Chayanov revisited: A model for the economicsof complex kin unitsE. A. Hammel*Departments of Demography and Anthropology, University of California, Berkeley, CA 94720Contributed by E. A. Hammel, March 24, 2005Chayanovsmodelofthepeasanteconomyisbasedonautarkicnuclear family households. Expansion to the more complex house-holds and kin groups common in peasant societies shows that thesharp changes Chayanov observed in the consumerproducer ratiooverthedomesticcyclearesmoothedbytheintergenerationalstructureofcomplexhouseholdsandextendedkingroups. Thisamelioration may be retarded by competition between constituentunits. Understanding the dynamics of the developmental cycle andmicropoliticsofdomesticgroupsisauseful correctiontoChay-anovs widely used formulation, especially in developing countrieswhere complex kin structures are common.economy household peasantsThe prominent theoretical model of the economics of peasanthouseholdsisthatadvancedbyA. V. Chayanov, inworksfromabout 1910to1930, basedonextensivesurveydataofRussian peasants (1, 2). He intended his theories to be applicableto cultivators who do not hire labor and are part of a partiallymonetizedeconomy; thus, thetheoriesshouldberelevant tomost peasant cultivators since the dawn of civilization. A seriesof anthropological investigations and some theorizing show thathis ideas are broadly useful even if not exhaustive. Nevertheless,his formulation is limited by a failure to incorporate domesticstructures broader than the isolated nuclear family household.Headmitstheirexistencebutdeniestheirrelevance. Nuclearhouseholdsmayhavebeensufficienttohispoliticalandmac-roeconomicgoalsbut fail toreveal microeconomicdynamicsimportant to the management of peasant life.Chayanovs theorization and empirical research were designedto evaluate the nature of the peasant agricultural economy andtheroleof thepeasant inthetransitionfromfeudalismtosocialism, in the Russian political context after the revolutions of1905 and 1917. The basic Marxist-theoretical question waswhether peasants must pass through a capitalist stage or whetherpeasant agriculture was a stable system that could exist withinsocialism.The basic question from neoclassical economic the-ory was Chayanovs formulation that peasant productivity was afunctionof theconflictingforces of thesubjectivemarginalutility of labor and of the marginal disutility of effort. Inoperationalizing these concepts (ref. 1, pp. 7089 and ref. 2, pp.7089),hescaledhouseholdmembersaccordingtotheirpar-ticipation as producers andor consumers, using weightings byageandsex. Hethencomparedtheconsumerproducerratio(andothermeasuresofhouseholdsizeandcomposition)withagricultural output and income. In his view, effort on the familylabor farm was designedtosatisfy a locally homogeneousacceptable standard of consumption; when that was achieved (attheintersectionofthecurvesofmarginal utilityoflaborandmarginal disutility of effort), the self-exploitation of thepeasant laborer ceased. Thus, peasants worked no harder thanthey had to and stopped when consumption demand was satis-fied. They neither saved nor invested. Chayanovs efforts werepart of a broadeffort over time andinmany countries tomodernize, rationalize, and incorporate traditional peasant ag-riculture into a national economy as different regions began toindustrialize and to increase agricultural output so that peasantagriculturecouldfeedthegrowingindustrial workforce. Thateffort continues today, and his ideas are still relevant.Criticisms of Chayanovs work and that of his commentatorsare of several kinds. The Marxist criticism is that he consideredthe peasantry to be locally homogeneous and ignored theimportance of class differences among them, both with respectto the local consumption standard and to factors like differentialchild mortality (35). More technical arguments focus onwhether he or some of his commentators interpreted the num-bers, ratio, and balance of consumers and producers correctly, onwhether theformulations canbeextendedtoother kinds ofeconomies (e.g., nonmonetized, strictly monetized), and on thedegree towhichthe underlying statistical data are reliable.Extensive testing of Chayanovs ideas (611) lends general butnot complete support, even though commentators differ amongthemselves.Much of these debates focuses on a macrolevel issue: the roleof peasants in the general economy or in economic history andthesourcesof differentiationof peasant householdswithinaregional economy (demography for Chayanov, class for theMarxists). This article is not about those issues. Closer to its spiritis work in economic demography that examines the contributionsof childlabortothefamilyeconomyandeffectsonoldagesecurity and intergenerational transfers (1215) or at what pointpeasants elect to stop working (68). This article is not aboutthoseissues, either. Rather, it isabout otherimplicationsofChayanovs theoryandadeepinsight of his that havebeenneglected in the anthropological literature and that he himselfdid not pursue.Chayanovs unpursued insight is that each household can beexpectedtomoveacrosslevelsofwell-being, governedbythenumber of its producers and consumers (all else being equal), asit progresses through the domestic cycle. He thus anticipated thework of Fortes (16) and Goody (17) in recognizing the dynamicquality of the cycle of domestic groups. Indeed, the changes inwell-being predicted by Chayanov can be seen as an importantdriving force in the domestic cycle itself, if pursued beyond theindividual conjugal unit.In this article, anthropological terms have the followingdefinitions: conjugal, husband and wife; nuclear family, conjugal(oritsremnants)plusanychildren; consanguineal, relatedbyblood; affinal, related by marriage; agnatic, related only throughmale consanguineal links; lineal, consanguineally related byascent or descent; collateral, consanguineally related through asibling link at any generational level; patrivirilocal, bride joinsAbbreviation: CP, consumerproducer.*Towhomcorrespondenceshouldbeaddressedat:DepartmentofDemography,2232Piedmont Avenue, Universityof California, Berkeley, CA94720-2120. E-mail: gene@demog.berkeley.edu.Chayanovspositionwasthelatter,closertoBukharins,andcontradictedLenins,forwhichdifferenceof opinionheultimately paidwithhis life. Chayanov was arrestedJuly 21,1930 and incarcerated in the Butyrka prison for 4 years, then banished to Alma-Ata inKazakhstan. He continued to write on the peasant economy. He was sentenced to be shoton October 3, 1937, and the sentence was carried out the same day. He died at the ageof 49. 2005 by The National Academy of Sciences of the USAwww.pnas.orgcgidoi10.1073pnas.0501987102 PNAS May 10, 2005 vol. 102 no. 19 70437046ANTHROPOLOGYhousehold of husbands father; polygamy, marriage with multiplewives; corporate, having a unitary nature.My attempt to broaden Chayanovs work has three parts. Helimitedhis explicit model of peasant households tonuclearfamily households, on the grounds that complex families were athing of the past (ref. 2, pp. 54 and 56). Nevertheless, it is clearfromhisownandotherdatathatpatrivirilocal residencewascommonandthat patrilineallyextendedif not fraternal jointfamilies occurred (ref. 2, pp. 54, 56, 59, and 60). His work wouldbe more broadly useful if it included consanguineally extendedhouseholds and kin groups or even affinally extended ones, suchas polygamous units, or affinal exchange systems. All of these arecommon in many contemporary world areas outside Europe andthe Americas, and historically even within Europe, Japan, China,and other regions (ref. 2, p. 54, note 1). Some analyses (e.g., ref.15) note the possibility of extended intergenerational transfers;the focus here is on collateral rather than lineal relationships.Chayanov limited the span of the developmental cycle of thehousehold to 26 years (ref. 2, p. 57). This span is too short fora population in which complex households were expectable andin which collateral ties between households were important.He considered the household as a firmwithout internalcontradictions, ignoring differences in status and power within it.Thesefactorsareespeciallyimportantincomplexhouseholdswithpotentiallycompetingratherthanfullycooperatingsub-units. The importance of this factor became clear in recent workonmaternal mortality inthehistorical Balkans, inwhichitemerged that the size and composition of the husbands agnatickin group and a womans social rank within it played a major rolein the risk of death in childbirth (18).Chayanovconsideredhouseholdsasautarkicunits, isolatedexcept for their articulation with the monetized regional econ-omy. Thus, he ignored frequently reported mechanisms ofinterhousehold exchange of labor, even if not of goods (refs. 19and 20, among others).It is important to note that these criticisms apply to Chayanovsformal model, not necessarily to his sometimes discursive verbalcommentary, especiallywhenhedefends himself against hiscritics. I propose to embed the corrections in the formal modelitself.A simple exploration of Chayanovian process across succes-sive generations of patrivirilocal residence can be shown with anonstochastic model with enough population growth to achievehousehold complexity, with productivity and consumptionscaled by age and sex. Although motivated by it, this model doesnot focus on the marginal utility and disutility of labor; rather itfocuses on the consumerproducer (CP) ratio generated overtimeinthedevelopmental cycle. Oneversionof themodelspecifies nointrahouseholdor intranetworkcompetition(ri-valry). The other includes increasing political strain and privat-ization of production by conjugal subunits in the interests of theirown children. This kind of sequestering of output is typical wheresubunits seek to accumulate resources in anticipation of eventualfission. Itisalsofacilitatedbyincreasingmonetizationoftheeconomy, because it is easier to sequester cash than most othergoods. One might conceptualize such internal rivalry as a rottendaughter-in-law theorem, withdissensioncontrolledby thehousehold matriarch (the daughter-in-laws husbands mother)or by the ideal solidarity of brothers, but withdiminishingefficacy over time (see ref. 21).Table 1 shows the schedules of production and consumptionby age and sex that apply in the model here presented (H), as wellastheweightsChayanovusedinhisownexplication(C). Forexample, in the Hschedule, a male under 2 produces nothing andconsumes a tenth of a unit, whereas a male aged 1650 producesoneunitandconsumesoneunit. Afemaleinthatagerangeproduces 0.8 units and consumes 0.8 units. Females under age 15are more productive than males under age 15. The values in Hare derived from those used by Chayanov (C) but differentiatemore finely by sex and age and in particular gradually phase inchild productivity earlier than Chayanovs absolute threshold of15. These values seem ethnographically more realistic, at leastforpeasants, andforyoungfemalesingeneral. TheCmodeltruncates at the ages shown (ref. 1, pp. 90, 218, and 219; ref. 2,pp. 57 and 58).The weights are applied without change in the noncompetitivevariant of the H model. In the competitive version, the produc-tivity of a sons wife is a function of the number of her children,reflecting an assumed tendency to sequester output as her ownfamily grows. Where Psw is the productivity of a sons wife, Pfx isthe base productivity of a woman of the same age, x, and c is thenumberofherchildren, thenPswPfx(1c). Elaborationscouldincludedependencyonageandsexofchildren, nonlin-earities, etc., but this simplistic adjustment is sufficient togenerateavisibleandplausibledifferencebetweenthenon-competitive and competitive variants. (The same effects can ofcourse be generated by modifying the productivity of the son orof the conjugal pair jointly; the device used was for computa-tional convenience.)In the Cmodel, men marry at age 25, women at 20, and womenbear nine children, starting in year 2 of the marriage and spaced3 years apart thereafter. This schedule implies a somewhatunrealistic growth rate of 4.6%. Children are not distinguishedby sex. The model is truncated at year 26. In the H model, menmarry at 22, women at 20, men and women die at 60 (but notbefore), and wives bear four children, spaced two years apart,alternating males and females. This schedule implies a growthrateof 2.9%. Other schedules areof coursepossible; anyreasonableschedulewill producethesamemainresults de-scribed below.Fig. 1 shows the CP ratios produced by the noncompetitiveand competitive H models and by the C model. Over the first1015 years of the history of a household, all models show anincrease in the CP ratio, as children are born to the two adultproducers.TheincreaseisgreaterintheCmodelandhasanalmost identical slope to that of the H model, but lasts longer,because the Cmodel has higher fertility and greater birthspacing. TheCPratiobeginstodeclineaschildrenbecomeproductive. Thedeclineis deeper intheHmodel, becausechildren are more productive sooner and appear earlier in themarriage. The optimal points for a household in the first cycleare at the beginning and about year 1820 in the H model andyear 25 in the C model. Chayanovs model stops at that point. Hisnuclear households dissolve and start anew.Table 1. Schedules of production and consumptionWeightsProduction ConsumptionMale Female Male FemaleAge Units Age Units Age Units Age UnitsChayanov (C) 2 0 2 0 3 0.1 3 0.1 9 0.3 9 0.315 0 15 0 15 0.5 15 0.520 0.7 20 0.7 20 0.7 20 0.750 1 45 0.8 51 1 46 0.8This model (H) 5 0 5 0.0 2 0.1 2 0.17 0.1 6 0.2 5 0.3 5 0.39 0.2 10 0.5 9 0.5 6 0.512 0.5 15 0.7 12 0.7 10 0.715 0.9 20 0.7 15 0.8 12 0.850 1.0 60 0.8 50 1.0 60 0.8100 0.8 100 0.7 100 0.8 100 0.77044 www.pnas.orgcgidoi10.1073pnas.0501987102 HammelThat viewof household formation is simplistic. In manysocieties,parents,children,andgrandchildrencontinuetoco-reside, and, if households do not grow too rapidly, the unit maypersistforgenerations, sothattheparticipantsarepartlycol-lateral kin. Evenif descendants of thefoundingpair donotco-reside in the same house, they often continue to live close byin the same compound or ward and may maintain strongcooperation in exchange of labor, goods, and services. Indeed,similar patterns may befoundeveninurbancontexts (22).Althoughtheseexchangesmaysometimeslooklikeunilateraltransfers,thereismoreoftenanexpectationofreciprocation,evenif longdelayed. Indeed, insomekinshipsystems, thesereciprocations continue after death, as sacrifices and gravesidegifts from the living are exchanged for supernatural protectionor in gratitude for the gift of life itself (23). It therefore behoovesus to continue in time, using a prototypical patrivirilocal house-hold formation algorithm as an example. Sons stay, daughters-in-law move in, daughters move out.Fig. 1 also shows the results of the noncompetitive H modelcontinued past the first domestic cycle. The CP ratio falls as adaughter-in-lawenters and rises as a daughter leaves. Thischangehappens twice, becausetherearetwosons andtwodaughters. The ratio then begins to rise as children are born, thenfallsaschildrenbecomeproductive, asinthefirstcycle. Thissamecyclerepeatsonemoretimeinthisthree-cyclemodel.Note, however, that the peaks of the CP ratio are damped insuccessive cycles. In part, this damping is because the householdstructurebecomesgenerationallytop-heavy. Inthefirstcycle,there are two adults and four children. In the second, while thoseadults arestill alive, therearesixadults andeight children,yielding an improvement in the CP ratio. Further, there is somescattering of events over time, even in this mechanical model,which further damps swings of the CP ratio; that damping wouldbe stronger if the model were stochastic. This scattering wouldalso increase if the span of childbearing and interbirth intervalswere longer.Fig. 1 also shows a similar picture for the competitive variantof the H model. In this variant, the damping of CP peaks is notas strong, and the overall level of the CP ratio does not fall asmuch; however, the broadening of the peaks as events scatter intime is the same, because event timing does not differ betweenthe two variants of the model.Fig. 1istruncatedat75yearsbecausenonewchildrenarebeing produced in the three generational model after that point.There are two outcomes of this patterning. Mature complexhouseholds are optimal. Their CP ratios do not rise much above1.0, because the proportion of low producers is relatively small.Intramural competition worsens this picture because some pro-duction is privatized. Of course, some demands such as dowryand brideprice might have to be met from the common resourcepool even in the noncompetitive model. Mature complex house-holds are also likely to be more efficient because labor can bespecialized; such patterns of specialization are especially appar-entinsocietieswithcomplexhouseholdstructuresandmixedagriculturalpastoral economies.Nevertheless there are strains within such households, some ofthemintrinsictothehouseholddemographiccycleitself. Theoption of fission is always available and often taken, all at onceor one or more subunits at a time. These kinds of strains mayincreaseasthechildrenofsomesubunitsapproachfull adultproductivity, so that their subunits are on the verge of a quitefavorable CP ratio. Situations like this are particularly likely ifthe overall CP ratio is unfavorable and concentrated in only oneorafewofthesubunits. Forexample, onebrothermayhavemany children who are immature, whereas another brother mayhave only a few children, but approaching maturity. It is note-worthy that, whereas household complexity smoothes the CPratio over time and thus smoothes fluctuations in the demand forlabor and of microeconomic crisis, internal competition not onlyreducesthisbeneficial effectbutbecomesrelativelymorede-structive over time as household complexity increases. Both thedifferencebetweenandtheratioof theCPratios for thecompetitive and noncompetitive models become more extremewith time. In a sense, the complex household, although offeringFor example, in this model, brothers are 4 years apart in age. The entry of their wives intothe household will be separated by 4 years. Their sons are separated by 4 years. The oldestson of the oldest brother is separated from the youngest son of the youngest brother by8years. Thewives of thosecousins will enter thehouseholdover an8-year span. Inthenextgeneration, the span will be 16 years.Fig. 1. Consumerproducer ratios produced by the noncompetitive and competitive H models and by the C model.Hammel PNAS May 10, 2005 vol. 102 no. 19 7045ANTHROPOLOGYadvantages over the nuclear, contains the seeds of its owndestruction. Other issues mayalsostimulatefission, suchascrowdedhousingconditionsorinsufficiencyofexploitablere-sources such as farmland or pasture. Unequal inheritance pro-visions (e.g., customary ultimogeniture, primogeniture) may ofcourse set the scenario for household division if non-heirs depart[as in much of historical Britain or with the hidalgos (hijos dealgo, or roughly, somebodys children) of Spain].There are numerous examples of these factors in the ethno-graphicliterature, especiallyinthatofAfrica, theNearEast,Central and South Asia, and the Balkans. In my own fieldworkin the Balkans (24), peasants made it clear that they hadpreferred large, joint households and regarded them as wealth-ier. They spoke in detail about the strains between constituentunits, which they regarded as caused by the wives of otherwisesolidarybrothers. Theydescribedhownewlymarriedcouplesmightusetemporaryquartersinmildseasonsinoutbuildingsconstructed for their use, so that serious crowding and dissension(not to mention loss of personal privacy) in the main house werelimited to the winters. They spoke in detail about the rules andworkingoutofhouseholddivisionunderthesupervisionofadisinterested maternal relative, and also how cooperation couldbecontinuedevenafterfission. All of thisdiscourseiscom-mensurate with the competition model, both before and afterdivision.Chayanovs insight into the relationship between the demog-raphy and microeconomics of households can be deepened bybroadeningitsscopebeyondthedecisionabouthowmuchtowork. This broadening may not help much in understanding therole of peasants in a regional market economy or as a stage onthe road to socialism. It does help to understand what actors mayactually do. Some of their actions may be Malthusian; that is,theymayact directlytomaketheCPratiomorefavorable,throughabortionorinfanticideoradoptionandfosteringbe-tween kin and neighbors. Some of their actions may be Boseru-pian; that is, they may manipulate the social technology of thehousehold economy by merging, dividing, and exchanging laborand goods. The smoothing that is evident over time within thecomplexhouseholdhasananalogyinsmoothingacrossspacebetween contemporary units of more distant kin connection oreven only of propinquity. All of these techniques are wellattested in the ethnographic and historical literature.Chayanovs already useful formulation is sharpened by beingmore realistic about cooperative and competitive behavioramongkinwhoshareacorporateestate. Maintenanceof asuccessful social unitisanoutcomeofconflictingforces: thebalancebetweenproducersandconsumers, thedegreeofco-operationbetweenproducers, theemergenceof divisiveself-interest, all encompassed by cultural notions of what is right andproper behavior between kin. Our viewof the conduct ofeconomicandsocial lifeamongprimaryproducerswouldbeclearer if observations could include the broader field of socialaction within which actors operate, not limiting it to the conjugalcouple and its immediate quarters. In general, lifting the focusfrom the nuclear household reveals that more complex organi-zation of households and of kin groups further smoothes pro-duction and consumption across the domestic cycle of the groupand the life cycles of its members. Complex group organizationaccomplishesbysharinginternallywithinautarkicunitswhatexchangewouldaccomplishbetweentheir subunits or morebroadlybetweencontemporarykinorneighborsregardlessofco-residence. Because the productive capacities and consump-tion needs of domestic units are driven by the demography of thedomestic cycle, social units based in kinship seem to be ideallylarger rather than smaller, to the degree that size enhances thesmoothing of supply and demand and that the micropolitics ofinternal competition permit.I am indebted to Ronald Lee, Gregory Grossman, and Bernardo LanzaQueiroz for comments. The 1989 Russian collection appeared as a resultofglasnost(transparency)reformandcontainsitemsandinformationthat are not in the 1966 English collection. I am indebted to GregoryGrossman for access to the 1989 work.1. Chayanov, A. V. (1989) The Peasant Economy: Collected Works (Ekonomika,Moscow).2. Chayanov, A. V. (1966)A. V. ChayanovontheTheoryof Peasant Economy(Univ. of Wisconsin Press, Madison).3. Patnaik, U. (1979) J. Peasant Stud. 6, 375420.4. Lenin, V. I. (1956)TheDevelopment of CapitalisminRussia(ForeignLan-guages Publishing House, Moscow).5. Harrison, M. (1975) J. Peasant Stud. 2, 289417.6. Smith, A. E. (1979) J. Anthropol. Res. 35, 477480.7. Sahlins, M. (1972) Stone Age Economics (Aldine, Chicago).8. Sahlins, M. (1971) in Studies in Economic Anthropology, ed. Dalton, G. (Am.Anthropol. Assoc., Washington, DC), pp. 3051.9. Durrenberger, E. P. (1984) in Chayanov, Peasants, and Economic Anthropology, ed.Durrenberger, E. P. (Academic, Orlando), pp. 3950.10. Durrenberger, E. P. (1980) J. Anthropol. Res. 36, 133148.11. Chibnik, M. (1984) Curr. Anthropol. 25, 335340.12. Cain, M. (1977) Popul. Dev. Rev. 3, 201227.13. Hawkes, K., OConnell, J. & Jones, B. (1989) in Comparative Socioecology: TheBehavioral Ecology of Humans and Other Mammals, eds. Standen, V. & Foley,R. A. (Basil Blackwell, London), pp. 341366.14. Kaplan, H. (1994) Popul. Dev. Rev. 20, 753791.15. Lee, R. D. & Kramer, K. (2002) Popul. Dev. Rev. 28, 475499.16. Fortes, M. (1949) in Social Structure, ed. Fortes, M. (Clarendon Press, Oxford),pp. 5484.17. Goody, J. R. (1958) The Developmental Cycle in Domestic Groups (CambridgeUniv. Press, Cambridge, U.K.).18. Hammel, E. A. & Gullickson, A. (2004) Popul. Stud. 58, 145159.19. Kohler, H.-P. & Hammel, E. A. (2001) J. Popul. Econ. 14, 2149.20. Hammel, E. A. & Kohler, H.-P. (1996) Hist. Fam. 1, 407423.21. Becker, G. S. (1981) ATreatise on the Family (Harvard Univ. Press, Cambridge, MA).22. Stack, C. B. (1974) All Our Kin: Strategies for Survival in a Black Community(Harper and Row, New York).23. Mauss, M. (2000)TheGift: TheFormandReasonfor ExchangeinArchaicSocieties (Norton, New York).24. Hammel, E. A. (1968) Alternative Social Structures and Ritual Relations in theBalkans (PrenticeHall, Englewood Cliffs, NJ).7046 www.pnas.orgcgidoi10.1073pnas.0501987102 Hammel