powerpoint presentationgsme.sharif.edu/~econ_seminars/files/cct3.pdf · best frontier with...
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•𝒖𝒒 𝒄,𝒒
𝒖𝒄 𝒄,𝒒
𝒒 =𝒄
𝒑
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𝒒
• 𝒒𝒎𝒂𝒙 = {𝒗 𝒑, 𝒚𝒉 − 𝑻 ≥ 𝒖 𝒒 , 𝒚𝒉 − 𝑻 }
• 𝒒𝒎𝒊𝒏 = {𝒗 𝒑, 𝒚𝒍 − 𝑻 ≤ 𝒖 𝒒 , 𝒚𝒍 − 𝑻 }
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𝒗 𝒑, 𝒚𝒍 +𝒎 𝒒 − 𝑻 = 𝒖 𝒒 , 𝒚𝒍 − 𝑻
𝑫𝑾𝑳 = 𝒎 𝒒 − 𝒑𝒒
𝒒 ∗ = 𝒒(𝒑, 𝒚𝒍 − 𝑻 + 𝒑𝒒 ∗)
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𝒒
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𝑵 = 𝒑𝒒 + 𝒕 𝑵 − 𝑻 𝑵
𝒒 = 𝒒 𝒑, 𝒚𝒍 +𝑵
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𝑵 = 𝟎 → 𝑻 𝑵 = 𝟎
𝒖𝒉 𝒒 , 𝒚𝒉 − 𝑻 𝑵 + 𝒕 𝑵 = 𝒗𝒉 𝒑, 𝒚𝒉 − 𝑻 𝑵
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𝒖𝒍 𝒒 , 𝒚𝒍 + 𝒕 𝑵 − 𝑻 𝑵 = 𝒗 𝒑, 𝒚𝒍 + 𝒕 𝑵 − 𝑻 𝑵 +𝒎 𝒒
𝑫𝑾𝑳 = 𝒎 𝒒 (𝑵) − 𝒑𝒒 𝑵 − 𝒕(𝑵)
𝒒 𝑵 = 𝒒 𝒑, 𝒚𝒍 − 𝑻 𝑵 + 𝒕 𝑵 + 𝒑𝒒 𝑵
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𝑵𝑩𝑪 = 𝑵𝑮𝑴
𝒖𝒍 𝒒 𝑵 , 𝒚𝒍 − 𝑻 𝑵 + 𝒕 𝑵 > 𝒖𝒍 𝑸 , 𝒚𝒍 − 𝑻
𝒗 𝒑, 𝒚𝒍 − 𝑻 𝑵 + 𝒕 𝑵 +𝒎 𝒒 > 𝒗 𝒑, 𝒚𝒍 − 𝑻 +𝒎 𝑸
𝒚𝒍 − 𝑻 𝑵 + 𝒕 𝑵 +𝒎 𝒒 > 𝒚𝒍 − 𝑻 +𝒎(𝑸 )
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𝒎 𝑸 ≤ 𝒑𝑸 & 𝒎 𝒒 𝑵 = 𝒑𝒒 𝑵 + 𝒕(𝑵)
𝒚𝒍 − 𝑻 𝑵 + 𝒕 𝑵 +𝒎 𝒒 > 𝒚𝒍 − 𝑻 +𝒎(𝑸 )
𝑨 → 𝟐𝒕 𝑵 − 𝑻 𝑵 + 𝒑𝒒 𝑵 > 𝒑𝑸 − 𝑻
𝑵𝑩𝑪 = 𝑵𝑮𝑴
𝑩 → 𝒑𝑸 − 𝑻 = 𝒑𝒒 𝑵 + 𝒕 𝑵 − 𝑻(𝑵)
𝑨,𝑩 →
𝟐𝒕 𝑵 − 𝑻 𝑵 + 𝒑𝒒 𝑵 > 𝒑𝒒 𝑵 + 𝒕 𝑵 − 𝑻(𝑵)
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𝒒 ∗ < 𝒒𝒎𝒂𝒙
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