英文贝克尔一种婚姻理论1Becker_1973 A Theory of Marriage Part 1

A Theory of Marriage: Part I Gary S. Becker The Journal of Political Economy, Vol. 81, No. 4. (Jul. - Aug., 1973), pp. 813-846. Stable URL: http://links.jstor.org/sici?sici=0022-3808%28197307%2F08%2981%3A4%3C813%3AATOMPI%3E2.0.CO%3B2-4 The Journal of Political Economy is currently published by The University of Chicago Press. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/ucpress.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers, and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community take advantage of advances in technology. For more information regarding JSTOR, please contact support@jstor.org. http://www.jstor.org Mon Sep 10 07:31:40 2007 Journal of Political Economy Volume 81 Number 4 July/August 1973 Articles A Theory of Marriage: Part I Garq' S. Becker Stabilization Policy and Lags Stanley Fischer and J . Phillip Cooper The Specification of Technology with Several Kinds of Output Robert E. Hall Currency Depreciation, Hoarding, and Relative Prices Rudiger Dornbusch Policy CIhoices in an Open Economy: Some Dynamic Considerations Sven W. Arndt The Expansion of Firms Paul H. Rubin Profit Maximization and the Extinction of Animal Species Colin W. Clark Communications A Model of Imported Inflation Yoichi Shinkai The Effect of Konneutral Taxation on the Use of Capital by Sector David J. and Attiat F. Ott Investment and C:orporate Taxation M. T. Sumner The Effects of Property Taxes and Local Public Spending on Property Values Comment by I-lenry 0. Pollakou,ski Reply by Wallace E. Oates A (:PI-Futures Market Michael C. Love11 and Robert C. Vogel 1013 Denison and the Contribution of Education to National Income Growth: A Comment P. R. G. Lajard Miscellany 1017 Lt'hdt Economists Think of Their %Journals Robe~t G Haztkzns, Lazcrence S . Rztte~, and Ingo Il'alter 1033 A Milton Friedman-Sir Dennis Robertson Correspondence 1040 Book Reviews Jagdish Bhagwati et al., eds., Trade, Balance of Payments and Growth: Papers in International Economics in Honor of Charles P . Kindelb~rger Anne 0.Krueger William Breit and Roger L. Ransom, The Academic Scribblers: American Economists in Collision Kenneth E . Boulding Albert 0. Hirschman, Exit, L'oice, and Loyalty: Responses to Decline in Firms, Organizations, and States Joe D. Reid, Jr. Norman Jacobs, 12fodernization without Det'elopment: Thailand as arz Asian Case Study T. H. Silcock Gustav Ranis, ed., Got'ernment and Economic Deoelopment S. G. Triantis Theodore M:. Schultz, Investment in Human Capital Ray Richardson A Theory of Marriage: Part I Gary S. Becker l,izi~.ersi!p o f Ct~icago nnd Xational Bureau o f Econo7rlic Research I present in this paper the skeleton of a theory of marriage. T h e two basic assumptions a re that each person tries to do as well as possible and that the "marriage market" is in equilibrium. IVith the aid of s e ~ e r a l additional simplifying assumptions, I deri\-e a number of significant implications about behavior in this market. For example, the gain to a man and woman from marrying compared to remaining single is show11 to depend positively on their incomes, human capital, and relative diffcrence in wage rates. The theory also implies that men differing in physical capital, education or intelligence (aside from their effects on wage rates), height, race, or many other traits will tend to marry women with like values of these traits, whereas the correlation between mates for wage rates or for traits of men and women that a re close substitutes in household production ~vi l l tend to be negative. T h e theory does not take the di\-ision of output between mates as gi\-en, but rather derives i t from the nature of the marriage market equilibrium. The division is deter- mined here, as in other markets, by marginal productivities, and these are affected by the human and physical capital of different persons, sex ratios (that is, the relative numbers of men and omen), and some other variables. 1. Introduction In recent years, economists have used economic theory more boldly to explain behavior outside the monetary market sector, and increasing numbers of noneconomists have been follo\ving their examples. As a result, racial discrimination, fertility, politics, crime, education, statistical Submitted for publication October 1, 1972. Final version received December 2 1, 1972. I have benefited from the discussion of several earlier drafts at the IVorkshop in Applications in Economics of the University of Chicago and in seminars at the National Bureau of Economic Research, North~vestern University, and the Population Council. Very helpful comments were received from H. Gregg Le~vis, Gorge J. Stigler, T. \V. Schultz, iVilliam Brock, hIarc Nerlove, .Alan Frieden, and two referees. Michael Keeley provided valuable research assistance. Lly research has been supported by the National Bureau of Economic Research but this paper is not an official SBER publication since it has not been reviewed by the SBER board of directors. 814 JOURNAL OF POLITICAL ECOXOklY decision making, adversary situations, labor-force participation, the uses of "leisure" time, and other behavior are much better understood. Indeed, economic theory may well be on its way to providing a unified framework for all behavior involving scarce resources, nonmarket as well as market, nonmonetary as well as monetary, small group as well as competitive. Yet, one type of behavior has been almost completely ignored by economists,' although scarce resources are used and it has been followed in some form by practically all adults in every recorded society. I refer to marriage. Marital patterns have major implications for, among other things, the number of births and population gro\vth, labor-force participa- tion of women, inequality in income, ability, and other characteristics among families, genetical natural selection of different characteristics over time, and the allocation of leisure and other household resources. Therefore, the neglect of marriage by economists is either a major over- sight or persuasive evidence of the limited scope of economic analysis. In this essay, it is argued that marriage is no exception and can be successfully analyzed within the framework provided by modern econornics. If correct, this is compelling additional evidence on the unify- ing power of economic analysis. Two simple principles form the heart of the analysis. The first is that, since marriage is practically always voluntary, either by the persons marrying or their parents, the theory of preferences can be readily applied, and persons marrying (or their parents) can be asslumed to expect to raise their utility level above what it would be were they to remain single. The second is that, since many men and women compete as they seek mates, a market in marriages can be presumed to exist. Each person tries to find the best mate, subject to the restrictions imposed by market conditions. These two principles easily explain why rnost adults are married and why sorting of mates by wealth, education, and other characteristics is similar under apparently quite different conditions. Yet marital patterns differ among societies and change over time in a variety of ways that challenge any single theory. In some societies divorce is relatively com- mon, in others, virtually impossible, and in Western countries it has grown rapidly during the last half-century. Some societies adjust to legal difficulties in receiving divorces by delaying marriage, whereas others adjust by developing more flexible "consensual," "common-law," or "trial" marriages. I n many the bride brings a dowry, in others the groom pays a bride-price, and in still others couples marry for "love" and disdain any financial bargaining. In some the newly married usually set up their own household, in others they live with one set of parents. ' To the best of my knowledge, the only exception prior to my own work is an un- published paper by Gro~lau (1970). His paper helped stimulate my interest in the subject. A THEORY OF MARRIAGE 815 I do not pretend to have developed the analysis sufficiently to explain all the similarities and differences in marital patterns across cultures or over time. But the "economic" approach does quite well, certainly far better than any available a l t e r n a t i ~ e . ~ I t is hoped that the prcsent essay will stimulate others to carry the analysis into these uncharted areas. Section 2 considers the determinants of the gain from rnarriagc com- pared to remaining single for one man and one woman. The gain is shown to be related to the "compatibility" or "complementarity" of their time, goods, and other inputs used in household production. Section 3 considers how a group of men and women sort themselves by market and nonmarket characteristics. Positive assortive mating-a positive correlation between the values of the traits of husbands and wives -is generally optimal, one main exception being the sorting by the earn- ing power of men and women, wllcre a negative correlation is indicated. Empirically, positive assortive mating is the most common and applies to I Q , education, height, attractiveness, skin color, ethnic origin, and other characteristics. Section 4 considers how the total output of a household gets divided between the husband and wife. The division is not usually fixed, say at 50-50, or determined mechanically, but changes as the supply of and demand for different kinds of matcs changes. Part 11, to be published in a later issue of this Journal, dcvclops various extensions and modifications of the relatively simple analysis in this part. "Caring" is defined, and some of its effects on optimal sorting and the gain from marriage are treated. The factors determining the incidence of polygamous marital arrangemcnts are considered. The assumption that the charactcristics of potential mates are known with certainty is dropped, and the resulting "search" for mates, delays in marriage, trial marriage, and divorce are analyzed. Divorce and the duration of marriage are also related to specific investments made during marriage in the form of children, attachments, and othcr wavs. We also brieflv explore the implications of different marital patterns for fertility, genet- ical natural selection, and the inequality in family incomes and home environmcnts. 2. The Gain from Marriage This section considers two persons, ,Cf and F, who must decide whether to marry each other or remain single. For the present, "marriage" simply means that they share the same household. We assume that Some of the best work has been done by Goode (1963), but there is no systematic theory in any of his fine work. 8 I 6 JOURNAL OF POLITICAL ECOXOMY ~narriagcoccurs if, and only if, both of them are made better off-that is, increase their ~ t i l i t y . ~ Following reccnt developments in the theory of household behavior, xvc assume that utility dcpcnds directly not on tlic goods and services p~lrchased in the market place, but on the commoditie.; produccd "by" cacli household." They arc produccd partly xvith market goods and services and partly xvith the own tinlc of different liouschold members. llIost important for present purposes, con~moditics arc not marketable or transferable among households, although they may bc transferable alnong nienlbcrs of the same household. Household-produced commoditie~are numerous and include the quality of rncals, tlic quality and quantity of children, prestige, recreation, cornpanionship. loarc, and health status. C:onscqucntly, they cannot be identified with consumption or output as usually ~ilcasurcd: they cover a much broader range of liuman actiaitics and aims. We assurne, howearer, that all colnmodities can be combined into a singlc aggregate, denoted by Z. A suflicicnt condition to justify aggregation with fixed weights is that all conilnoditics have constant returns to scale, use factors in the same proportion, 21nd are affected in the same way by productivity-augmlenting varial~les, such as cducatio~i. Then different commodities could be converted into thcir equivalent in terms of any singlc commodity by using tlie fired relative conlmodity prices as weights.' Tlicsc weights xvould be indepcndcnt of tlic scale of conimodity outputs, the prices of goods and the time of different mcnlbcrs, and the level of productivity. SIaxirriizing utility thus becomes equivalent for each person to maximiz- ing the arnount of Z that he or shc receives. Moreover, our concentration on tlie o~l tput and distribution of Z does not presuppose transferable utilities, tlic salric preference function for different members of the same household, or otlicr special assumptions about prcfcrcnccs. Each household has a production function that relates its total output of Z to different inputs : where tlie ,xiare various rriarkct goods and services, the t j are the time hiore prcciscly. if they expect to increase their utility, since the latter is not knolvn with certainty. Pal t I1 discusses some co~~sequcnces of this uncrrtair~ty, especially for the tilnc spent searching for an appropriate mate and the incidence of divorce and other marital separations. " :In exposition of this approach is given in Rlichael ancl Beckcr (1'372). 0 n r serious lirllitation of thesr assurllptions is that they exclude thc output of com- tnoditie5 from entering the production filnctions of other cornnloclities. \Vith such "'joint productlon," thy relative pricc of a commodity \voulcl depend partly on the outputs of' other comrnoditics (Grossman 1971). Joint production can result in compleme~~tari ty in consurnptio~~, ancl thereby affect thc gain from marriage and the sorting of' mates. See the brirf'cliscussion in section 3. 817 A THEORY OF MARRIAGE inputs of different household members, and E represent5 "environmental" variables. Thc budget constraint for the ,z, can be written as: CW I p,.xi = Ch Zejlj + i'. \vhrre n, is the w,!ge rate of the j th member, 1, the time he spends working in the market sector, dnd LI proprrtb income. ' rhc 1, and tJ are related b? the bas~c time constraint l j + t , = T all j , (3) \vhrsc T is the total time of each member. By substituting equation (3) into (21, the goods and time co~lhtraints can be combined into a single " f~~ l l "income constraint : ~vlirreS stands for full income, the maximum money incon~e acliieval~le, if the z i , j arc constants. il'e assume tliat a reduction ill the household's total output of Z makes no rncnlber better off and some worse off.' Consequently, each n~einbcr lvould be willing to cooprrate in the allocation of his tinlr and goods to lielp ~nasirrlize the total output oS Z. Xeccssi~ry conditions to mazirnizc Z include If tlie liouscliold time of t l ~ c kth menll)er = T,then \vl~cre 2 z t i, is tllc "sl~adoit" piice of tlie time oS k. .Mso Lac11 11len111er must coo1)crate and allocate 1115 time 11et\\ec11 the i l~arket ,ind nonn~,irkct sec tors in the appropriate pr opor t~ons . I f .\Iand 1: are mar1 icd. their lio~~scllold theis assunled to contain o n l ~ t\vo tililc inputs /,, and i, ; for simplicity, tile tirrle of children and others living in tlie same hor~schold is ignored. As long ar they remain rnarricd, T,,,= T,.= 24 hours per day, 168 Iiours per iveck, and so forth, and conditio~ls(5) to ( 7 ) dcterminc tllc- allocation of the time of J I and F I~ct\vccn the ~na rk r t and nonrnarket hectors. hlorc time ~vould I,e allocated to the ~ i i ;~ rke t 1.' (less to tlic nonrnarket sector) if scctor 11y L\Ithan 1))- Thih ahsumption is tnodificcl i11 scction 3 ancl i11 Part 11. 8I 8 JOURNAL OF POLITICAL ECONOMY zr,,, > z t , , \\.hen tf t,,. Indeed, F \\~ould specialize and if .ZfPtI2 .LIPtn, = in the nonmarket sector ( I , = ,bIP,,/LCfP,m0) if either i i ' , / ~ t ~ ~ or were sufficiently large. X singles household is take11 to be exactly the same as a married one except tliat Tf = 0 when .\I is single and T,,= 0 when F is single. -4 singles household allocates only its own time between the market and nonrnarket sectors to satisfy equation (7). Single persons generally allocate their time differently than married persons because the former do not have tiiiie and goods supplied by a rnate. These differences depend partly on the elasticities of substitution among the xi, t,, and t,, and partly on the differences between the market wage rates w,, and ui,. For example, single F are more likely to "work" more than married F and single M less than married ,\I, the greater the percentage excess of w,,over w,. Empirically, single women clearly "work" more than married women and single men less than married men.' If Z,,, and Z,, represent the maximum outputs of single M and F, and ni,,, and A,,, their incomes when married, a necessary condition for .\Iand 1; to marry is that If nl,,,, + A,,, the total income produced by the marriage, is identified \vitli the output of the marriage,' a necessary condition for marriage is then that Since most rricn and women over age 20 are married in all societies, cquation (9, must generally hold because of fundamental reasons that are not unique to time or place. \l-e have a useful framework for discover- ing thesc reasons. The obvio~~s explanation for marriages between men and women lies in the desire to raise own children and the physical and emotional attraction between sexes. Nothing distinguishes married households more from singles households or from those with several members of the same sex than the presence, even indirectly, of children. Sexual gratifica- tion, cleaning, feeding, and other services can be purchased, but not own ~ h i l d r e n : ~both the man and woman are required to produce their own children and perhaps to raise them. The physical and emotional involve- ment called "love" is also primarily between persons of the opposite sex. 'See, e.g., Bizplojment Status and Cf i rk Experience (U.S., Bureau of the Census 1963), tables 4 and 12. * Income and output can differ, howcver, because some output may be jointly con- sunled. See the discussion in section 3 and Part 11. The market in adoptions is used primarily by couples experiencing difficulties in having their o\vn children and by couples paid to raise other persons' children. 819 A THEORY OF MARRIAGE Moreover, persons in love can reduce the cost of frequent contact and of resource transfers1 between each other by sharing the same household. Economies of scale may be secured by joining households, but two or more males or females could equally well take advantage of these economies and do so