Econ 5 - 1 Utility Function Deriving MRS 1 14.01 Principles...

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Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 1 1 Utility Function, Deriving MRS 14.01 Principles of Microeconomics, Fall 2007 Chia-Hui Chen September 14, 2007 Lecture 5 Deriving MRS from Utility Function, Budget Constraints, and Interior Solution of Optimization Outline 1. Chap 3: Utility Function, Deriving MRS 2. Chap 3: Budget Constraint 3. Chap 3: Optimization: Interior Solution 1 Utility Function, Deriving MRS Examples of utility: Example (Perfect substitutes) . U ( x, y ) = ax + by. Example (Perfect complements) . U ( x, y ) = min { ax, by } . Example (Cobb-Douglas Function) . c U ( x, y ) = Ax b y . Example (One good is bad) . U ( x, y ) = ax + by. An important thing is to derive MRS. dy MRS = = Slope of Indifference Curve . dx | |
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10 9 8 7 6 U(x,y)=ax+by=Const y 5 4 3 2 1 0 0 2 4 6 8 10 x Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 2 1 Utility Function, Deriving MRS Figure 1: Utility Function of Perfect Substitutes y 10 9 8 7 6 5 4 3 U(x,y)=min{ax,by}=Const 2 1 0 0 2 4 6 8 10 x Figure 2: Utility Function of Perfect Complements
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2 4 6 8 10 y U(x,y)=Ax a y b =Const 0 0 2 4 6 8 10 x 10 9 8 7 6 U(x,y)=−ax+by=Const y 5 4 3 2 1 0 0 2 4 6 8 10 x Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu),
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