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A Choice Model of Status and Fertility
Unformatted Document Text:  component will be smaller in magnitude: -(1-½) 2 = -.25. The value of the status component will be identical, -.25, whenever a person’s own status matches his or her background status. Finally, if the person’s background status is minimal (B = 0) and he or she manages to attain the highest possible status (S = 1), the status component will be of the smallest possible magnitude, 0, connoting maximal satisfaction. We use our assumption that investment in status is investment not in fertility to create a simple model for fertility: F = 1 - λI. (2) The parameter λ indicates the tradeoff between investment in status and investment in fertility, 0 ≤ λ ≤ 1. For modern women, we take the tradeoff to be complete: we take λ to be 1. We introduce λ to compare men and women, for we assume that for men there is less of a tradeoff, that investment in status can have some payoff in fertility. Thus, for men, λ < 1. Our model for the relationship between investment in status and status is more complicated because background status also plays a role. We assumed the relationship to be linear, such that to maintain a person’s background status, he or she would have to put in a investment equal to that status, with model parameter R (0 ≤ R ≤ 1) giving the slope of the effect of excessive or deficient investment. R also can be seen as the proportional size of the range over which personal status can vary. This model is: S = B + R(I – B). (3) If R = 1 in eqn. 3, then background status plays no role in determining a person’s own status; own status is determined entirely by investment in status. We expect, however, that background status has a positive effect on a person’s own status, which is conveyed by eqn. 3 when R < 1, and is increasingly true as R decreases toward 0. 4

Authors: Hopcroft, Rosemary. and Whitmeyer, Joseph.
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background image
component will be smaller in magnitude: -(1-½)
2
= -.25. The value of the status
component will be identical, -.25, whenever a person’s own status matches his or her
background status. Finally, if the person’s background status is minimal (B = 0) and he
or she manages to attain the highest possible status (S = 1), the status component will be
of the smallest possible magnitude, 0, connoting maximal satisfaction.
We use our assumption that investment in status is investment not in fertility to
create a simple model for fertility:
F = 1 - λI.
(2)
The parameter λ indicates the tradeoff between investment in status and investment in
fertility, 0 ≤ λ ≤ 1. For modern women, we take the tradeoff to be complete: we take λ to
be 1. We introduce λ to compare men and women, for we assume that for men there is
less of a tradeoff, that investment in status can have some payoff in fertility. Thus, for
men, λ < 1.
Our model for the relationship between investment in status and status is more
complicated because background status also plays a role. We assumed the relationship to
be linear, such that to maintain a person’s background status, he or she would have to put
in a investment equal to that status, with model parameter R (0 ≤ R ≤ 1) giving the slope
of the effect of excessive or deficient investment. R also can be seen as the proportional
size of the range over which personal status can vary. This model is:
S = B + R(IB).
(3)
If R = 1 in eqn. 3, then background status plays no role in determining a person’s own
status; own status is determined entirely by investment in status. We expect, however,
that background status has a positive effect on a person’s own status, which is conveyed
by eqn. 3 when R < 1, and is increasingly true as R decreases toward 0.
4


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