A Treatise on the Family

Enlarged Edition

Gary S. Becker

• Publisher: Harvard University Press
• Year: 1993
• Print ISBN:
  9780674906990
  9780674906983
• eBook ISBN:
  9780674252332
• Topic: Economics
• Subtopic: Economic Theory
• Index: Economics

Imagine each family as a kind of little factory—a multiperson unit producing meals, health, skills, children, and self-esteem from market goods and the time, skills, and knowledge of its members. This is only one of the remarkable concepts explored by Gary S. Becker in his landmark work on the family. Becker applies economic theory to the most sensitive and fateful personal decisions, such as choosing a spouse or having children. He uses the basic economic assumptions of maximizing behavior, stable preferences, arid equilibria in explicit or implicit markets to analyze the allocation of time to child care as well as to careers, to marriage and divorce in polygynous as well as monogamous societies, to the increase and decrease of wealth from one generation to another.

The consideration of the family from this perspective has profound theoretical and practical implications. For example, Becker's analysis of assortative mating can be used to study matching processes generally. Becker extends the powerful tools of economic analysis to problems once considered the province of the sociologist, the anthropologist, and the historian. The obligation of these scholars to take account of his work thus constitutes an important step in the unification of the social sciences.

A Treatise on the Family will have an impact on public policy as well. Becker shows that social welfare programs have significant effects on the allocation of resources within families. For example, social security taxes tend to reduce the amount of resources children give to their aged parents. The implications of these findings are obvious and far-reaching. With the publication of this extraordinary book, the family moves to the forefront of the research agenda in the social sciences.

CHAPTER 1

Single-Person Households

The traditional theory of consumer and household behavior developed by economists ignores cooperation and conflict among members, in essence assuming that each household has only one member. This theory focuses on the effects of changes in money income and money prices on the allocation of income among market goods. The theory of single-person households has been greatly expanded during the past twenty years, from a rather limited analysis to a powerful tool with many applications. The new analysis includes allocation of time as well as of money income and introduces household production of skills, health, self-esteem, and various other “commodities.”

This short chapter outlines the traditional theory and its recent enlargement as a preparation for the discussion of families in the rest of the book. There is now a sizable amount of relevant literature; interested readers are referred to Michael and Becker (1973) for a more elaborate discussion.

Traditional Theory

In the simplest version of traditional theory, a single person spends his (or her) given income to maximize his utility function U of goods and services (for simplicity, called “goods”) purchased in the marketplace. That is, he maximizes the function

subject to the budget constraint Σp_ix_i = I, where p_i is the price of the ith good x_i, and I is his money income. The well-known equilibrium condition is that the marginal utility MU of each good is proportional to its price:

where λ is the marginal utility of income.

The main implication of these equilibrium conditions is that the quantity demanded of any good is negatively related to its price: the “law of negatively sloped demand curves.” This law has been extremely important in practical applications and is one of the most significant and universal laws in the social sciences, even though it results more from limited resources than from utility maximization (Becker, 1962).

A rise in income increases the demand for most goods because the additional income must be spent, where “spent” includes adding to cash balances and other assets. The equality between total expenditures and income implies that

where η_i = [(dx_i)/(dI)] · (I/x_i) is the income elasticity of demand for the ith good, and s_i is the fraction of income spent on that good. The average income elasticity equals unity, so that “luxuries” (η_i > 1) must be balanced by “necessities” (η_i < 1).

A more complicated and more realistic version of the theory recognizes that each person allocates time as well as money income to different activities, receives income from time spent working in the marketplace, and receives utility from time spent eating, sleeping, watching television, gardening, and participating in many other activities. The utility function, Eq. (1.1), then is extended to

where t_hj. is the time spent at the jth activity. A time-budget constraint joins the money-income constraint:

where t is the total time available during some period, such as 24 hours a day or 168 hours a week, and t_w is the time spent working for pay.¹

One important implication of this extension is that money income is no longer “given” but is determined by the allocation of time, inasmuch as earnings are determined by the time allocated to work. Therefore, the goods and time-budget constraints are not independent and can be combined into one overall constraint:

or

where w is the earnings per hour of work, v is property income, and S is “full” or potential income (or the money income when all time is allocated to the market sector). The terms on the left show that full income is spent in part directly on market goods and in part indirectly on the time used to produce utility rather than earnings.²

The equilibrium conditions from maximizing the utility function (Eq. 1.4) subject to the full-income constraint, Eq. (1.7), include

The marginal utility from all uses of time are equal in equilibrium because they have the same price (w), and the marginal rate of substitution between time and each good equals the “real” wage rate, where the price deflator is the price of that good.³

The main implications of these equilibrium conditions are generalizations of the negatively sloped demand curves derived with the simpler model. A compensated rise in the price of any good—a rise offset by a sufficient rise in property income to keep real income constant—reduces the demand for that good and increases the demand for “most” other goods. It also reduces the time spent at work and increases the t...

Table of contents

• Cover
• Title
• Copyright
• Dedication
• Contents
• Preface to the Enlarged Edition
• Introduction
• 1 Single-Person Households
• 2 Division of Labor in Households and Families
• 3 Polygamy and Monogamy in Marriage Markets
• 4 Assortative Mating in Marriage Markets
• 5 The Demand for Children
• 6 Family Background and the Opportunities of Children
• 7 Inequality and Intergenerational Mobility
• 8 Altruism in the Family
• 9 Families in Nonhuman Species
• 10 Imperfect Information, Marriage, and Divorce
• 11 The Evolution of the Family
• Bibliography
• Index