On the Economics of Polygyny

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On the Economics of Polygyny

• Ted Bergstrom
• Economics Department
• UC Santa Barbara

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Poly Families

• PolygamyMultiple mates of unspecified sex and
  number
• Polygyny---One man with many wives
• Polyandry---One woman with many husbands
• Polygynandry---More than one person of each sex

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Murdochs Ethnographic Atlas

• 1170 recorded societies.
• 850 are polygynous.
• Polyandry is rare, but is found in Himalayan
  regions.
• In African countries, percentage of women living
  in polygynous households ranges from 25 to 55.

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Two questions

• Why is polygyny common and polyandry rare?
• Why is bride price in Africa positive and not
  negative?

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Proposed Answers

• Polygyny is more common than polyandry because
  of reproductive technology.
• People value reproduction.
• Sperm is abundant, wombs are scarce.
• A woman with a shared husband is about as fertile
  as with one or more husbands.
• A man s fertility increases sharply with number
  of wives.

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Evolution of Sex ratios Natures choice and
efficient markets

• Why do most mammals produce about equal numbers
  of males as females.
• Wasteful Nash equilibrium, since one male can
  mate many females. (Waste less if males help
  raise offspring.)
• DarwinFisher equilibrium theory.

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African polygyny and bride price

• In cattle-raising societies of Africa, polygyny
  is the norm.
• Most wealth is cattle. Men trade cattle for
  wives.
• Price is usually high, 20 or more cattle. Very
  significant fraction of individual wealth.

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Two more questions, one answer

• Is a dowry a negative bride price?
• Why do many agricultural societies have dowries?
• Answer 1 No, bride price is paid to the brides
  male relatives by groom. Dowry is paid to the
  newly wed couple by brides relatives.
• Proposed Answer 2 comes later.

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Trading Material
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Wives for Cattle by Adam Kuper

• If a man had 3 wives, he would have 3 separate
  estates. Each estate had a right to the products
  of its gardens, the calves and milk of its cows,
  the earnings of the wife and her minor children,
  and the bridewealth received for its daughters.
  If the bridewealth for a daughter was used to
  acquire a wife for the son of another wife or to
  acquire another wife for the husband, then a debt
  was created.

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A formal model

• Mens utility U(x,k) k is number of surviving
  children and x is own consumption.
• Production function for children nf( r) n is
  the number of wives, r is consumption goods given
  to wife and her children.
• Fertility function of a wife f( r)

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Bride prices, gross and net

• Value of woman js labor wj
• Bride price of woman j bj
• Assume all women equally fertile, in equilibrium
  all have same net cost, pbj-wj.
• Net cost of buying a woman and giving her r units
  of goods is pr.

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The efficient way to spend Z on raising children

• Solve equation f(r )f(r)(rp) for r
• Let nZ/(rp)
• Buy n wives. Give each wife r units of
  resources for herself and her children.
• You will then get nf(r)Z f(r)/(rp)
  children.
• Note constant returns per dollar. Price of a kid
  is f(r)/(rp).

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More about the solution

• In equilibrium, all wives are treated the same,
  whether they marry rich or poor man, and whether
  they are more or less productive as workers.
• This simplifies pricing, parents dont care who
  daughter marries. (In contrast to case of dowry.)
• See Borger-Mulderhoff for empirical work on
• Bride prices among Kipsigis.

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The integer problem

• Wives come in indivisible units. Possible ways of
  dealing with this nuisance.
• Lottery solution.
• To buy 1/10 of an expected wife, bet p/10 at
  odds 10 to 1. If you win, you get p which you
  spend on an additional wife. If you lose, you add
  no wife.
• Time-sharing
• Polyandry
• Urban Underclass model. W.J. Wilson, R. Willis

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Comparative statics

• Rogers Law The more you have to pay for a
  bride, the better you will treat her.
• This is a comparison across equilibria. For
  proof, see diagram.
• Normal goods theorem- Demand curve for wives
  slopes down if demand curve for kids slopes
  down.

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General Equilibrium Question

• What determines price?
• Where does wealth to pay for brides come from?
• Does need to purchase brides reduce other
  productive investment?
• Wealth comes from the sale of sisters.
• Bride price is both source of income and of
• Expenditurecancels out on average. Just a
  matter of moving existing cows around.

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Time for transparency
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Concord at the Campfire

• Suppose that Alice and Bob real concern is only
  for the size of the fire.
• Each values berries only as an instrument to
  giving them strength to build the fire bigger.
• Then both agree on the amount of berries each
  should pick and the amount of firewood each
  should gather.

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No Bargaining Needed

• Alice specializes in wood-gathering and Bob
  gathers berries.
• Bob gives Alice berries to keep up her strength
  for wood-gathering.
• Alice and Bob agree perfectly on how much berries
  Alice should pick and how much she should give
  Bob.

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Monogamy and Domestic Harmony

• Are monogamous couples of fitness maximizers
  like Alice and Bob the fire maximizers?
• If the only children that either will have are by
  the other, then whatever actions increase the
  number of descendants of one increase the number
  of descendants of the other.
• Environment for selfless love?

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The In-law Problem

• Even in the Eden of perfect monogamy, the snake
  of conflict can be found.
• Hamiltons kin selection theory. Each spouse
  values his or her siblings and other relatives,
  but the sibling of one is unrelated to the other.
  
• Hence inclusive fitness functions conflict
• Conflict returns, though muted.

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More trouble in Eden

• High death rates of people of fertile age
• Remarriages of widows and widowers likely
• And adultery
• Philandering and cuckoldry. (Hawkes, Rogers, and
  Charnovthe males dilemma

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Conflict of interest

• Children by previous marriage dont get good care
  from non-related spouse
• Daly and Wilson Homicide
• Evidence of bad outcomes for children without
  resident biological father (Comanor and Phillips,
  Kelly Bedard and Heather Antecol)

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Physical evidence of mating historyComparing
primates

• Correlation across species between size
  difference of sexes and degree of polygyny
• Claimin polygynous species there is a bigger
  return to males fighting other males. Size
  advantage yields more mates
• Examplesgorillas and orangsgibbonschimps and
  bonobos

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Whose are bigger?

• Chimps are highly promiscuous and sexes differ by
  only about 6
• Gorillas are not promiscuous, (though
  polygynous). Females stay with same male
• The testes test
• Gorillas, chimps, humans?

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So where do humans place?

• By these physical tests, humans come out as
  moderately promiscuous and moderately polygynous
• In accord with what is known about modern
  hunter-gatherers

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Conflict over Birth Intervals?

• ArgumentChildren are much more expensive to
  women than to men. Therefore we should expect
  women to want fewer children than their husbands
  do
• Hold onWhat about Alice and Bob the
  fire-builders? Wont monogamists want the same
  thing?

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• Difference in interests arise with inlaw problem,
  early death of one spouse, adultery and rape.
• What are these differences?
• Differential values of previous children relative
  to new one.
• Differential values of potential future children
  relative to present new one
• Fidelity threshold and contributions to mans
  sisters children

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• Battle between mother and fetus for resources is
  a battle between fathers genes and mothersDavid
  Haig
• With high cuckoldry probabilities, men will tend
  to want shorter birth intervals than their wives

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A partial explanation for reduced birth rates?

• Tug-of-war model between sexes over birth rates.
  Each sets a target beyond its preferred point.
• As womens social power rises, so does their
  influence in household decisions.

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Competing Theory

• Becker et al attempt to explain demographic
  transition by relative prices
• But this doesnt account well for the fact that
  with large increases in income, number of
  children diminish. Are they inferior goods?
  Wouldnt evolutionary theory suggest that they
  are normal goods?

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Leverage in Tug-of-War

• Perhaps the major explanator of changes in birth
  rates is not changes in prices and incomes faced
  by a single rational decision-maker
• But rather a shift in bargaining power from those
  who favor higher birth rates to those who favor
  lower birth rates.

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