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(1) ¡¡x = sl
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(2) ¡¡y = x¡Ýt(x)
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(3) ¡¡max u(l,y), subject to (1) & (2).
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(4)¡¡ max u(l, sl¡Ýt(sl))
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(5)¡¡l(t)¡ál*
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(6)¡¡(s l(t)¡Ýt(s l(t)), t(s l(t)))
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(7) max W(y1, y2), subject to y1¡ás l(t)¡Ýt(s l(t)) & y2¡át(s l(t))
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(8)¡¡max y1¡Üy2, subject to y1¡ás l(t)¡Ýt(s l(t)) & y2¡át(s l(t)).
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