4. Formation of Families

See, for example, Dawkins (1976).

Under the present technologies, the marriage of a man and a woman is no longer necessary for a baby to be born. Can these technologies solve the problems of the low fertility in developed countries?

For example, creation and prohibition of chances for matchmaking, contraception, and abortion were traditionally available means to control births. Due to the technological progress in contraception and fertility treatment, the controllability of the number of children has been greatly improved in recent times. The impact of technological progress in birth control on our society is immense.

Such a motivation may sound that we will have a child just to increase our own level of satisfaction. However, it also corresponds to the motivation that our genes incite in us to nurture their ancestors by giving us joy in raising our children. Many people say that they want to have children because they think it is natural, which we regard as one of the motivations for the consumption-purpose (c.f. Fig. 8.​2) because they feel better by having children.

Having children by such a motivation is sometimes referred to as “old-age security hypothesis.” There are very few species that expect their children to support their lives after they are no longer able to get food. In many species, “adults” actually die soon after they give birth to children. Although having such expectation from our children to support them after we have no reproductive ability may sound very selfish, it may not be so because it may be one of the reasons why human beings, as a species on the earth, have survived for so long time. Unlike other species, our decisions, including ones on marriage and children that are critical for the survival of our genes, are critically dependent on intelligence and wisdom which accumulate as we live longer and can be transferred by “words” to the next generations. Our living longer with the support of our children may contribute to the survival and their spread. See Chap. 5 for more discussion on intergenerational transfers, that is, interactions between parents and children.

This real number of children here can be seen as the average number of children in one generation in a more sophisticated model with heterogeneous individuals or uncertainty.

In economics, there are many researches that explicitly analyze the bargaining and strategic games between a husband and a wife over resource allocation that affect the female’s decisions on children and labor participation. See, for example, Lundberg and Pollak (1996), Persson and Jonung (1997) and Bergstrom (1997). In Sect. 4.3, we also demonstrate a model in which bargaining and interactive decisions of couples are explicitly considered.

For the goods required to raise a child, we can think of composite goods and services that include foods, clothes, nursery services, and education for each child.

See Sect. 3.​2.​2.

The Langrange multiplier represents the marginal utility of income, that is, an increase in utility caused by an increase in one unit of income. Hence, the value of marginal utility \(U_c\) divided by the Lagrange multiplier (\(\lambda \)) can be interpreted as the monetary value of marginal utility from consumption.

The mathematical symbol \(\equiv \) here means “defined by”.

This is not the only case when the female wage increases. Although the increase in the female wage has a negative substitution effect, it can have a positive income effect on the number of children allowing the couple to raise more children. Hence, higher education of women need not entail a decline in fertility. See Remark 3.​2 for the explanation on substitution effect and income effect.

See, for example, Willis (1973), Becker and Lewis (1973) and Lundholm and Ohlsson (2002).

Considering the effects in a diagram with N and Q as the horizontal and vertical axes may be useful for understanding the argument.

The model here is based on Apps and Rees (2004).

The argument and results here are based on Apps and Rees (2004, Proposition 3). In general, an increase in the number of children is expected to increase women’s time for raising children. However, if the number of children is increased as a result of an increase in the goods for raising children, and not the increase in the time for children, there will be a rise in the tax revenue that can be used to increase the subsidy for families. Needless to say, the increase in the number of children will, in general, increase the future tax revenue, and thus the effects of such policy can be even larger if we consider the long-run effects.

There are many researches on marriage contracts and legal issues of divorces from the viewpoints of contract theories. For example, see Rowthorn (1999), Chiappori et al. (2002) and Weiss and Willis (1985).

See Sect. 3.​3.​2 for backward induction to solve a sequential game.

For example, housewives and househusbands who accumulate knowledge and ability that are valuable mainly for their spouses and children, that is, make relation-specific investment in human capital, will face low possibility of finding a good job in the labor market after divorce. Hence, the bargaining powers of the housewives and househusbands in their marriages are generally low, which may result in domestic violence and moral harassment in marriage. One of the reasons that many Japanese women obtain higher education even if they prefer to be housewives may be to gain bargaining power in the marriage by raising the conditions at divorce.

Notice that an increase in the expected utility from not getting married \(u^0_i\) will decrease the marriage rate. For example, an increase in social security payment or an development of the market economy will raise \(u^0_i\) and thus will lower the marriage rate and the fertility rate.

It is calculated to be \(p^*_i = {\theta _i V(I^*_1, I^*_2) - u^0_i \over (\theta _i - \gamma ^D_i \pi _i)V(I^*_1, I^*_2)}\).

Here, we basically consider the investment in the quality and quantity of children. As examples of investment in the quality of children, we can think of the money spent on the children’s education as well as the time spent with the children.

We assume \(C^L_i< \bar{C}_i < C^H_i\).

For example, there are special child allowances and tax measures for single mothers in Japan.

Needless to say, lowering female wages and public support for single mothers, which raises the cost of divorce, can contribute to lowering the divorce probability and raising the number of children. Such policies may not be desirable in Japan if we consider other policy goals. For example, see Bougheas and Georgellis (1999) for analyses of the effects of increase in divorce cost on marriage and divorce rates.

Despite such conjecture, the number of marriages after couples found to have their babies is increasing in Japan. Our model suggests that having babies before the couples engage in a marriage contract is a risky behavior, especially for women. Traditionally, women have been expected to avoid such behavior because there are high risks of getting an abortion or becoming a single mother. One can explain such behavior as a strategy to get a good partner in the competition among women under the social norm that children must be raised by married couples. Another explanation may be that the cost of such behavior has been lowered in modern societies where the cost of “out-of-wedlock childbearing” is lowered by the increase in social and public support for single mothers and the decrease in the stigma associated with it. For example, see Willis (1999) and Akerlof et al. (1996) for economic analysis of “out-of-wedlock childbearing”.

For example, see Clark (1999) and Smith (2003) for the analyses of marriage contracts from the perspective of law and economics.

The review of literature includes well-known studies such as Keely (1977), Pollak (1985), Cigno (1991), Grossbard-Shecktman (1993), Bergstrom (1997), Weiss (1997), Ermisch (2003), and Bryant and Zick (2006, Chap. 8).