A negative correlation between Wm and maximizes total output
because the gain from the division of labor is maximized. Low-wage F
should spend more time in household production than high-wage F
because the foregone value of the time of low-wage F is lower; similarly,
low-wage M should spend more time in household production than highwage
M. By mating low-wage F with high-wage M and low-wage M
with high-wage F, the cheaper time of both M and F is used more extensively
in household production, and the expensive time of both is
used more extensively in market production.
All persons have been assumed to participate in the labor force. During
any year, however, most married women in the United States do not
participate, and a significant number never really participate throughout
their married life. My analysis does predict that many women would
have only a weak attachment to the labor force since low-wage women
would be discouraged from participation both by their low wage and by
the high wage of their husbands.3'
If some women are not in the labor force, however, the wage rates of
men and women need not be perfectly negatively correlated to maximize
total output. For assume that all women with wage rates below a certain
level would not participate in the labor force with a perfectly negative
correlation between the wage rates of men and women. These women have = 0,32 and, thus, Zim = 0; therefore, up to a point, they could
switch mates without lowering total output. Consequently, other sortings
having weaker negative, and conceivably even positive, correlations
would also maximize total output; that is, many sortings would be
equally good, and wage rates would not be a decisive determinant of the
optimal sorting.
If M and F differ only in their stock of nonhuman capital, Km and
K1, and if everyone participates in the labor force, 0CI0Km = ÔC/3K1 = 0
since the value of time is measured by the market wage rates. If the rate of
return on K, denoted by r, depended positively on the amount of time
allocated to "portfolio management," r would be- positively related to
K.33 It then follows that