第3章-消費者理論-wenkub
2023-03-16 00:02:44 本頁面
【正文】 ted by a continuous realvalued UF. – The representation does not depend on convexity and monotonicity. ~ ? ~ ? The Utility Function ? Theorem : If the binary relation is plete, transitive, continuous and strictly monotonic, then there exists a continuous realvalued function u: Rn+ ? R , which represents . Proof: Debreu (1954), or JR:pp1416 ? Notes: – Naturally enough, any additional structure we imposed on the preferences will be reflected as additional structure on the UF that representing them. – By the same token, whenever we assume the UF to have properties beyond utility, we will in effect be invoking set of additional assumptions on the underlying preferences relations. ~ ? ~ ? The Utility Function ? Theorem : Invariance of the UF to positive monotonic transformation Let be a preference relation on Rn+ and suppose u(x) is a utility function that represents it. Then v(x) also represents iff v(x) = f (u(x)) for every x, where f: R ? R is strictly increasing on the set of values taken on by u. ? Theorem : Properties of preferences and UF Let be represented by u: Rn+ ? R then: 1. u(x) is strictly increasing iff is strictly monotonic. 2. u(x) is quasiconcave iff is convex. 3. u(x) is strictly quasiconcave iff is strictly convex. ~ ? ~ ? ~ ? ~ ? ~ ? ~ ? The Utility Function ? Assumption : If the binary relation is plete, transitive, continuous, strictly monotonic , and strictly convex on Rn+ , it can be represented by a realvalued function that is continuous, strictly increasing and strictly quasiconcave on Rn+ ~ ? Topic 3: Indifference Curve Indifference Curves ? Take a reference bundle x’. The set of all bundles equally preferred to x’ is the indifference curve containing x’。 00:01:4100:01:4100:013/16/2023 12:01:41 AM ? 1以我獨沈久，愧君相見頻。 2023年 3月 16日星期四 上午 12時 1分 41秒 00:01: ? 1比不了得就不比，得不到的就不要。 上午 12時 1分 41秒 上午 12時 1分 00:01: ? 沒有失敗，只有暫時停止成功！。 00:01:4100:01:4100:01Thursday, March 16, 2023 ? 1不知香積寺，數(shù)里入云峰。 2023年 3月 上午 12時 1分 :01March 16, 2023 ? 1少年十五二十時，步行奪得胡馬騎。 00:01:4100:01:4100:013/16/2023 12:01:41 AM ? 1越是沒有本領(lǐng)的就越加自命不凡。 :01:4100:01:41March 16, 2023 ? 1意志堅強的人能把世界放在手中像泥塊一樣任意揉捏。 上午 12時 1分 41秒 上午 12時 1分 00:01: MOMODA POWERPOINT Lorem ipsum dolor sit amet, consectetur adipiscing elit. Fusce id urna blandit, eleifend nulla ac, fringilla purus. Nulla iaculis tempor felis ut cursus. 感謝您的下載觀看 專家告訴 。 2023年 3月 上午 12時 1分 :01March 16, 2023 ? 1業(yè)余生活要有意義，不要越軌。 00:01:4100:01:4100:01Thursday, March 16, 2023 ? 1知人者智，自知者明。 上午 12時 1分 41秒 上午 12時 1分 00:01: ? 楊柳散和風(fēng)，青山澹吾慮。 2023年 3月 16日星期四 上午 12時 1分 41秒 00:01: ? 1楚塞三湘接，荊門九派通。 00:01:4100:01:4100:013/16/2023 12:01:41 AM ? 1成功就是日復(fù)一日那一點點小小努力的積累。 2023年 3月 上午 12時 1分 :01March 16, 2023 ? 1行動出成果，工作出財富。 00:01:4100:01:4100:01Thursday, March 16, 2023 ? 1乍見翻疑夢，相悲各問年。 . ? The general equation for an indifference curve is U(x1,x2) = k, a constant. Totally different
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