of asset 𝑎(0) is not zero hold here as well, since it can be inherited from parents
in the form of a “bequest” that I discuss in the next section.
The present-value Hamiltonian is:
𝐻 = 𝑒 −𝜌𝑡 𝑒 −(𝜎𝜑)𝑡
𝑐 1−𝜃
+ 𝜇(𝑡)[𝜔 + 𝑎(𝑡)𝑟 − (1 − 𝜑)𝑐(𝑡)]
1−𝜃
(5𝑎)
FOCs:
𝐻𝑐 = 0: 𝑒 −𝜌𝑡 𝑒 −(𝜎𝜑)𝑡 𝑐 −𝜃 − 𝜇 (𝑡)(1 − 𝜑) = 0
(5𝑏)
𝐻𝑎 = −𝜇̇ : − 𝑟𝜇 = 𝜇̇
(5𝑐)
lim 𝜇 (𝑡) 𝑎(𝑡) = 0
(5𝑑)
𝑡 →∞
Taking logs of 𝐻𝑐 :
ln(𝑒 −𝜌𝑡 ) + ln(𝑒 −(𝜎𝜑)𝑡 ) ln(𝑐 −𝜃 ) = ln 𝜇 (𝑡) + ln(1 − 𝜑)
(6𝑎)
−𝜌𝑡 − 𝜎𝜑𝑡 − 𝜃 ln(𝑐 ) = ln 𝜇 (𝑡)
(6𝑏)
Differentiating w.r.t. time:
𝑐̇ 𝜇̇
−𝜌 − 𝜎𝜑 − 𝜃 = = −𝑟
𝑐 𝜇
(6𝑐)
𝑐̇
Rearranging w.r.t 𝑐 yields Keynes-Ramsey rule (Euler condition):
𝑐̇ 1
= [𝑟 − (𝜌 + 𝜎𝜑)]
𝑐 𝜃
𝑐̇
𝑐
𝑐̇
𝑐
𝑐̇
𝑐
(6𝑑)
> 0 , if 𝑟 > 𝜌 + 𝜎𝜑
(7𝑎)
= 0 , if 𝑟 = 𝜌 + 𝜎𝜑
(7𝑏)
< 0, if r < 𝜌 + 𝜎𝜑
(7𝑐)
Interpretation: an individual will increase the consumption of norms over time as long as his or
his/her non-pecuniary returns, which takes form of social status continues to be greater than the
total disutility of doing so discounted over time. On aggregate level, it means the norms of the
society are maintained and reinforced. This has a major implication on the level of societies and
institutions, notably why one of the major problems in many developing countries such as corrupt
institutions are so hard to eradicate. Once corrupt – always corrupt!
In the following exercise I use the overlapping generation model (OLG) to further explore this
idea of endurance of norms across generations.
Overlapping Generations Model (OLG)
OLG model was first introduced by Allais (Economie et interet, 1947) but became well-known
due to Paul Samuelson (An Exact Consumption-Loan Model of Interest with or without the Social
Contrivance of Money, 1958) and Diamond (National Debt in Neoclassical Growth model, 1965)
The main finding in the OLG model is that the competitive equilibrium violates the First
Fundamental Theorem of Welfare Economics, i.e. the Walrasian equilibria are not Pareto-optimal
(over-accumulation of capital is possible).
For the model I use OLG model with altruism from the central planner perspective. The basic setup of the model is as follows (based on the OLG lecture slildes, ECON 602):

Overlapping generations of individuals who live 2 periods:, 𝑡 and 𝑡 + 1
o At time 𝑡 individuals are young. They work, consume and save
o At time 𝑡 + 1 individuals are old. They do not work but consume

Individuals consume 𝑐1𝑡 , when young and 𝑐2𝑡+1 , when old

The savings of the young in period 𝑡 generates the capital used to produce output in period
𝑡 +1 in combination with labor supplied by the young in period 𝑡+1
I apply the same concept of consumption, savings, wages and returns as in the previous exercise.
The key assumption of OLG model is that individuals have finite time horizons, i.e., they do not
care about their descendants, which is not a realistic assumption, as more often than not people do
care about their descendants. To make the OLG model more realistic it is assumed that there are
strong intergenerational altruism, resulting in transfers that effectively make the time horizon
infinite (Barro & Sala-i-Martin, 2004).

The presence of altruism implies that parents can give bequests, 𝑏𝑡 ≥ 0, to their children.
In my model 𝑏𝑡 may be thought of the “good name” of the parents that affects what position
a child takes in the society even before the child is grown enough to perform norm related
activities. For example, being born into a lower caste versus higher caste family in India
has a major implications on the child’s social status throughout his/her life. Or, being born
in the chief’s family in the Sentineli tribe has major implications for the rest of the life of
the child.
The central planner maximizes the following utility function
∞
𝑈 = ∑(
𝑖=0
𝑖
1−𝜃
1+𝑛
1
𝑐 1−𝜃
1
𝑐2𝑡+1+𝑖
) [
[𝑢 ( 1𝑡+𝑖 ) +
𝑢(
)]]
(1 + 𝜌)(1 + 𝛾) 1 + 𝜎𝜑
1−𝜃
1+𝜌
1−𝜃
(8𝑎)
Subject to instantaneous budget constraint of an individual born in time 𝑡:
𝑐1𝑡 + 𝑠𝑡 = 𝜔𝑡 + 𝑏𝑡
𝑐1𝑡+𝑖 + 𝑠𝑡+𝑖 = 𝜔𝑡+𝑖 + 𝑏𝑡+𝑖 ,
(8𝑏)
𝑖 = 1,2,3 … …
𝑐2𝑡+1 + (1 + 𝑛)𝑏𝑡+1 = (1 + 𝑟𝑡+1 )𝑠𝑡
(8𝑐)
(8𝑑)
Intertemporal budget constraint:
𝑐1𝑡 +
1
𝑐1𝑡+1
𝑐2𝑡+1
𝜔𝑡+1
𝑏𝑡+1
1+𝑛
+
= 𝜔𝑡 +
+ 𝑏𝑡 +
−
𝑏
(1 + 𝑛) 1 + 𝑟𝑡+1
(1 + 𝑛)
(1 + 𝑛) 1 + 𝑟𝑡+1 𝑡+1
(8𝑐)
𝑡
(1+𝛾) − weight of generation 𝑡 in the objective of the central planner, 𝛾 ≥ 0. If 𝛾 = 0, all
generations have the same weight. If 𝛾 > 0, future generations have less weight.
In order for utility to be bounded when 𝑐1𝑡+𝑖 and 𝑐2𝑡+𝑖 are constant over time, we condition 1 + 𝑛
< (1 + 𝜌)(1 + 𝜑) must be imposed.
Substitute for values of 𝑐1𝑡 , 𝑐1𝑡+1, 𝑐2𝑡+1 and so on from the instantaneous budget constraint and
derive w.r.t 𝑠𝑡, 𝑏𝑡+1 :
∞
max
(𝑏𝑡+1 ,𝑐2𝑡+1 )
𝑈 = ∑(
𝑖=0
+𝑢 (
+
𝑖
1+𝑛
1
) [
[𝑢 (𝜔𝑡 + 𝑏𝑡 − 𝑠𝑡 )
(1 + 𝜌)(1 + 𝛾) (1 + 𝜎𝜑)
𝜔𝑡+𝑖
𝑏𝑡+𝑖
𝑠1𝑡+𝑖
)
+
−
(1 + 𝑛) (1 + 𝑛) (1 + 𝑛)
(9𝑎)
1
𝑢((1 + 𝑟𝑡+1 )𝑠𝑡 − (1 + 𝑛)𝑏𝑡+1 )]]
1+𝜌
(1 − 𝜃 ) ∗ (𝜔𝑡 + 𝑏𝑡 − 𝑠𝑡 )−𝜃
𝜕𝑈
1
= −
(
(1 − 𝜃 )
𝜕𝑠𝑡
(1 + 𝜎𝜑)
1
(1 − 𝜃)(1 + 𝑟𝑡+1 ) ∗ ((1 + 𝑟𝑡+1 )𝑠𝑡 − (1 + 𝑛)𝑏𝑡+1 )−𝜃
)
+(
)= 0
(1 − 𝜃 )
1+𝜌
(9𝑏)
Euler Equations:
1/𝜃
𝑐2𝑡+1
1 + 𝑟𝑡+1
]
=[
𝑐1𝑡
(1 + 𝜌)(1 + 𝜎𝜑)
(9𝑐)
𝑐2𝑡
= [(1 + 𝛾 )(1 + 𝜎𝜑)]1/𝜃
𝑐1𝑡
(9𝑑)
Conclusion
The results derived through the OLG model are similar to the insight offered by the Ramsey growth
model but they give greater insight into the process of norm preservation across generations
regardless of their detrimental effect at a period of time. OLG demonstrates that as long as return
to norms are high enough, older generations, who have achieve a certain level of social status will
always be the backbone of the norms of the society, which means greater consumption of norms.
As discussed earlier consumption of norms implies norm-reinforcing behavior which inadvertently
leads to the oppression of any kind of norm weakening or norm-violating behavior endangering
the status quo.
I propose this very aspect of the model to explain the Queen Bee syndrome. Although the
syndrome was observed in the context of the developed societies, where gender equality (at least
on the surface) is enforced, there is an agreement that the workplace especially in the higher
echelons is a male dominated environment. Thus the rules of the game are governed by men. Just
like a woman in Tajikistan who jumps through hoops to finally achieve the position of the
matriarch in the male dominated society who are the rule setters, an ambitious woman in the
corporate world has to also jump through hoops, albeit of a different nature. Professional women
striving to climb up the career ladder must abide by certain rules of behavior, for example, be more
aggressive and tough in conduct, delay or forego child bearing. Child bearing that necessitate
interruptions in the professional career is shown to negatively affect promotion prospects. Briefly,
a woman must act like a man. To her, just like to her Tajik peer, females junior represent a potential
threat to the order of things that endowed her with the power. It is observed that men in senior
position do not exhibit Queen Bee behavior, i.e., do not mistreat treat junior male employees. The
explanation is simple: junior males do not threat the rules of the game set by men.
The Ramsey and OLG models also provide insight into the persistence of the hunter-gatherer life
style as the one among the Sentineli Islanders. The preservation of norms can be best understood
through how norms are produced and reproduced through deliberate norm-reinforcing behavior of
the community members. These process also provides an insight into why corrupt institutions may
remain corrupt for a long a time.
Understanding the process and motivations behind the norm favoring behavior, no matter how
detrimental, may help in devising better programs for empowering women in the word’s most
traditional societies.
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