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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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¤È¤³¤í¤Ç¡¢¼Ò²ñ¸üÀ¸´Ø¿ô W(y1, y2)¤¬¤É¤¦¤¤¤¦·Á¾õ¤Ç¤¢¤ë¤«¤Ï¡¢¤½¤ÎÀ¯Éܤò¹½À®¤¹¤ëÀ¯ÅÞ¤ÎÀ¼Á¤Ë¤è¤Ã¤Æ°ã¤Ã¤Æ¤¯¤ë¤Ç¤·¤ç¤¦¤¬¡¢°ìÈÌŪ¤Ë¤Ïy1µÚ¤Ó y2ÁÐÊý¤Ë¤«¤ó¤·¤ÆÃ±Ä´Áý²ÃŪ¤Ê¡¢Ï¢Â³Èùʬ²Äǽ¤Ê¼Â¿ôÃÍ´Ø¿ô¤È¤¤¤¦À¼Á¤òͤ·¤Æ¤¤¤ë¤È²¾Äꤷ¤Þ¤¹¡£¤Ç¤Ï¡¢Åµ·¿Åª¤Ê¿·¼«Í³¼çµÁÀ¯ÉܤǤ¢¤ë¸½ºß¤Î°ÂÉôÀ¯¸¢¤¬°ÅÌÛŪ¤Ë»ý¤Ä¼Ò²ñ¸üÀ¸´Ø¿ô¤Ï¤¤¤«¤Ê¤ë·Á¾õ¤È¤·¤Æ¹Í¤¨¤é¤ì¤ë¤Ç¤·¤ç¤¦¤«¡©°ÂÉôÀ¯¸¢¤ÏŽ¢·ÐºÑÀ®Ä¹½Å»ëÀ¯ºöŽ£¤ò·Ç¤²¤Æ¤¤¤Þ¤·¤¿¡£·ÐºÑÀ®Ä¹½Å»ë¤È¤Ï¹ṉ̃½êÆÀ¤òºÇÂç²½¤µ¤»¤ë»ö¤òÌÜŪ¤È¤¹¤ë¤â¤Î¤È²ò¼á¤Ç¤¤Þ¤¹¡£¤¹¤ë¤È¡¢¤³¤³¤Ç¹Í¤¨¤Æ¤¤¤ë¥â¥Ç¥ë¤Ç¤Ï¹ṉ̃½êÆÀ¤Ïy1¤È y2¤ÎÁíϤˤʤê¤Þ¤¹¡£¤¹¤Ê¤ï¤Á¡¢°ÂÉôÀ¯¸¢¤¬°ÅÌÛŪ¤Ë»ý¤Ä¼Ò²ñ¸üÀ¸´Ø¿ô¤È¤Ï¸ùÍø¼çµÁŪ¼Ò²ñ¸üÀ¸´Ø¿ôy1¡Üy2¤Ë¤Ê¤ê¡¢¤½¤Î·ë²Ì¡¢¾å¤ÎÌäÂê(7)¤Ï°Ê²¼¤Î¤è¤¦¤Ë½ñ¤´¹¤¨¤é¤ì¤Þ¤¹¡§
(8)¡¡max y1¡Üy2, subject to y1¡ás l(t)¡Ýt(s l(t)) & y2¡át(s l(t)).
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(9)¡¡max min{ y1, y2}, subject to y1¡ás l(t)¡Ýt(s l(t)) & y2¡át(s l(t)).
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