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u ' (μ ˆ X 1
) = λu ' (μ ˆ X 2
) +
< λu ' (μ ˆ X 2
) +
⎡
< ⎢ λ +
⎣
(1 − λ)
2μ
(1 − λ)
2μ
u' ( X ˆ
2
) (1)
(1 − λ)
2μ
u' (μX ˆ
2
)
⎤
⎥ u ' (μX ˆ
2
)
⎦
≤ u ' (μ ˆ X 2
) ⇒ μ ˆ X 1
> μ ˆ X 2
In contrast, homosexual couples do not face different survival probabilities for each of their
members, because the two partners share the same gender (same
for both). Their objective
function therefore becomes:
U = 2u(μX 1
) + 2λu(μX 2
)
subject to the same budget constraint described above. We consider the same set of preferences of
opposite-sex couples, without imposing dissimilar utility functions as the channel through which
sexual orientation may affect savings. The first order condition follows:
2μu ' (μ ˆ X 1
) = 2λμu ' (μ ˆ X 2
) (2)
u ' (μX ˆ
1
)
u ' (μX ˆ
2
) = λ
From the first order condition (1), we have that u ' (μ ˆ X 1
) > λu ' (μ ˆ X 2
) for opposite-sex couples, and
from first order condition (2) we have that u ' (μ ˆ X 1
) = λu ' (μ ˆ X 2
) for gay couples (both members face
'
the same uncertain survival probability λ ⎢
'
⎣u
( μXˆ
1
2
) ⎤
⎥
)
⎦
hetero
'
⎡u
( μXˆ
> ⎢
'
⎣u
( μXˆ
1
2
) ⎤
⎥
)
⎦
gay
= λ
with λ