I showed in Part I that if all men and all women were identical,
if the number of men equaled the number of women, and if there were
diminishing returns from adding an additional spouse to a household,
then a monogamous sorting would be optimal, and therefore would
maximize the total output of commodities over all marriages.74 If the
plausible assumption of diminishing returns is maintained, inequality in
various traits among men or in the number of men and women would be
needed to explain polygyny.
An excess of women over men has often encouraged the spread of
polygyny, with the most obvious examples resulting from wartime deaths
of men. Thus, almost all the male population in Paraguay were killed
during a war with Argentina, Brazil, and Uruguay in the nineteenth
century,75 and apparently polygyny spread afterward.
Yet, polygyny has occurred even without an excess of women; indeed,
the Mormons pract1ced polygyny on a sizable scale with a slight excess of • men.76 Then inequality among men is crucial.
If the "productivity" of men differs, a polygynous sorting could be
optimal, even with constant returns to scale and an equal number of men
and women. Total output over all marriages could be greater if a second
wife to an able man added more to output than she would add as a first
wife to a less able one. Diminishing marginal products of men or women
within each household do not rule out that a woman could have a higher
marginal product as a second wife in a more productive household than as
the sole wife in a less productive household.