Journal of Socio-Economics 31 (2003) 609–645
A consumer theory with competitive markets
for work in marriage
Shoshana Grossbard-Shechtman∗
Department of Economics, San Diego State University, 5500 Campanile Drive,
San Diego, CA 92182-0379, USA
Accepted 14 March 2002
Abstract
The theory presented here aims at explaining individual consumer behavior inside marriage and
prior to marriage. It is a New Home Economics (NHE) model in the sense that it assumes the existence
of household production. It is an intra-household bargaining model in the sense that it assumes that
husbands and wives typically have different economic interests with respect to marriage, and they
try to negotiate arrangements that suit them best. The more resources they have, the more they may
obtain results that favor them rather than their spouse. It is a market theory similar to standard labor
market theory. This theory throws light on gender differences in demand for commercial goods that
have home-produced substitutes. This theory leads to an explanation why women are charged more
for dry-cleaning. The theory can also explain differences in demand for different products. Predictions
include that of a sex ratio effect on consumption. For example, it is predicted that in countries with
more emigration of men than women, women will be expected to make higher contributions to newly
weds’ costs of housing. It is also predicted that there will be compensating differentials in marriage. For
instance, women married to considerably older men are expected to have relatively more control over
the use the couple’s income than women married to men who are close to their own age. In contrast
to bargaining theory, the insights presented here apply to both married individuals and to those who
anticipate being married in the future.
© 2002 Elsevier Science Inc. All rights reserved.
JEL classification: D11, J16
Keywords: Consumer theory; Marriage; Competitive markets; Intra-household allocation
∗
Tel.: +1-619-594-5468; fax: +1-619-594-5062.
E-mail address: [email protected] (S. Grossbard-Shechtman).
1053-5357/02/$ – see front matter © 2002 Elsevier Science Inc. All rights reserved.
PII: S 1 0 5 3 - 5 3 5 7 ( 0 2 ) 0 0 1 3 8 - 5
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1. Introduction
By living in capitalistic economies we naturally develop a sense that competitive markets
influence our lives. Evidence of the operation of markets bombards us every day, be it of
markets for stocks, food, housing, or professional football players. Competitive market models
that help explain how these markets work have traditionally been the most popular models in
economics.
Marriages are like firms. Marriages also deal with the basic economic questions of allocation,
production, and distribution, as has been recognized at least since the New Home Economics
(NHE) models were developed at Columbia University (Mincer, 1962, 1963; Becker, 1965;
Lancaster, 1966). Metaphors of marriage are often applied to bonds between devoted employees and their firm. Even though a number of economists have pointed to the similarities
between marriages and firms (e.g., Becker, 1973; Ben Porath, 1980; Pollak, 1985), economic
analyses relying on the assumption of competitive markets are applied considerably less to
studies of marriage than to studies of decision-making by firms, consumers, and workers. Even
when competitive marriage market models have been applied to marriage, as in Becker (1973,
1991), Lundberg and Pollak (1993), Grossbard-Shechtman (1984), Lemennicier (1988), or
Cherry (1998), these models have not exerted much influence on consumer theory.
When economists do not analyze human interaction in terms of market models, they typically
analyze these interactions as bargaining processes between two parties. Bargaining models
have first been applied to marriage by Manser and Brown (1980) and McElroy and Horney
(1981). Since the 1980s these and other bargaining models have been extensively applied to
economic research on consumption (see Haddad et al., 1997; Wooley, in press). These models
recognize that remarriage market conditions expected at divorce influence what is called “threat
points” (the term used in McElroy and Horney) or “distribution factors” (the term used by
Bourguignon (1984) and Chiappori (1988)) and therefore influence intra-marriage allocation.
However, “bargaining models do not directly imbed the alternatives married people have in a
marriage market.”1
The reluctance to use market models of marriage derives in part from the fact that the output
of firms is more marketable than the output of marriages: such is the case of the most valuable
output in most marriages: children. However, many other outputs of marriage have commercial
substitutes, such as childcare, cleaning, and food preparation. Economists’ reluctance to expand
the applicability of market models to marriage may also be tied to Western culture, the culture
that most influenced economics.2
Economic theories of firms and marriage differ not only in relative emphasis on market models and bargaining models, but also in the degree to which they integrate analyses of production,
allocation, and distribution. While these analyses are integrated in business economics, the
analyses of consumption in marriage, labor supply in marriage, and marriage formation are
rarely integrated. For instance, there has been little cross-fertilization between consumption
analyses based on bargaining theories and recently published economic studies of labor supply and earnings that recognize the endogeneity of marriage,3 or between these labor market
analyses and models of consumption in marriage and economic research that has focused on
explaining marriage formation and dissolution (e.g., Becker, 1973, 1991; Grossbard, 1978;
Keeley, 1979; Lemennicier, 1988; Lehrer, 1995; Brien, 1997).
S. Grossbard-Shechtman / Journal of Socio-Economics 31 (2003) 609–645
611
This paper contributes to the integration of analyses of consumption and marriage. The
novel models of consumer choice in Section 3 apply a market analysis of competitive marriage
markets conceived as labor markets and show how this helps understand production in marriage
and consumption. The theory draws on the NHE models of Mincer and Becker. The models
with marital public goods were inspired by the economic literature on the provision of public
goods (see Bergstrom, 1997).
Following Becker’s (1973) market theory of marriage it will be assumed that individuals
continue to be separate consumers after marriage.4 This recognition of individual agency in
consumption stands in contrast to the assumption of household agency in consumption and
the unitary household utility functions found in most NHE models (including Becker, 1965).5
In contrast to most previous theories of household decision-making, the following theory
also assumes individual agency in household production. Most previous economic theories
incorporating household production—including Becker’s theory of marriage and bargaining
theories of marriage—have implicitly assumed that households have a “unitary production
function.”6 Exceptions include the bargaining theories of Wooley (1988) and Lundberg and
Pollak (1993).
In the following theory it is assumed that like firms, marriages are limited enterprises in
which workers and entrepreneurs make individual decisions regarding the allocation of their
resources. The same individuals who decide to marry and possibly bargain over the distribution of marital resources are also assumed to make rational decisions related to household
production and work. This theory is in line with standard theories of consumption and labor
supply in that it assumes that individuals have control over their private resources of time
and income. A major divergence from other NHE models is that it is assumed that there are
activities of home production that are work in the sense that they have an opportunity cost,
even if the person is not employed outside the home.
The households inhabiting most economic analyses of consumption in a NHE framework
(including analyses of fertility) often resemble collective farms or communist systems, the
joint ownership of resources being justified by concepts such as altruism or biology. To most
economists marriages are very different from the firms that demand labor and where workers
supply their labor. These firms and workers are typically modeled as having control over
the use of their private resources of time and income. In stressing the question of agency in
production this paper is in the tradition of economic theories, including neo-classical, Marxist,
and Austrian economic theories, that place an emphasis on the issue of control over productive
resources but only in the context of firms.
In most household production models labor force opportunities generate the only opportunity costs of engaging in household production. This implies, for instance, that household
members’ time is valued either at their market wage in the labor force (if the individual belongs
to the labor force) or at a reservation wage obtained by assuming that household members spend
all their time producing goods jointly consumed in the household (see Willis, 1974).7 The individual worker inhabiting such household production models does not distinguish between
regular and overtime household production. Right before she is about to reach her physical
limits, she does not experience a higher opportunity cost. Nor will he mind performing tasks
that conflict with personal commitments to friends or relatives: all resources are assumed to
“belong” to the household. That is not the case here.
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Other models of intra-household allocation such as Chiappori (1992) or Wooley (1996)
have avoided the problematic assumption of unitary household production by assuming that
there is no household production. Such drastic assumption precludes the analysis of theoretical
implications related to household production issues.8 By assuming no household production
we disqualify the theory from addressing issues such as substitution between commercial
goods and household produced goods.
The following theory leads to a number of new insights: that marriage market conditions
and the income of a potential spouse affect consumption of singles anticipating marriage; that
price, wage, and income effects on individual consumer choice are affected by marriage choices
and marriage market conditions; and that individual consumption is related to compensating
differentials in marriage. Compensating differentials operate in marriage markets in ways that
resemble the operation of compensating differentials in labor markets.
A number of insights from the theory deal with male/female differences in consumer behavior. In particular, it is predicted that men’s demand for consumer products replacing household
production will be more price elastic than women’s demand for such products. It is also predicted that men’s elasticity of demand with respect to own wage is more likely to be positive
than women’s own wage elasticity of demand. As is the case with other models of marriage
markets it follows from the model presented here that in a society with an excess supply of
women, men are likely to obtain a larger share of marital output than in a society without
such excess. Vice versa, in a society with an excess supply of men, men are likely to obtain
a smaller share of marital output than in a society without such excess.9 It also follows that
consumption in marriage depends on the individual income of each marriage partner, rather
than on a pooled household income.
Section 2 presents the theory’s assumptions in a detailed way. Section 3 presents a short
run theory assuming that marriage market conditions are given. Section 4 presents a long
run equilibrium model that allows for changes in marriage market conditions. Both sections
include a number of testable implications regarding consumer behavior.
2. The assumptions
The theory’s assumptions are now examined and compared with the assumptions of other
economic models.
2.1. Rationality, individual agency, and divisibility
It is assumed that individuals are rational decision-makers who after marriage continue to
manage their own personal resources of working time and capital. It is assumed that individual
resources are divisible and do not automatically belong to the marriage, assumptions that
are typically made about firms but not about families.10 While some economic models may
consider firms as organizations acting as a single purposive actor and influencing private
consumption and leisure decisions, many other economic models view firms as organizations
composed of purposive actors, i.e., those models assume individual agency on matters of
private behavior.11
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613
In a similar vein, marriages can be viewed as organizations composed of purposive individual actors. The following model assumes that after marriage individuals continue to allocate
part of their resources of time and income as individual agents who may not be exclusively concerned with goals shared with their marriage partner. Instead, they may be concerned with the
achievement of personal goals. In an advanced industrialized society consumption of private
goods by individuals who are married is expected to be substantial. It is assumed that the private
consumption of a potential marriage partner does not enter an individual’s utility function.12
Some of the models presented here assume that individual marriage partners allocate part
of their resources towards the production of jointly consumed goods.13 Such goods will be
termed marriage commonwealth goods. Examples of jointly consumed goods include a clean
home, happy intimate relations, or successful and helpful children.
2.2. Production in marriage
Marriages are defined as institutions organizing the production and consumption of goods,
including private goods and commonwealth goods. The production of all goods—private and
commonwealth—may involve no time inputs or may involve the time of one or both spouses.
Time is also devoted to self-maintenance activities such as sleep, a use of time that is not
expected to vary much whether marriage occurred or not. Time contributed to a spouse’s
consumption is defined as work to the extent that it has the opportunity cost of not being one’s
favorite activity.14 To distinguish work for a spouse from work for a firm, it will be termed
“Work-In-Marriage (WIM).” Two kinds of WIM are defined: time allocated to the production of
a spouse’s private goods (including a wife doing her husband’s laundry or a husband cooking
his wife’s meals) and time allocated to the production of marital public goods that will be
termed “Work-On-Commonwealth” or WOC. Commonwealth goods include the well-being of
a couple’s children. In practical terms, separating between these uses of time is complex: what
is personal WIM and what benefits the couple? It depends. As for distinguishing between any
form of WIM and leisure, the criteria is whether the activity is the person’s favorite activity or
not.15 Historically most Workers-In-Marriage have been women, a tendency that continues to
prevail today, even in the U.S. Surveys indicate that most tasks likely to be included in WIM
are performed by women (see Hersch, 1997).
One expects differences between the supply of private WIM and the supply of WOC. The
supply of any form of WIM is a willingness to work at tasks benefiting the spouse. The
opportunity cost of WIM is the foregone value of self-produced self-consumed goods. Supply
is also influenced by the utility from work. The marginal utility of an hour of WIM or WOC
may be positive if the individual enjoys that work, something that is more likely to occur in
the case of WOC, tasks producing goods the individual consumes herself, than in the case of
other forms of WIM. Another factor affecting the disutility of WIM is the amount of WIM
supplied.16 Labor supply models analyze the number of hours an individual is willing to work
prior to the establishment of an actual employment relationship, assuming a range of given
wages. There is much that also needs to be assumed regarding these wages, as discussed below.
The supply of WIM is entirely comparable to the supply of labor to a firm, except that the
wages are harder to define. It is not far-fetched to assume that the wage is given in the case
of work producing goods consumed solely by others. The supply of WOC (time producing
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joint consumption in marriage) is more complex, for here the total compensation from work
is not given. There is an element of public good production here, as the supply also depends
on expected contributions of time and goods by a spouse.17
The demand for WIM for the purpose of producing private goods will also differ from
the demand for WOC. Like firms, marriages have a demand for workers. In monogamy, this
amounts to one person having a demand for the WIM supplied by another. Labor demand
models analyze the quantities of labor that firms are willing to buy prior to the establishment
of an (explicit or implicit) contract with a worker, assuming a range of given wage values.
In a similar vein, the following model derives an individual willingness to pay for WIM. An
individual demand for WIM used to produce privately consumed goods is derived assuming
a range of given “wages” for WIM and assuming spouses can establish contracts at least as
binding as the contracts binding workers and firms. Here too, the demand for WOC is more
complex, as it involves own consumption and possible complementarity in production.
As is the case with other organizations dealing with production, marriages need to face
issues of transaction costs and moral hazard.
2.3. Markets for Workers-In-Marriage
If many people willing to supply WIM and/or many people willing to demand WIM compete
with each other, there will be markets for Workers-In-Marriage. In these markets, the market
demand is an aggregate of individual demands and the market supply is an aggregate of
individual supplies. The marriage markets analyzed here are analyzed as labor markets, i.e.,
markets for WIM performed by spouses or potential spouses. Operationally, marriage is thus
defined as a situation where at least one spouse engages in WIM.
As is the case in labor markets, the quantity dimension in a market for Workers-In-Marriage
involves a participation variable of a categorical nature and hours of WIM, a variable of
an incremental nature. Conditions in markets for Workers-In-Marriage can possibly affect
equilibrium hours of WIM in a representative marriage and participation in WIM markets.18
The advantage of using categorical variables in studies of WIM lies in their measurability. One
dimension of participation in a market for Workers-In-Marriage includes the choice between
marriage (or cohabitation) and non-marriage. Active dating can be part of the search process
leading to marriage and shares many of the characteristics of job search (see Keeley, 1974;
Becker, 1991; Mortensen, 1988).19 People who date with the goal of a serious relationship
can be viewed as participants in a WIM market.20 Another variable related to the quantity
dimension in markets for Workers-In-Marriage is number of mates or the categorical variable
polygamy versus monogamy.21 Informal forms of polygamy, such as extramarital affairs, have
also been studied by economists (see Lemennicier, 1988). Divorce, i.e., the equivalent of job
termination in labor markets, is another measurable categorical variable that is related to the
operation of WIM markets.
2.4. WIM wages
It is assumed that when WIM markets clear, some kind of price mechanism operates.
In labor markets it is obvious that a price mechanism operates. Wage differentials facilitate
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615
matching between workers of varying skills and jobs of varying productivity and encourage
human capital investments. Even though non-price mechanisms operate in labor markets too,
the evident operation of a wage mechanism indicates that non-price matching mechanisms do
not account for the entire process of allocation of workers into jobs. Even though pecuniary
wage mechanisms barely operate in markets for WIM, this difference does not imply that a
labor market analysis cannot be applied to markets for WIM.
There may not be a pecuniary wage, but there often are pecuniary benefits that can be
conceived of as a quasi-wage. Depending on the cultural context, we may observe a variety of
pecuniary benefits or transfers that are related to WIM. Individuals who prefer to replace their
own time in household production with WIM (possibly consisting of WOC as in the case of joint
parenting) often induce their spouse to engage in such WIM by paying for commercial products
benefiting the production of jointly consumed goods (ex. air conditioning for the home) or the
WIM worker’s private consumption (e.g., in the form of a car the Worker-In-Marriage uses at
his own leisure). Such in-kind benefits can be viewed as quasi-wage payments for WIM.22
In-marriage transfers that possibly indicate the functioning of a wage mechanism in markets
for WIM include the following: weekly allowances, country-club memberships, access to
credit cards, health benefits or pensions.23 Good working conditions—including kindness
and demonstrations of emotional attentiveness by the WIM-user—may be considered as a
non-pecuniary benefit that adds to the total compensation for WIM. Violence perpetrated by
a spousal employer against a Worker-In-Marriage creates non-pecuniary costs that reduce the
quasi-wage for WIM.24
Quasi-wage for WIM mechanisms may also include premarital transfers, such as pre-nuptial
payments (dowry or brideprice), dating costs, or wedding costs. While rare in industrialized countries, pre-nuptial payments are common in less industrialized countries.25 Asymmetric dating costs are another culture-specific aspect of wages for Workers-In-Marriage. In
the U.S. today, dating is a much more popular institution than in most European countries.
The U.S. norm that men pay the costs of dating is strange to visitors from England, France,
or Sweden.26
Indications of the existence of a price mechanism influencing the allocation of time to WIM
can be obtained from litigation data. If time spent in household production is compensated at
time of divorce or death, this indicates that while the person (often a homemaker) was involved
in what I call WIM, his time was valuable (see Hersch, in press) not only to himself but also to
others. Compensations paid to the survivors (in case of wrongful death) or to a divorcee (in case
if divorce) indicate that the survivors were benefiting from the deceased’s WIM or that the WIM
of the divorcee was valuable to a spouse prior to divorce. Interestingly, the two methods that
are used most frequently in divorce litigation surrounding the value of household production
time are the opportunity cost method and the replacement cost method (see Hersch, 1997).
The replacement cost method recognizes that there is a demand for the products of marital
household production and therefore WIM is valuable (but this method leads to the inclusion
of production that privately benefits the deceased or divorcee). The opportunity cost method
recognizes that WIM is being supplied and that Workers-In-Marriage are choosing between
alternative uses of their productive capacity.27
Laws regulating WIM are similar to laws regulating labor relations in the business world.
Contracts often specify an agreed-upon compensation for WIM in the form of benefits, i.e.,
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various aspects of the quasi-wages. If entered voluntarily these contracts often mean more to
people than labor contracts, especially to the extent that spouses are bound by love for each
other more often than is the case between workers and employers. Type of marriage—civil
versus religious, informal versus formal marriage, regular versus covenant marriage,28 —may
be related to quasi-wage for WIM: a marriage offering more job security being generally more
attractive to Workers-In-Marriage. Governments and organized religious groups often regulate
markets for WIM. The modernization process has been accompanied by an increased role of
governments and a decreased role of religious organizations in the regulation of markets for
Workers-In-Marriage (see Grossbard-Shechtman and Lemennicier, 1999). There exist large
culturo-political differences in reliance on such government regulation. One indication of such
differences can be found in the widespread skepticism and disapproval in Japan when after
World War II the U.S. forced the Japanese to legislate that marriages should be motivated by
mutual love rather than determined by parental authority (see Hendry, 1985).
Even though some type of wage mechanism seems to operate in all markets for Workers-InMarriage, the absence of a formal wage system makes the study of these markets more difficult
than the study of other labor markets.29 The following theory of consumer behavior assumes
that an implicit wage mechanism operates in markets for WIM.
2.5. Competition
It is assumed that markets for Workers-In-Marriage are competitive. This is more likely to
be the case when there are larger numbers of market participants, potential substitution among
these participants is larger, information is more easily accessible, WIM is more homogeneous,
and more protection is given to the rights of individual market participants (i.e., marriage
contracts are more binding).
The first condition of competition—large numbers of participants—readily applies to the
case of marriage: in most societies it is clear that large numbers of men and women could
possibly compete for marriage partners. The assumption of substitutability applies to marriage,
even though substitution is not expected to be perfect: the people possibly interested in marriage
who participate in the same markets for Workers-In-Marriage may all be unique in some way.
However, as long as some individual marriage candidates can be substituted for others, the
market process may operate.
Substitution is more likely to occur when no special ties have yet been established between
people, i.e., at the pre-marriage stage, than after people are already married and have ties to
a spouse. However, just like those workers who are currently employed may be looking for
jobs, those currently married may be looking for alternative spouses, which sometimes leads
to infidelity.30 The lower the divorce probability, the less it is likely that people participate in
marriage markets after they marry.
Substitutability among potential marriage partners is expected to vary with the heterogeneity of the market participants. The more homogeneity in the nature of WIM and in the
desirable traits of Workers-In-Marriage, the more the markets for Workers-In-Marriage will
be competitive. One expects that there will be non-trivial levels of heterogeneity in markets for
Workers-In-Marriage, which is reminiscent of the existence of heterogeneity in labor markets.
Operationally, this may imply the need to consider separate sub-markets for particular kinds
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617
of Workers-In-Marriage, in line, for instance, with the distinction between markets for skilled
and unskilled workers often found in analyses of labor markets.
2.6. Long run versus short run
Like models of the firm the following models distinguish between short and long run. In
the short run people decide what to consume and produce at home, assuming equilibrium
conditions in markets for WIM, which implies given quasi-wages for WIM. Note that this
short run is long enough to allow for life time planning. In the long run (see Section 4), people
can acquire marriage-related human capital and enter or exit marriages, and market equilibrium
conditions can change. Section 3 presents the micro-foundations of the theory and Section 4
is a market-level macroanalysis.31
The models of demand for commercial consumer goods presented in Section 3 assume that
paid work is solely an income-generating activity; i.e., work does not enter the utility function.
It is assumed that all consumers participate in the labor force and consider producing the goods
they consume with the help of either commercial products or WIM. It is also assumed that
competitive markets for Workers-In-Marriage operate and are in equilibrium.
3. Short run models of individual consumer demand with competitive marriage
markets
This section considers three models of consumer choice. Two models assume all consumption in marriage is private consumption. In the simplest model (WIM1) there is a single private
good Z that the individual plans to produce with the help of WIM and commercial inputs. The
second model (WIM2) assumes that the consumer consumes two private goods, each using
WIM in its production. The models lead to the derivation of demands for commercial goods
and for WIM. Formal derivations of consumer demands are presented. The third model (WOC)
assumes only one composite commonwealth good consumed jointly with a (potential) spouse.
All models assume that individuals are selfish in the sense that their potential spouse’s
private consumption does not enter their utility function.32 It is assumed that all couples are
heterosexual, so that if individual i is a man, individual j is a woman, or vice versa. It is also
assumed that total time available to an individual is set to 1 and that prices p of commercial
inputs are given to the individual. It is assumed that when the individual engages in consumer
choice, production functions and the equilibrium wage for the relevant type of WIM are given
from the perspective of an individual market participant. Production functions are assumed to
have constant returns to scale.
3.1. The WIM1 model
Define Z as a vector of privately consumed goods, x as a vector of commercial inputs, s as
leisure time, mj as WIM supplied by (potential) spouse j, h as work for a firm, w as wage,
I as non-wage income, and y as the given wage for a spouse’s WIM. This wage could have
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been established at a competitive marriage market equilibrium. It is assumed that all WIM
contributes to the production of privately consumed goods.
The model is defined by the following program:
Max U(Zi ) subject to Zi = Zi (xi , si , mj ),
1 = hi + si and Ii + wi hi = yj mj + pi xi .
(WIM1)
Using the definition of full income found in Becker (1965), the time and income constraints
can be restated as a full income constraint
Fi = Ii + wi = Πi Zi ,
where Π is the implicit price of the composite good consumed by the individual.
Appendix A solves problem WIM1 and derives an individual’s demand for commercial
products xi .33 The following notations are used: letters with dot on top are percentage changes,
σ xs is the elasticity of substitution in production of Z when goods x are substituted for the
individual’s own time s, αZm is the share of WIM costs in producing Z, and σ xm is the elasticity
of substitution between commercial inputs x and WIM m. The derived demand for a commercial
good xi is:
w
Ii
Z
ẋi = İi − (αZx + αsZ σxs + αm
σxm )ṗi +
+ (σxs − 1)αZs ẇ + (σxm − 1)αZm y.
˙
(D1 )
F
F
This demand for commercial products D1 contains familiar results: a positive income effect, a negative price effect, and a wage effect. The income elasticity is the coefficient of
the percentage change in I, the price elasticity is the coefficient of the proportional change
in price, and the wage effect is the coefficient of the percent change in wage. It can be seen
that both the price effect and the wage effect depend on the elasticity of substitution between time and goods and on the share of the various inputs in the household production
function.
What distinguishes this demand from that derived from previous household production models in the NHE tradition is principally the identity and circumstances of the decision-making
unit. In other NHE models the decision-making unit is a multi-person household. In contrast,
here we have a demand by an individual who is also making a decision about getting married
or remaining single. In this model individual i’s decision to marry depends on her gains from
employing a spouse to provide WIM mj at given WIM wage yj .34
Viewing the decision-making as that of an individual who is not necessarily married implies
that the possibility of substituting WIM for purchased commercial inputs affects the (price)
elasticity of demand. Furthermore, there also is an elasticity of demand with respect to the
quasi-wage for WIM. To the extent that quasi-wage y has been established in a market for WIM,
it follows that any factors that influence market conditions in markets for Workers-In-Marriage
and therefore quasi-wage for WIM y will have an impact on the demand for commercial
products. Such factors are discussed in Section 4. The following propositions deal with the
law of demand, i.e., the price effect.
As expected from the law of demand, the price elasticity of xi (the coefficient of ṗi in
demand D1 ) is negative. That coefficient is composed of three components, all of which take
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619
on a negative sign: a full income effect that is a function of the weight of commercial goods in Z,
an effect of substitution in production between commercial products and own time (including
term σ xs ) and an effect of substitution in production between commercial products and WIM
(including term σ xm ). It can be seen from D1 that:
Proposition A (Law of demand and substitution in production). The elasticity of demand
for xi will be larger (in absolute terms) the higher the elasticity of substitution in production
between commercial products and WIM.
This implies, for instance, that the more customers have the option of relying on a spouse
to satisfy a particular need, the higher the price elasticity of demand. In turn, the lower the
elasticity of demand, the higher the prices that restaurants and other products that are substitutes
for home-produced goods are likely to charge, assuming that the suppliers of these various
commercial goods and services have some degree of monopoly (perhaps local monopoly).
This is one of the reasons why one is more likely to find expensive restaurants where many
people are single, as is the case in Manhattan, for instance.
This proposition implies that commercial products that can possibly be substituted for goods
produced with WIM will have a more elastic demand than products that cannot possibly get
such substitute. For instance, the demand for restaurant meals is expected to be more elastic
than the demand for movies (at least prior to the introduction of home cinemas) or than the
demand for bar services.
Proposition B (Law of demand and share of WIM costs). The effect of a given elasticity of
substitution in production on the price elasticity of demand for commercial goods is weighted
by other factors’ share in the costs of production.
It can be seen from D1 that the effect of σ nm , the elasticity of substitution in production
between commercial products x and WIM, on the price elasticity of demand is a function of
the share of WIM costs in production, αZm . We learn from here that, given a high elasticity of
substitution between a commercial input and WIM, the more an individual i relies on WIM
in the production of Zi (i.e., the higher the weight of WIM costs in total costs), the higher the
price elasticity of that individual’s demand for commercial consumption good xi .
For instance, assume that Zi stands for the cleanliness of the individual’s garments, and
assume that there is a high elasticity of substitution between the labor of a spouse washing
that individual’s garments and the services of a commercial cleaner.35 The more the individual
plans to use WIM to get her garments cleaned, the higher the price elasticity of demand for
commercial laundry services xi . Or consider the example of “nutrition,” another product that
can be produced in three ways: alone, with commercial products such as frozen dinners, or
with a spouse’s WIM. The more an individual intends to employ a spouse in food production,
the more his demand for frozen dinners will be price elastic. The intuition behind this is that if
people know that a spouse is available to perform a service benefiting them, they will be less
willing to pay a high price for a similar service provided commercially.
This proposition can be tested by comparing the price elasticity of various commercial
products aimed towards individual consumers differing in expected elasticities of substitution
or cost shares in home production. This proposition may help us interpret differences between
male and female demand for the same product.
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B1. male/female differences
To the extent that men rely on WIM more than women (see Hersch, in press), women will
have lower price elasticities of demand for commercial goods that serve as substitutes for
WIM. For instance, if (1) αZm is larger for men than for women, and (2) for both men and
women the elasticity of substitution in production σ xm exceeds elasticity σ xs ,36 then men’s
elasticity of demand for (WIM-substitutable) consumption goods will be higher than women’s
elasticity of demand for similar consumption goods.
For instance, if women do more laundry than men, men’s demand for dry-cleaning is
expected to be more elastic than women’s demand for dry-cleaning. This analysis can help
explain why dry cleaners often charge more for women’s clothing items such as blouses than
for analogous men’s clothing such as shirts.37 The higher prices that dry cleaners charge for
women’s garments follow from a less elastic demand for dry-cleaning on the part of women
than men.38 This assumes that dry cleaners have some monopoly power and can take advantage
of customers who systematically have a less elastic demand.39
Another task that women typically engage in more than men is home cleaning. Consequently,
men’s demand for commercial cleaning help is expected to be more elastic than women’s
demand for such help, and women are likely to pay more than men for a given quantity of
cleaning help. This may be the case in Paris.40 The same logic also implies that to the extent that
women engage in more cooking-related WIM than men, men’s demand for frozen dinners is
expected to be more elastic than women’s, and frozen meals catering more to female customers
are likely to be more expensive than frozen meals catering more to male customers.41 It also
follows that the demand for gardening, car maintenance, or carpentry products geared to
women is likely to be more elastic than the demand for such products geared to men, since
women are more likely to rely on a spouse to perform such tasks.
Observed male/female differences in the elasticity of demand for cigarettes may also be
interpreted in light of this analysis. It has been found that women’s demand for cigarettes is
less elastic than men’s (Chaloupka and Pacula, 1998). When the price of cigarettes increases,
the smoking habit becomes more of a nuisance and an individual’s derived demand for a good,
defined as “non-smoking habit,” increases. In line with the production function of Z assumed
in this model “non-smoking habit” can be produced with own time, a significant other’s WIM
(contributed by a spouse, cohabitant, or date), or commercial anti-addiction products and
services. A spouse nagging a smoker is thus a substitute for a commercial product aimed at
freeing a person from a smoking habit. If women can rely less on this kind of WIM relative to
men, women will find it more difficult to free themselves from a smoking habit, and therefore
will be more likely to continue to smoke after the price of cigarettes rises. Also, women’s
demand for commercial anti-smoking products and services is expected to be less elastic than
men’s. It follows from this model that:
Proposition C (Income pooling). When analyzing effects of income on in-marriage consumption one has to consider the effects of the income of each spouse separately, and that
income pooling is inappropriate.
In demand equation (D1 ) the coefficient of the percentage change in income (İi ) gives us the
individual income elasticity of demand for commercial products x. That income elasticity of
demand is a function of the size of individual (non-work) income relative to full income, and
S. Grossbard-Shechtman / Journal of Socio-Economics 31 (2003) 609–645
621
marriage only involves the household production of private consumption goods (Z). Individuals decide on their (potential) consumption in marriage before consulting with a spouse, and in
the case of individuals not yet married, before having met with the person who may eventually
become a partner in marriage. A (potential) spouse’s income enters the individual’s demand
D1 only to the extent that this income is expected to influence the given value of WIM wages
yj . To the extent that that value is established in a market equilibrium, it will be influenced by
conditions in markets for Workers-In-Marriage. For instance, if many individuals using or supplying WIM experience increases in income, increases in aggregate demand for WIM or supply
of WIM will result, and equilibrium quasi-wages for WIM will be affected as explained in
Section 4. A further discussion of income effects on consumption in marriage is found in that
section.
This proposition regarding income pooling has also been derived by bargaining theorists.
Most bargaining theories model conflicts of interest regarding consumption in marriage assuming individual utility functions and unitary household production. Income changes may
affect husbands’ and wives’ relative bargaining position in marriage and therefore their individual consumption. We agree on the need to consider individuals as having their own utility
functions. Where we differ, is that it is recognized here that conflicts of interest may occur not
only regarding the distribution of household produced goods but also regarding the production
of these goods.42 Income pooling is inappropriate not only because an increase in one spouse’s
income is more likely to increase that spouse’s relative consumption of commercial products
(as has been pointed out in the bargaining literature on marriage), but also because an increase
in one spouse’s income is likely to have different effects on an individual demand for various
kinds of household production time: a positive effect on i’s demand for j’s WIM mj , and a
negative effect on demand for i’s own time si .43
Proposition D (Own wage effects). Demand D1 also includes an elasticity of demand for
x with respect to own wage, i.e., the coefficient of ẇi . This elasticity contains a real income
effect and an effect of substitution in the production of private good Zi . Own wage elasticity
of demand depends on the share of various factors of production in the costs of producing Z
and on the elasticity of substitution in production between own time and commercial goods.
The positive effect of own wage on demand for consumption goods via an effect of substitution in production is a function of the share of own time costs αZs in producing good Z.
The larger αZs , the more it is likely that this substitution effect will dominate and reinforce the
positive income effect. To the extent that married men are less likely to engage in WIM than
married women, this share αZs is likely to be larger for women than for men. It follows that the
elasticity of demand for private consumption goods with respect to own wage is more likely to
be positive for women than for men.
It also follows from derived demand D1 that the demand for commercial products will be a
function of the equilibrium value of WIM wages, yj (see Section 4).
3.2. The WIM2 model
The WIM1 model included one composite private good in the individual’s utility function.
By considering two composite goods, we make room for more substitution effects. The model
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is defined by the following program of utility maximization subject to production functions
with constant returns to scale, a time constraint, and a budget constraint:
Max Ui (Zi1 , Zi2 )
1 = hi +
si1
+
si2
subject to Zik = Zik (xik , sik , mkj ),
and
Ii + wi hi =
yj m1j
+
yj m2j
k = 1, 2,
+ p1i xi1 + p2i xi2 .
(WIM2)
The full income has the same sources as before, but it can now be spent on two goods Z1
and Z2 :
Fi = Ii + wi = Π1 Zi1 + Π2 Zi2 ,
where Π 1 and Π 2 are the implicit prices of private goods Zi1 and Zi2 consumed by the individual.
By solving problem WIM2 we can derive an individual’s demand D2 for a commercial
product xi1 (see Appendix B). This demand is very similar to D1 , except that it also includes
effects of substitution in consumption between the two goods, income elasticities of demand,
and shares of consumption in total income:
I
1
σxm ]ṗ1 − (η1F − σC )k2 α2x p˙ 2
ẋi1 = η1F İ − [(η1F k1 + σC k2 )α1x + αs1 σxs + αm
F
w
+
− (η1F k1 + σC k2 − σxs )α1s − (η1F − σC )k2 α2s ẇ
F
− [(η1F k1 + σC k2 − σxm )α1m + (η1F − σC )k2 α2m ]y,
˙
(D2 )
where η1F is the full income elasticity of demand for composite good Zi1 , σ C is the elasticity
of substitution in consumption, and k1 and k2 are the shares Π1 Zi1 /F and Π2 Zi2 /F .
Comparing D1 (the derived demand for commercial products derived from the previous
model) with demand D2 , it appears that due to effects of substitution in consumption all the
effects discussed before are now more complex. The effects of price, income, and wages now
also depend on the elasticity of substitution in consumption, on the weights of inputs in both
cost functions, and on the income elasticities. Propositions A, B, and D derived from the
simpler WIM1 program need to be reassessed in light of the WIM2 program. It can be seen
from equation (D2 ) that the effect of the share of spousal labor costs on own elastiticity of
demand may now be dwarfed by other differences influencing the price elasticity of demand,
including differences in income elasticity and in elasticity of substitution in consumption. The
Propositions E and F include insights defined from the WIM2 model.
Proposition E (Law of demand and substitution in consumption). It can be seen from
equation D2 that the effect of the elasticity of substitution in consumption is mitigated by the
share of commercial costs out of total costs of producing good Z. The more WIM has been
substituted for commercial products, the smaller this share is going to be and therefore the
elasticity of demand is less likely to be affected by the elasticity of substitution in consumption
in cases where more WIM enters home production.
This implies that even if men and women have the same elasticity of substitution in consumption, its effect on men’s own elasticity of demand may be smaller than for women, to the
extent that the share of factor x is smaller for men.
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623
This insight also applies to comparisons across products. Price elasticity of demand is
generally larger for products with higher elasticity of substitution in consumption. However,
this effect depends on the share of x, and possibly on the share of WIM as it affects the share of
x in total costs. A product Z with a smaller share of WIM, such as music enjoyment, is likely
to be more price elastic for any given elasticity of substitution in consumption than a product
with a larger share of WIM, such as food enjoyment.
Proposition F (Cross-price elasticity). It follows from this analysis that the cross-price
elasticity of demand for a commercial product x1 as a function of the price of another good x2
depends among other factors on the share of WIM in total costs. When people rely more on
WIM to produce a good Z, the cross-elasticity of demand may be low even if the elasticity of
substitution in consumption is high.
Both models WIM1 and WIM2 have assumed that marriage only entails private consumption, and have ignored that production in marriage often involves jointly consumed goods,
such as children and a pleasant home atmosphere. The next model addresses this aspect of
household production in marriage.
3.3. The WOC model
This model assumes that marriage only entails jointly consumed goods or commonwealth
goods (also called marital public goods) and that the representative consumer only has one
q
commonwealth good in his or her utility function, Zi . In this case we will call the time m that
a spouse contributes towards the production of such good WOC. The individual counts on a
q
given amount Zjo of the good to be produced by potential mate j at no cost. Beyond that level,
it is assumed that the individual can obtain more Zq from a spouse j by paying spouse j some
q
“wage” yj . For simplicity, it is assumed that the individual does not contribute own time to
q
the production of Zi .44 The model is defined by the following program:
q
Max U(Zij )
q
q
q
q
q
q
subject to Zij = Zjo + Zi ,
q
Zjo > 0,
q
Zi = Zi (xi , mj ) with constant returns to scale,
1 = hi a time constraint,
q
q q
q
q
q
Ii + wi hi = pq xi + yj mj , a budget constraint, xi = xij − xjo ,
(WOC)
q
where xjo is the amount of commercial products contributed by the (potential) spouse.
q
It is worth noting that the wage the individual expects to pay for WOC, yj , may be lower
than wage y paid for private WIM (see Section 4). In comparison to the WIM models above,
there now is an additional source of full income: the value of goods contributed by (potential)
spouse j. The time and income constraint can be rewritten as full income constraint
q
q
¯ jo = ΠZij ,
Fi = Ii + wi + ΠZ
q
where Π is the implicit price faced by i. When evaluating the contribution of a mate Zjo , i
values that contribution at a given Π̄.
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S. Grossbard-Shechtman / Journal of Socio-Economics 31 (2003) 609–645
q
q
¯ , which implies that Żij =
It follows from the full income constraint that Ḟ = Żij − Π
q
q q
Ḟ − αx ṗ − αm ẏj . To derive i’s demand for the commonwealth good we replace Ḟ by its
components and use the results obtained earlier (see Appendix A). As a result, the demand for
q
all commercial products needed for obtaining Zij will be
q
ẋij = İ
q
xi
¯ jo
ΠZ
I
w
q
q
˙¯
+ ẇ + (ΠZ
σxm )ṗq + (σxm − 1)αqm y˙ j .
− (αxq + αm
jo )
F
F
F
(D3a )
The amount of commercial goods the individual is willing to pay for is the difference
q
q
q
= xij − xjo . Consequently, i’s demand for goods xi is:
q
q
q
ẋi = βẋij − (1 − β)ẋjo ,
q
(D3b )
q
q
where ẋij is obtained from (D3a ) and β = (xij /xi ) is the inverse of the proportion of commercial
products entering the commonwealth good that is paid by individual i. It is assumed that this
proportion is given, possibly based on customs and bargaining by previous generations of men
and women.
It follows from this model that the positive income effect on the demand for goods includes
the effect of the value of commonwealth goods that the potential spouse is expected to contribute. At the same time, individual i’s demand for commercial goods decreases as a function
q
of the commercial goods xjo contributed voluntarily by the spouse. Even if the elasticity of
substitution in production between commercial goods and WIM is the same in all models, one
expects less individual demand for commercial goods in the WOC model than in the WIM1
model.45 This simple WOC demand model above does not incorporate private consumption
goods consumed by individual i, Zi . However, private goods consumed by spouse j’s, Zj , enter
this model indirectly via their effect on spouse j’s asking wage for WOC. That asking wage is
a function of both demand for WOC and WOC supply and takes account of spouse j’s utility
from private consumption goods (see below).
One expects individual consumers’ utility to include both private goods (as in the WIM
models) and marital public goods consumed jointly with a spouse (as in the WOC model). A
full model could integrate WIM and WOC. One of the expectations is that the wage of WIM
or WOC and the share of WIM in total costs of producing a good Z will have an impact on
any demand for commercial products.
4. Long run (macro) equilibrium models of consumer demand
In the models of individual consumer demand presented above it was assumed that wages for
WIM were given and possibly established in marriage markets. In the WOC model it was also
assumed that potential spouses j would offer a given contribution to commonwealth goods. This
section examines factors influencing equilibrium values of wages for Workers-In-Marriage
according to a market analysis considering demand and supply of WIM.46
Market demand: The individual demands for WIM that aggregate to a market demand can
be derived from models similar to the models of demand for commercial inputs analyzed in
Section 3. Demands for WIM mj (WIM or WOC) are similar to demands for commercial goods
S. Grossbard-Shechtman / Journal of Socio-Economics 31 (2003) 609–645
625
x, as they are both inputs into the Z’s that provide utility to the consumer. As usual for demands,
it is assumed that all prices are given, including quasi-wages for WIM. Own price elasticity of
demand for WIM will be a term similar to the coefficient of ṗi , where quasi-wage y replaces pi .
The cross-price elasticity will be a term similar to the coefficient of ẏ, where p replaces y. The
rest of the effects can also be obtained by replacing x by m. It follows from such analysis that
(assuming normality in income effects) individuals with higher incomes will demand more
WIM, that own price effects will be negative, and that under most assumptions the demand for
WIM will be smaller after decreases in the price of commercial inputs substitutable for WIM.
This demand is related to the decision to marry or remain married.47
Market supply: Market supplies of Workers-In-Marriage aggregate individual supplies that
are also derived from similar rational choice models. The individuals j supplying WIM usually
differ in gender from individuals i on the demand side. Simple models of individual supply
are derived next. The following models of individual supply call attention to a number of
factors that are expected to affect the market value of WIM and therefore the long run demand
for consumer goods. Models of individual supply of WIM have to be consistent with the
models of individual demand. Here too it is assumed that total time is equal to 1 and that all
prices are given. The first supply model (Section 4.1) corresponds to the WIM1 and WIM2
models of demand and assumes that the only kind of WIM is private WIM. Supply model 2
(Section 4.2) assumes that the only kind of WIM is WOC.
Section 4.3 considers the interaction of aggregate demand and supply. Next comes a discussion of factors that may affect consumer choices via their effect on equilibrium wages for
WIM. The factors considered are income (4.4), cultural preferences and ideology (4.5), sex
ratios (4.6), personal attractiveness (4.7) and compensating differentials (4.8).
4.1. Supply of private WIM
This model assumes that all WIM is contributed to the household production of privately
consumed goods. The model consists of the following program:
Max U(Zj ) subject to Zj = Zj (xj , sj ), a production function,
yj mj = pj xj , a budget constraint,
T = mj + sj , a time constraint.
(S1 )
In this model individuals j are workers willing to work in marital household production.
Model S1 is reminiscent of a traditional leisure/goods trade-off, the difference being that
here the only employment available is in private WIM, and that instead of a wage there is a
quasi-wage for WIM y. Maximization leads to the equilibrium condition:
MUsj
yj
= .
pj
MUxj
The supply of individual j’s WIM is expected to be positively sloped, as long as the substitution effect of wage y dominates its income effect. This is analogous to the case of a regular
labor supply.48 If the model is expanded to include non-work income as a source of income it
is easy to show that if own time in household production (usually called leisure) is normal: an
increase in income will cause a decrease in j’s willingness to supply WIM.
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The WIM models presented here diverge from earlier NHE models of household production
with respect to their implications for the estimation of the value of time of household members
who do not participate in the labor force. It has been assumed here that such value of time
is given. It could correspond to the equilibrium quasi-wage in a market for WIM. This WIM
quasi-wage serves as a reservation wage and also influences individual labor supply decisions.
Here labor supply, household production time, and marriage (as participation in markets for
WIM) are simultaneously determined by the optimizing individual. In contrast, in Willis (1974)
and Gronau (1977) the value of individual time of a marriage partner involved in marital
production depends on that person’s labor force participation. These models consider the
value of time of an individual who does not participate in the labor force as determined at the
intersection of the “household’s” demand for that person’s time in household production and
the perfectly inelastic supply of time. Marriage market forces do not play a role in Willis’ or
Gronau’s models of value of time in household production.
4.2. Supply of Work-On-Commonwealth
q
In this model it is assumed that individual j consumes a commonwealth good Zj with
potential spouse i while also consuming his own private good Zj . The individual supplying
WOC may not necessarily consider this as work, for she also consumes the fruits of this labor.
The program can be presented as follows:
q
Max U(Zj , Zj )
q
q
subject to Zj = Zj (xj , sj )
and
q
yj mj = pj xj + pq xj , a budget constraint,
q
q
q
q
q
q
q
Zji (xji , mj ), production functions,
q
1 = sj + sj , a time constraint and xij = xj + xio , where xio > 0 is given.
q
(S2 )
q
It is assumed that the production function Zji perceived by j is the same as Zij perceived by
(potential) spouse i.
Solving this program leads to maximization condition
q
q
yj
MUm
MUs
−
= q.
MUx
MUx
pj
This program leads to an upward-sloping supply of WOC to the extent that the substitution
effect dominates the income effect.
q
We can interpret yj in program S1 and yj in program S2 as reservation wages. It can be seen
that individual j is likely to require a lower wage to supply a given amount of WOC relatively
to the wage needed to induce that individual to supply the same amount of private WIM. This
result follows from the fact that when supplying WOC individual j also enjoys the fruits of that
q
labor, the jointly consumed good, and therefore MUmj > 0. This implies that for any given
income level received by individual j, the individual’s supply of WOC lies to the right of the
supply of private WIM.
At the same time, the total income received by a supplier of private WIM is likely to be
smaller than that received by a supplier of WOC, for income includes the value of commercial
inputs that potential spouse i is likely to contribute to individual j. A given positive transfer of
goods causes j’s supply of WOC to lie to the left of the supply of private WIM. Adding these
S. Grossbard-Shechtman / Journal of Socio-Economics 31 (2003) 609–645
627
two effects (different utility and different total incomes), it is not clear whether the supply
of private WIM will be to the right or to the left of the supply of WOC.49 To the extent that
aggregate supplies of WOC lie to the right of aggregate supplies of private WIM, without
corresponding differences in demand for the various kinds of WIM, the equilibrium wage for
WOC will be lower than the equilibrium wage for private WIM.
4.3. Markets for Workers-In-Marriage
Markets for privately consumed WIM are very much like labor markets. In both cases it is
assumed that all individual agents (on the supply side and the demand side) consider the wage
as given, and buyers and sellers are not interdependent due to joint consumption. If WIM is
of the WOC type the analysis is more complex, since WOC demand and WOC supply are
inter-related: the more commercial inputs xio are supplied by i the less j will be willing to
q
supply WOC without a positive compensation yj . Therefore, j’s value of time and willingness
to marry varies positively with xio . At the same time, j also determines a willingness to supply
xjo that will be considered as given by individual i. In turn, the determinants of amounts xio
and xjo also follow from a maximization process. A full analysis of WOC models is beyond
the scope of this paper.
Even if public goods problems are assumed away, the task of deriving a market equilibrium is
not trivial. The complexity of the problems involved in analyzing a marriage market equilibrium
is not very different from that characterizing the analysis of any market, including labor
markets. Institutions matter, but when performing comparative statics in labor or other factor
markets, most economists keep these institutional factors in the background. In the case of
WIM markets, since these markets operate without much public awareness, it takes more
imagination to perform a market analysis and comparative statics involves keeping more
unidentified factors in the background. Institutions facilitating the operation of markets for
WIM exist and vary from country to country. They narrow the choices available to individuals
and thereby make it easier for matches to occur. The institutional context creates rigidities
and places constraints on individual opportunities for negotiation between a particular i and
a particular j. This is similar to the institutional rigidities and constraints on hours of work,
work conditions, and wages, that help define labor market opportunities as they are perceived
by individual labor market participants. The longer the time period considered when studying
a particular market for either workers or Workers-In-Marriage, the fewer the rigidities and the
more institutional changes will be observed.
A market equilibrium entails that an equilibrium quasi-wage for WIM has been established.
It can be assumed that a general equilibrium exists in the sense that other WIM markets and
related markets cleared at the same time (see Grossbard-Shechtman, 1984). When markets for
WIM operate, one can derive many more valuable insights about consumer demand. Those
effects are outlined in the next sub-sections.
4.4. Income effects via WIM markets
It follows from a market analysis that (a potential) spouse’s income may influence the consumption of a representative individual i, this insight applying to both extant marriages and
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S. Grossbard-Shechtman / Journal of Socio-Economics 31 (2003) 609–645
potential marriages. The effect is related to both consumption and production. In contrast, it
follows from a bargaining theory that a spouse’s income will influence individual consumption
only in extant marriages, and most bargaining theories do not include income effects on home
production.
According to bargaining analysis an individual will benefit more from an increase in own
income than from a comparable increase in the income of potential spouses.50 Bargaining analysis considers couples as engaged in a war over the consumer goods the couple can purchase.
The higher own income, the more an individual marriage partner is likely to obtain a consumption package he or she enjoys. Both the market theory presented here and bargaining theories
help explain why men in the U.K. were bitterly opposed to their government’s decision to pay
child subsidies to married mothers rather than to married fathers (see Lundberg et al., 1997).
The consumer theory presented here offers an additional reason why individual income matters when studying consumption: it influences the opportunity cost of the labor that individual
spouses devote to household production, i.e., WIM.51 Where marriages involve asymmetric
exchanges of WIM, one’s reaction to increases in the income of a (potential) spouse depends on
whether one expects to be more of a supplier or a consumer of WIM. Increases in a (potential)
spouse’s income are expected to be detrimental to consumers of WIM, as the spouse is then a
Worker-In-Marriage. However, for individuals of type j who supply WIM increases in the income of their potential spouses i are not necessarily harmful and could be beneficial. The effect
of (own) income on consumption of commercial goods depends on whether one is a consumer
or supplier of WIM. For WIM-consumers who do not supply WIM, the income effect is as specified in D1 above. For individuals who supply WIM and do not consume it, the income effect
can be modeled by expanding program S1 to include income from sources other than WIM.
The supply of WIM worker j is expected to be negatively related to j’s income, similarly to
the income effect on a regular labor supply. The negative impact of an increase in j’s income
on j’s supply of WIM implies that either fewer hours of WIM will be supplied at a given WIM
wage y, or that a higher WIM wage y will be charged for a given amount of WIM. One expects
ceteris paribus that demand for consumer goods will grow more as a result of an increase in
the income of WIM users than as a result of an increase in the income of WIM suppliers, as
WIM suppliers also spend some of their income on consuming their own time in household
production.
This analysis carries implications regarding gender differences in relative preference for
increases in own income versus spouse’s income. To the extent that men are more often the
users of WIM and women its suppliers, an increase in (potential) spouse’s income (causing a
reduction in the spouse’s willingness to supply WIM) is more likely to hurt men than to hurt
women. In such an asymmetric world the detrimental effect of increases in women’s income
on men’s well-being is likely to exceed the detrimental effect of increases in men’s incomes
on women’s well-being.
This leads more generally to the consideration of effects of one spouse’s income on the
consumption by the other spouse, i.e., cross-income effects. Again, these effects can operate
via bargaining in extant marriages or via market effects in a competitive model with men and
women looking for WIM partners at given quasi-wages. Widespread changes in the income of
individual WIM suppliers j will have an impact on the aggregate supply of WIM available to
individuals of type i and therefore on equilibrium quasi-wages for WIM. Similarly, changes in
S. Grossbard-Shechtman / Journal of Socio-Economics 31 (2003) 609–645
629
the aggregate demand for WIM due to widespread changes in the income of individual WIM
users i’s will have an impact on equilibrium quasi-wages for WIM. It will also be the case that
the particular identity of an individual j who will match with individual i may change if large
numbers of individual WIM suppliers j’s experience income changes. For instance, a person
who may have been happy with marriage to a relatively less desirable i prior to an increase in
income may not be so any more after experiencing an increase in income. However, a change
in the income of one particular individual (other than self) is not expected to have an impact
on quasi-wages of Workers-In-Marriage, and therefore—assuming perfect competition—it
should not affect consumption by a particular individual i or j.52
If the net effect of a widespread increase in j’s income is a decrease in the supply of WIM
among individuals j, equilibrium wages for Workers-In-Marriage j will increase. In turn, such
higher wages for WIM are expected to cause an increase in individual i’s consumption of x
due to a substitution in production effect while causing a decrease in that consumption due to
a real income effect. It follows from a market analysis that consumers who are WIM users will
be hurt when WIM workers obtain higher incomes from other sources, causing higher WIM
wages y. The consumption of goods by WIM users will decrease due to a real income effect
and will increase due to substitution in production.
Introducing WOC into the analysis may modify this conclusion, as WOC suppliers also
consume what they produce and are likely to increase their consumption of commonwealth
goods as a result of their higher income. The more potential WIM workers j intend to spend
on commonwealth consumer goods and the more WIM consists of WOC, the less an increase
in WIM workers j’s income is likely to hurt individual WIM users i’s. It follows that the
more important commonwealth goods are to consumption in marriage, the less individuals
can expect to be hurt by increases in potential spouses’ income.
Given that women are more likely to supply WIM than men, it follows that men are more
likely to be hurt by increases in women’s income than vice versa. Consequently, men are
more likely to oppose policies leading to higher female incomes than women are likely to
oppose policies leading to higher male incomes. This helps explain why there have been and
continue to be numerous instances of men using collective action to limit the labor force
opportunities of women, but no instances of women using collective action to limit the labor
force opportunities of men.53 Such asymmetry between male and female income effects on
consumption in marriage and its consequences for public policy are more likely to be observed
in countries with a traditional emphasis on women performing most WIM. Opposition to
women’s labor force participation is less likely in traditional societies where WIM involves
more work on commonwealth goods (WOC): men will then be harmed less by increases
in women’s income. That is because when WIM includes much WOC, WIM suppliers will
presumably not use income increases as much to reduce their supply of WIM as would be
the case with private WIM suppliers. Also, the more women contribute market inputs to
commonwealth goods, the more increases in their income may benefit men. Therefore, in a
society with a traditional division of labor and rapid economic growth leading to increased
participation of women in the labor force, it is a smart strategy for men to convince women to
devote more of their consumption to commonwealth Z’s than to private Z’s.
The fact that in most countries women have traditionally engaged in private WIM more
than men helps explain why increases in income often have opposite effects on marriage rates
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of men and women. Higher income has been found to be associated with higher rates of
marriage among men and lower rates of marriage among women, e.g., by Goldscheider and
Waite (1986). Higher incomes push demands for WIM by WIM users (more often men) to the
right, implying higher marriage rates for WIM users. At the same time, higher incomes push
supplies of WIM by WIM workers (usually women) to the left, implying lower marriages rates
for WIM workers (see also Grossbard-Shechtman, 1993).
The inherent tension between income effects on demand and supply of WIM will also have
effects on demand for particular commercial products and services that can ease that tension.
Earlier in the twentieth century, rises in income in the U.S. have been associated with rapid
increases in employment of servants, indicating a high income elasticity of servants’ services
(Stigler, 1946). The rapid growth of commercially prepared food services can also be explained
in these terms. Reliance on such substitutes has been one way to facilitate matches between
high income men and women, after women experienced large increases in income (not only
due to increased labor force participation) and reduced their supply of WIM. Asymmetric
supply of WIM by men and women also helps explain larger non-wage income effects on
wives’ hours of labor relative to such income effects on husbands’ hours of work (see e.g.,
studies on the effects of Negative Income Tax experiments such as Rees, 1974; Robins et al.,
1980).
One does not need to assume total gender asymmetry in supply and demand of WIM to
obtain many of these results. Most of the statements made here apply as long as more WIM is
supplied by women than by men.
4.5. International differences in consumption
Consumption depends on preferences that are in part influenced by the culture in which an
individual lives, and cultures vary with language, nationality, ethnicity, religion, etc. Cultural
effects on demand and supply of WIM will influence individual consumption via effects on
equilibrium conditions in markets for WIM. It is in the best interest of WIM-users to convince
WIM suppliers that the object of their work is something they can also consume, i.e., to try to
get them to see the WIM that they supply as a form of WOC that they can also benefit from.
This relates to the concept of “caring” in Becker’s theory of marriage. If Workers-In-Marriage
care about the private consumption of their spouse, that consumption is not a private good
anymore, it becomes a commonwealth good. If a task such as feeding a spouse passes from
personal WIM to WOC, it will be cheaper for WIM users to get meals cooked by a spouse.
In this light, the emphasis on good homemaking could possibly be explained as an attempt to
get people to supply more WIM by making them see how they contribute to a commonwealth
good. Likewise, it is in the best interest of WIM suppliers to make WIM users want their
services more. The valorization of the “good provider” has traditionally encouraged men to
earn more so they will want to consume more WIM. It is therefore in the interest of women
supplying WIM to convince men of the importance of being a “good provider.”
Some cultures put more pressure on men to become “good providers,” leading men to
invest more in their income-earning human capital. Cultures may also make demands on men
to provide particular goods such as housing in order to qualify for marriage. This appears to
be relatively more the case in Italy, and helps explain why Italians, including single men, have
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631
tended to save more than people in most other industrialized countries.54 For instance, in 1980,
Italy had the highest savings ratio in a sample of seventeen countries, including most Western
European countries, the U.S., Canada, Australia, Japan and Korea.55
The high saving rates of Italian men may be the result of a culturally based higher preference that men have for women’s WIM, causing a higher demand for women’s WIM and
higher quasi-wages for women’s WIM relative to other countries where men are more satisfied
with substitutes for goods produced by a wife, such as own household-produced goods and
commercial goods.56 Overall, it is predicted that national savings rates will vary directly with
traditionalism in prescribed gender-based specialization in breadwinning and homemaking.
Women who supply WIM are not necessarily treated better in countries where men save more
for marriage. Even though they work harder at WIM, they may get fewer benefits such as
access to their spouse’s earning power and benefits from WIM performed by men.
Variations in quasi-wages for WIM due to cultural differences are expected to have implications not only for total consumption versus savings, but also for the content of consumption.
4.6. Effects of sex ratios
The higher the demand for WIM relative to the supply, the higher the expected market
level compensation for WIM, i.e., the quasi-wage will be higher. The higher the quasi-wage
for women’s WIM, the more women will consume relative to men. Therefore, the higher the
sex ratio (when men are scarce relatively to women in the same marriage market), the more
women will consume relative to men (see Grossbard-Shechtman, 1984). This is expected to
affect both individual consumption in marriage and consumption by single individuals who
either prepare themselves for marriage or are substitutable with married people.
This prediction also follows from a number of other theories of marriage, including Becker
(1973), McElroy (1990), and Chiappori et al. (1998). In the bargaining theories and Chiappori’s
theory this hypothesis is derived from the fact that husbands and wives bargain over the distribution of marital surplus. The higher the ratio of men to women, the better women’s opportunities
of remarriage after a potential divorce and the stronger women’s bargaining power in marriage.
In those other theories, the prediction only follows for married individuals. It follows from
the analysis presented here that sex ratios will also influence the spending habits of unmarried
individual men and women, an implication that does not follow from bargaining theories.
Whoever plans to marry—whether it is a first marriage or a later marriage—anticipates
certain levels of quasi-wages for WIM after marriage and is likely to develop spending habits
based on their expected earnings (if WIM supplier) or expenses (if WIM user). For instance,
given a traditional division of labor in the home, it is expected that young single women with
good quasi-wage for WIM prospects (high ratio of males to females) will spend a higher portion
of their current income on private consumption (e.g., expensive clothing, and travels abroad)
than comparable women without such prospects, whereas young men in these circumstances
are expected to spend less on themselves and save more towards marriage. Information on premarital income transfers can possibly indicate variations in quasi-wage for WIM. For instance,
when women pay dowry prior to marriage, this may reflect low quasi-wages for women’s WIM.
Low sex ratios may explain prevalence of dowry across various cultures. For instance, in
Greece and Ireland dowries have traditionally been more prevalent than in other European
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countries (see Grossbard-Shechtman, 1993; Rao, 1993). To the extent that the prevalence of
dowries reflects low quasi-wages for WIM, and that Greece and Ireland have had low sex
ratios (i.e., few available men per available woman) as a result of more emigration by men
than by women (related to the large number of maritime jobs in the case of Greece), traditional
prevalence of dowries seems to be negatively correlated with sex ratios.57 In Greece, a dowry
often included housing for the young couple. The need to accumulate a dowry is likely to
encourage savings by the potential bride and her parents.
Cross-cultural data on young people’s savings patterns, as well as those of parents of
potential brides and grooms, could be used to test the prediction that the ratio of single men’s
to single women’s savings is expected to increase with sex ratio. It would also be interesting
to see if savings rates by demographic group vary according to whether a country traditionally
expected dowries paid by women or premarital payments by men. One could also investigate
savings patterns by age and gender in India, comparing areas and social classes differing by
whether they expect bridewealth (dowry paid by men) or dowries to be paid prior to marriage
(see Bronfenbrenner, 1971 on observed variation in type of premarital payment in India).
4.7. Attractiveness in marriage and consumption
Any personal characteristic that increases the value of WIM to the WIM user is expected to
be associated with a higher demand for WIM and higher quasi-wages for WIM, as long as that
characteristic adds to a person’s human capital. A trait adds to a person’s marriage-general human capital of value in the marriage market whenever it is valued by many potential spouses.58
If a WIM supplier, the individual with higher human capital expects a higher WIM wage he
will therefore consume relatively more both before and after marriage. If a WIM consumer,
the individual with higher human capital expects to pay a lower WIM wage she will therefore
consume relatively more both before and after marriage. Factors that are likely to increase productivity in WIM (with or without WOC) include most characteristics known to be associated
with labor productivity in general, such as knowledge and health.
As applied to married individuals, this hypothesis also follows from Becker’s theory of
marriage and from bargaining theories of marriage. Again, however, the application to consumption by singles anticipating marriage and aware of their marriage related human capital
is unique to this WIM-based theory of consumption presented here. It also follows from this
theory that if other attractive WIM workers enter a given marriage market (e.g., because they
have invested in their human capital or migrated), this will reduce the quasi-wage available
to the existing WIM workers they compete with, thus reducing those people’s consumption
before and after marriage.
4.8. Compensating differentials in marriage
Compensating differentials in markets for WIM are conceptually similar to compensating
differentials in labor markets. They are likely to be found whenever workers make trade-offs
between pecuniary benefits from work and working conditions of non-pecuniary value. For
instance, labor economists explain why people working in high-risk jobs such as high-rise
construction get paid more than people working in low-risk jobs by assuming that workers
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633
prefer to supply work to occupations that involve low risks than to high-risk occupations. It
follows from competition in labor markets that employers offering high-risk jobs will have to
pay workers more to attract them.
Similarly, if marriage markets are competitive, WIM workers get paid, and most workers
find the same conditions attractive, compensating differentials in marriage will be observed.
WIM users who are less attractive will have to pay WIM workers more to get them away
from competing potential WIM users (see Grossbard-Shechtman, 1984, 1993). For instance,
if most people consider good looks, health, and intelligence as attractive traits, then WIM users
lacking these traits will have to pay quasi-wages for WIM that exceed the quasi-wages for
WIM that other WIM users who are good looking, smart, etc. have to pay in order to attract
the same WIM workers.
The prediction of compensating differentials in marriage does not follow from matching
models of marriage, such as Becker (1974) and Roth and Oliveira Sotomayor (1990), for these
models assume that there is a continuum of individual men and women varying in their characteristics and obtaining matches according to some positive assortative mating mechanism
other than the price mechanism. The prediction does not follow from household production
models where individual producers of household production—i.e., WIM suppliers—do not
own portable general human capital and therefore cannot move from one marriage to the next.
This hypothesis is also found in bargaining models, but only for married individuals. Good
looks and youth are attractive traits in marriage, and a person will be relatively unattractive in
marriage if he or she is substantially older than the (potential) spouse. Assuming traditional
gender roles, one expects that men who are substantially older than their wife are paying
compensating differentials in quasi-wage for WIM (see Grossbard-Shechtman, 1984).59
It follows that ceteris paribus the personal consumption of women married to substantially
older men is expected to be higher than the personal consumption of women married to
men closer to their own age. There is evidence supporting this proportion in Browning et al.
(1994). Wooley (in press) has tested this prediction based on data from a Canadian survey
whose purpose was to assess who controls family finances in married couples with children,
the husband or the wife. Results indicated that in this sample, women married to substantially
older men were more likely to be in charge of withdrawing cash from bank accounts than
women married to men who are closer to them in age. Presumably, whoever is more likely
to withdraw cash is also more likely to consume what they prefer relatively to what their
spouse prefers. This finding supports the idea that younger women are in a relatively more
advantageous bargaining position in their marriage, i.e., that men are paying compensating
differentials if they are substantially older than their wife.
In contrast to a bargaining theoretical approach, a WIM market approach leads to the
prediction that unmarried WIM workers with great looks who enter the marriage market and
plan on marrying older men will be able to expect large incomes and will tend to consume
more even when single. Likewise, those men who intend to use the WIM work of substantially
younger women will have to accumulate sufficient assets to afford the expensive tastes of
women who know their market value.
There is some anecdotal evidence that while in the marriage market less attractive grooms
had to pay higher quasi-wages for WIM in England three centuries ago. For instance, in
Laurence Sterne’s 18th century novel Tristram Shandy’s grandparents had a famous premarital
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negotiation about the appropriate financial compensation for the deficiency of Mr. Shandy Sr. in
the nose department (Sterne, 1760).60 With contemporary data it is more difficult to document
compensating differentials in premarital financial agreements, but there are ways to do so,
for instance by studying differential use of various forms of marriage contract in countries
where various forms of marriage coexist, as is the case of France and many other countries in
continental Europe (see Laferrere, 2001).
Lower labor force participation can also indicate a higher quasi-wage for WIM on the part
of WIM workers who are not very interested in their career. Consistent with the presence of
compensating differentials in marriage, Grossbard-Shechtman and Neuman (1988) found that
in Israel married women married to older men were less likely to participate in the labor force,
and Grossbard-Shechtman and Fu (2001) reported the same finding for a sample of Hawaiian
brides and grooms.
5. Conclusions
A theory of individual consumer choice was developed based on the assumption that individuals demand and supply WIM and participate in competitive markets for WIM. The models
are simpler if WIM is similar to labor supplied to commercial firms there is strict separation
between WIM workers and WIM users, and members of the two groups of WIM market participants do not consume commonwealth goods. A short run analysis of individual consumer
choice was presented assuming that marriage market conditions are given. This analysis led to
a number of implications regarding consumer demand, including predictions of male/female
differences in consumption and of differences in the demand for various products. This analysis of demand for WIM led to a number of implications regarding price and wage elasticity of
demand for consumer products, including predictions of male/female differences in consumer
patterns, differentials in demand for various products, and recommendations to avoid models
assuming income pooling in marriage. The analysis included implications for the effect of
marriage on price elasticity of demand, income effects, wage effects and cross-price effects
on demand.
In the long run, marriage market forces influence individual consumer choices via changes
in market equilibrium. Factors influencing marriage markets can help explain the consumer behavior of individuals who are either before or after marriage. A number of testable hypotheses
regarding consumption were presented, including hypotheses about sex ratio and productivity effects on consumption and effects related to compensating differentials in marriage and
human capital investments. Some of these hypotheses are novel. Others are also found in alternative theories of marriage: one of Becker’s theories of marriage, bargaining theories, and
matching theories. The insights obtained here are most similar to those obtained from bargaining theories, a major difference being that a WIM market theory applies to both marriages and
singles.
This theory of consumption shows that marriage market analysis has a bigger role to play in
economics than was previously thought. Much further work is needed. At the theoretical level,
the model recognizing that public goods are produced in marriage needs further development,
including more integration of the various models presented here.
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635
Most of the propositions presented here are untested, even though many of them could be
tested empirically. It is hoped that empirical researchers in the area of consumption, savings,
and marketing will find some of the analysis presented here useful.
Notes
1. Personal communication from Gary Becker.
2. Had more economic theorists been raised in India or Saudi Arabia, where premarital
market transactions are ubiquitous, they would have possibly been more open to the idea
that conditions in markets for brides and grooms influence consumption or labor supply.
It is interesting that the earliest economic article on marriage markets is a published
note on premarital monetary transfers in India by Martin Bronfenbrenner, published in
the Journal of Political Economy in 1971.
3. This includes labor supply analyses by Johnson and Skinner (1986), Peters (1986),
Grossbard-Shechtman and Neuman (1988), Persson and Jonung (1997), GrossbardShechtman and Neideffer (1997), Van der Klaauw (1996), and Fortin and Lacroix
(1997) and investigations of earnings and marriage such as Kenny (1983), Korenman
and Neumark (1991), and Daniel (1995).
4. Becker’s (1973, 1974) theory of marriage also contains other models. See also Becker
(1991). That assumption of individual agency in consumption can also be found in
the marriage market models of Grossbard-Shechtman (1984), Lemennicier (1988), and
Cherry (1998); in the intra-marriage allocation models based on bargaining theories such
as Manser and Brown (1980) and McElroy and Horney (1981); in the intra-marriage
allocation models based on non-cooperative games of Wooley (1988) and Lundberg
and Pollak (1993); and in the more general intra-marriage allocation models of Apps
(1981), Bourguignon (1984), and Chiappori (1988).
5. The term “unitary” is found in many of Chiappori’s recent papers.
6. This includes most game-theory models and Blau et al. (1998, Chapter 3). Most of these
theories do not even justify the assumption of unitary household production functions
with any of the concepts that have been used to justify unitary utility functions, such as
altruism, authority, harmony, love, or biology.
7. This amounts to assuming that the supply of time of a household member who does not
participate in the labor force starts as a horizontal line set at the wage level. The supply
of time in household production then becomes vertical when the time constraint is met.
The reservation wage is determined at the intersection of the derived demand for the
household member’s time and the vertical time constraint.
8. Chiappori’s model follows most others models of intra-household allocation in assuming that all resources of time and income owned by individual household members are
automatically contributed to a household pool of resources. Also, see Browning et al.
(1994).
9. The sociological literature has also analyzed the effects of excess supply of men or
women (sex ratio effects) on the occurrence of marriage, divorce, cohabitation, labor force participation of women, and on marital fertility. See, for instance, Heer and
Grossbard-Shechtman (1981), Guttentag and Secord (1983), and Wilson (1987).
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10. Even though workers often become extremely committed to their firm, it is typically
assumed that not all their resources of time and income belong to the firm.
11. This wording was inspired by sociologist Coleman (1990, p. 580), who described the
family “as a system of action composed of purposive actors in action.”
12. This assumption is similar to the assumption of no caring in Becker (1991). One does not
expect much caring to be present at the pre-marriage stage, when the potential spouse
is an unknown stranger, and the analysis presented here also applies to unmarried
individuals considering marriage.
13. Elsewhere these goods have been termed household public goods (e.g., Manser and
Brown, 1980). The distinction between private and public goods in models of decisionmaking in marriage is also found in Wooley (1996) and Lundberg and Pollak (1993).
14. Other models incorporating the idea that a person works on the household production
of her spouse’s consumption include Lundberg and Pollak (1993), Wooley (1996), and
Cherry (1998).
15. I often get asked whether my ideas about compensation for WIM cannot be associated
with prostitution. My answer is that to the extent that sex is a favorite activity to both
spouses, it is not considered work. Also, since my focus is on heterosexual marriages,
the connotation of this question is that women supply sex to men in marriage. I prefer
to think about marital sexual relations in more mutual terms.
16. This idea can also be found in Blau et al. (1998, Chapter 3). Also, see Wax (1997).
17. Adding up the demand or supply for different tasks in household production also has
its equivalent concept in labor economics, jobs being typically composed of sums of
separate tasks performed by the same workers. Jobs obviously include tasks benefiting
the employer, i.e., the equivalent of WIM in this application to marriage. Some tasks
performed in firms can be categorized as WOC to the extent that all members of a
firm engage in the production of a good that is a commonwealth good to the firm (for
instance, the firm’s reputation and goodwill).
18. The problem of indeterminacy of more than one dimension of quantity at a time has its
analogue in labor economics (see e.g., Prachowny, 1997).
19. Dating may be a unique North American phenomenon. Most Europeans do not have
such a concept. There is no word for “dating” in many languages, including French,
Spanish, or Hebrew.
20. If statistics on the number of people searching for a marriage partner were available,
one could calculate the size of the marriage market by adding all those who are married
or searching for a marital partner, in a manner analogous to the definition of labor force.
This analogy also leads to the insight that non-participants in markets for WIM include
discouraged workers and discouraged users of WIM, in addition to those who were
never interested in either supplying or using WIM (possibly including WOC).
21. Among the differences between markets for WIM and regular labor markets are differences in size, the typical firm being larger than the typical monogamous marriage.
22. Such payments in-kind are not likely to be observed in egalitarian marriages that involve
mutual exchanges of Work-for-Marriage.
23. Allowances paid by husbands to wives were very common in the U.S. at the turn of the
20th century. Despite demands by some women’s groups at the time, they were never
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24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
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institutionalized. Political actions by women dealing with these issues, including efforts
to do away with the condescending term “spousal support,” have been documented by
Folbre (1994).
For an economic analysis of violence in marriage, see e.g., Rao (1998).
This difference between industrialized and non-industrialized countries is possibly related to the fact that marriages in less industralized countries are often arranged by
parents. It may also be related to more control of husbands over their wives (see
Lemennicier, 1988).
The high costs of dating to U.S. men may be explained in at least two ways. Pre-marriage
generosity may accurately reflect in-marriage generosity and indicate that U.S. women
obtain higher compensations for WIM than their European counterparts. Alternatively,
pre-marriage generosity may be used by men as a means to bribe women into marriages involving low quasi-wages for WIM. The latter reasoning is similar to one of
Becker’s (1991) explanation for the existence of pre-marital transfers such as
dowries.
The opportunity cost method is flawed because it ignores demand and the replacement
cost method is flawed because it ignores supply. The latter is more about the use-value
as defined by classical economists. See Grossbard-Shechtman (1999).
Covenant marriages have been recently introduced in Louisiana. They imply that spouses
give up their right to divorce.
A formal wage system did not start operating in non-marriage labor markets until capitalism developed. The fact that a formal quasi-wage for WIM system has never been
instituted could in part be a function of the traditionally limited political power of
Workers-In-Marriage (mostly women) in the West, where most market-related institutional innovations (including the wage system) were introduced.
To the extent that the model is applied to individuals who are already married, the spousal
wage may diverge from its market equilibrium value, e.g., as the result of inter-spousal
bargaining.
The use of the terms “micro foundations” and “market analysis” can also be found in
Cherry (1998).
Relaxing this assumption does not have far-reaching implications.
The model also leads to a demand for WIM contributed by a spouse, mj , and a supply of
labor hi . An extended model including utility from work can also lead to the derivation
of a supply of own WIM mj (see supply models in Section 4).
There may be some fixed costs of marriage, so that even if there is a positive demand for
WIM, marriage may not necessarily follow. If there are fixed costs, the consumer surplus
generated by demanding WIM needs to exceed the fixed costs of participating in WIM
markets and being married. A similar problem occurs when modeling employment. It
does not pay for a firm to have one worker employed for just a few hours if there are
fixed costs.
This elasticity of substitution is also assumed to be high relative to the elasticity of
substitution between product x and own time s.
It makes sense that a spouse’s time is a better substitute for the time of professional
services than is the case with own time.
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37. Barbara Bergmann, personal communication. Her observation is based on data she
collected with the help of students in the Washington, DC area. Some states, including
California, have banned gender-based price differentials in dry-cleaning services (see
also Cohen, 1999).
38. Women thus seem to get penalized twice by men’s unwillingness to do their wives’
laundry. First, women rarely have the option of relying on that form of help in the home.
Second, they may get charged more for commercial services if they go to the cleaners,
as a result of their lower elasticity of demand which in turn is partially explained by the
low levels of WIM that men supply.
39. I thank Ed Lazear for pointing this out.
40. According to Louis Levy-Garboua’s casual observations (based on a personal communication). An alternative explanation is that most cleaning services are supplied by
women and that they prefer to work for men.
41. Again, this assumes that sellers can take advantage of buyers’ less elastic demand. The
demand for frozen dinners aimed at children is also expected to be very price-elastic as
both mothers and fathers may possibly substitute for their children’s cooking activities.
42. See also Lundberg and Pollak (1993), Cherry (1998).
43. An analysis along these lines can be found in Grossbard-Shechtman and Keeley (1993).
44. This model shares some common features with Lundberg and Pollak (1993).
45. The elasticity of substitution may differ in the two models.
46. This follows Grossbard-Shechtman (1984), in turn a general equilibrium extension of
Grossbard (1976).
47. There may be some fixed costs of marriage, so that even if the demand for WIM is
positive, marriage may not necessarily follow. The same holds regarding the decision
to participate in the labor force.
48. An optimization model including two forms of work in the utility function will lead to
a modified equation and an occupation choice model. These results can be shown upon
request.
49. Controlling for other factors.
50. See Lundberg and Pollak (1993).
51. This effect of income on the supply of household products consumed in marriage has
been overlooked by previous models such as Gronau (1977), where neither individual
agency in marital consumption nor individual agency in marital production were taken
into account, and by bargaining theories assuming either unitary marital production
(e.g., McElroy and Horney, 1981) or no household production at all (e.g., Chiappori,
1992).
52. The effect of own income on j’s supply of WOC is not so clear, as discussed above.
The lower the ratio of WOC in WIM, the more one expects that income will reduce the
supply of j’s WIM. Income changes may also have an impact on the nature of the long
run weight of WOC in the WIM exchanged in a representative marriage resulting from
particular marriage market circumstances.
53. See for instance, the imposition of marriage bars in the U.S. (Goldin, 1990) and Japan.
On this topic, see Folbre (1994). Restrictions on women’s labor force participation
currently enforced in Afghanistan are another case in point.
S. Grossbard-Shechtman / Journal of Socio-Economics 31 (2003) 609–645
639
54. It also helps explain why Italians marry late compared to most other Europeans.
55. The other European countries were Austria, Belgium, Finland, France, West Germany,
The Netherlands, Norway, Spain, and the U.K. See United Nations (1987).
56. Possibly due to of the influence of the Catholic Church. Belgium, another Catholic
country, also has high saving rates.
57. The correlation between sex ratios, polygamy, dowry, and bridewealth (a pre-nuptial
payment by the groom) has been discussed e.g., by Grossbard (1978) and Rao (1993).
58. The distinction between specific and general human capital (H.C.) was introduced by
Becker (1964). If H.C. is general, the human capital of individual Workers-In-Marriage
is portable. See also Becker et al. (1977), Lehrer (1990, 1995), and Hamilton (1999).
59. Differences in the age at marriage of men and women are an interesting phenomenon
that economists have also tried to explain. For instance, Bergstrom and Bagnoli (1993)
and Danziger and Neuman (1999).
60. John Treble contributed this reference.
Acknowledgments
Helpful inputs were contributed by Gary Becker, Barbara Bergmann, Eric Brunner, Christopher Clague, Edward Lazear, Bertrand Lemennicier, Louis Levy-Garboua, Gary Ramey, JeanMarc Robin, Joel Sobel, John Treble, participants at a session organized by the Society for
Advancement of Behavioral Economics (Boston in 2000), and participants at seminars at the
University of California, San Diego and York University, Toronto. The assistance of Michael
J. Bacci is greatly appreciated.
Appendix A
A.1. Derivation of D1 in the WIM1 model
Eq. (2) is a derived demand for input x. In this model, it is assumed that an individual derives
utility from only one home-produced good Z and that x, commercially purchased good, is one
input in the production of Z. Z can also be produced with two time inputs: own time (s) and
spouse’s WIM (m). Problem WIM1 is defined as
Max U(Z) subject to Z = Z(x, s, m), the production function,
1 = h + s,
I + wh = ym + px.
The individual obtains income from work h and from non-work sources. The individual
uses his income to purchase commercial goods x or WIM from a spouse. Prices for x, s, and
m are given and are p, w, and y, respectively. It is assumed the production function exhibits
constant returns to scale.
Step 1: The real full income effect on the demand for a product. Assume ΠZ = F(Π), where
F is full income and Π is the implicit price of Z. Let us take the differential of this equation:
dF = Π dZ + Z dΠ.
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S. Grossbard-Shechtman / Journal of Socio-Economics 31 (2003) 609–645
We now divide each side by F:
dF
Π dZ Z dΠ
=
+
.
F
ΠZ
ΠZ
Denoting percentage changes by dots, we obtain:
˙ or Ż = Ḟ − Π.
˙
Ḟ = Ż + Π,
(A.1)
Step 2: Separating the full income effect into an effect of income and wage. We now do
compose the full income component of the derived demand for home-produced good Z. Let
us assume there are two sources of income: non-work income I and wages w.
F = I + w.
We differentiate:
dF = dI + dw.
We divide both sides by F:
dF
I dI
w dw
I
w
=
+
, or F˙ = İ + ẇ .
F
F I
Fw
F
F
(A.2)
Step 3: Decomposing the implicit price effect. In step 1 we saw that Ż, the demand for Z, is
a function of the proportional change in Π̇, the price of household production. We assume that
this price is the average cost, an assumption consistent with the assumption that the production
function exhibits constant returns to scale (the marginal cost equals the average cost). We have
TC
ws + px + ym
=
.
Z
Z
We take the differential
s dw x dp m dy
dΠ =
+
+
.
Z
Z
Z
We then divide by Π
AC = Π =
dΠ
s dw x dp m dy
=
+
+
.
Π
ΠZ
ΠZ
ΠZ
Now ΠZ = C. We also divide and multiply dw by w, dp by p, and dy by y. Consequently
dΠ
sw dw px dp my dy
=
+
+
,
Π
C w
C p
C y
which we denote as
Π̇ = αs ẇ + αx ṗ + αm y,
˙
(A.3)
where αj is the share of input j in the costs of production. We now replace Π in Eq. (A.1) by
using Eq. (A.3), and we replace F by using Eq. (A.2). Thus,
I
w
˙
(A.4)
Ż = I˙ + w
˙ − αs ẇ − αx ṗ − αm y.
F
F
S. Grossbard-Shechtman / Journal of Socio-Economics 31 (2003) 609–645
641
Step 4: Derived demand for input x. It was assumed that the production function has constant
returns to scale. Consequently, the scale effect is separable from an effect of substitution in
production. The elasticity of substitution in production is defined between two factors of
production. The first elasticity of substitution of interest is that between x (commercial goods)
and m (spouse’s WIM), i.e., σ xm . It is defined as the percentage change in use of input x relative
to m as a result of a percentage change in the marginal rate of technical substitution between x
and m. If the individual is in equilibrium, the marginal rate of substitution is equal to the ratio
of input prices and the demand for an input can be expressed in terms of percent changes in
the prices of x and m. The second elasticity of substitution of interest is that defined between
x and s (own time). It can be shown that when the production function has constant returns to
scale (I thank H. Greg Lewis for this).
˙
ẋ = Ż − (αs σxs + αm σxm )ṗ + αs σxs ẇ + αm σxm y.
(A.5)
Step 5: Combining steps 3 and 4. Eq. (A.5) includes a percentage change in production, Ż.
We now replace Ż in (A.5) with Eq. (A.4). By combining terms we obtain equation (D1 ) in
the text.
Appendix B. Obtaining a demand for commercial goods; the case of two
home-produced goods
Step 1: Full real income effect. Define the income elasticity of demand for home-produced
good Z, as
η1F =
˙1
Z
¯
Ḟ − Π̇
.
This elasticity is defined with respect to full real income and the price level Π̄ is based on
the implicit prices of both home-produced goods.
˙¯ .
Re-arranging terms gives Ż1 = η1F (Ḟ − Π)
Replacing Π̄ by its components gives
¯ = k1 Π̇1 + k2 Π̇2 ,
Π̇
where k1 and k1 are defined as Z1 Π1 /F and Z2 Π2 /F ; i.e., the shares of Z1 and Z1 in full
income. Ż1 becomes
Ż1 = η1F Ḟ − η1F k1 Π1 − η1F k2 Π2 .
Step 2: The effect of substitution in consumption. Define the elasticity of substitution in
consumption as the percentage change in consumption of Z2 relative to Z1 divided by the
percent change in relative prices, i.e.,
σC =
percentage change in Z2 /Z1
.
percentage change in Π1 /Π2
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S. Grossbard-Shechtman / Journal of Socio-Economics 31 (2003) 609–645
Therefore,
Ż2 − Ż1 = σC (Π̇1 − Π̇2 ).
(B.1)
Full income is spent as follows: F = Z1 Π1 + Z2 Π2 .
Consequently,
Z 2 Π2
Z1 Π1
Ż1 +
Ż2 = k1 Ż1 + k2 Ż2
F
F
percentage change in Ż1 /F = Ż1 − Ḟ = Ż1 − k1 Ż1 − (1 − k1 )Ż2
= (1 − k1 )(Ż1 − Ż2 ) = −(1 − k1 )(Ż2 − Ż1 ).
Ḟ =
The last term can be expressed in terms of elasticity of substitution using B.1; and therefore
Ż1
= −(1 − k1 )σC (Π1 − Π2 )
(B.2)
F
Step 3: Combining steps 1 and 2. The left-hand side of Eq. (B.2) is the percentage change
in Z1 in proportion to F, full real income.
We can re-write percentage change in Ż1 /F as Ż1 minus η1F Ḟ and move the latter term to
the right-hand side.
Step 4: Demand for Z1 in terms of input prices. We now decompose Π̇1 and Π̇2 into their
components to Appendix A:
percentage change in
˙
Π̇1 = α1x ṗ1 + α1m ẏ + α1s w,
2
Π̇2 = α2x ṗ2 + αm
ẏ + α2s w.
˙
We now combine the real full income effect and substitution effect on Z1 and obtain
I
1
I˙ − [(1 − k1 )σC + η1F k1 ] − α1x − [(1 − k1 )σC + η1F k1 ]αm
F
+ (1 − k1 )(σC − η1F )α2m y˙
w
+ η1F − [(1 − k1 )σC + η1F k1 ]α1s + (1 − k1 )(σC − η1F )α2s ẇ
F
+ (1 − k1 )(σC − η1F )α2x ṗ2 .
˙ 1 = η1F
Z
Step 5: The demand for input x. Now we use Eq. (A.5) from Appendix A to get the effect
of substitution in the production of Z1 , and we replace Ż, by the expression above. We obtain
I
1
σxm ]ṗ1 − (η1F − σC )k2 α2x ṗ2
ẋi1 = η1F I˙ − [(η1F k1 + σC k2 )α1x + αs1 σxs + αm
F
w
+
− (η1F k1 + σC k2 − σxs )α1s − (η1F − σC )k2 α2s ẇ
F
− [(η1F k1 + σC k2 − σxm )α1m + (η1F − σC )k2 α2m ]y.
˙
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