Lecture 8 handout - Utility Functions and Choice

Lecture 8 handout - Utility Functions and Choice - 1 Four...

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1 Four Illustrative Utility Functions There are four important classes of preferences that we will use repeatedly in this course. 1.1 Cobb-Douglas Preferences Cobb-Douglas preferences are preferences that can be represented by utility function u ( x 1 ;x 2 ) = x c 1 x d 2 ; where c;d > 0 are constants. What do indi/erence curves for Cobb-Douglas preferences look like? Are they monotonic? Convex? Remember that any monotonic transformation of this utility function also represents Cobb-Douglas preferences. A particularly useful alternative way of representing them is: u ( x 1 ;x 2 ) = c ln x 1 + d ln x 2 . MRS = MU 1 MU 2 = c d x 2 x 1 . 1.2 Quasi-Linear Preferences Quasi-linear preferences are preferences that can be represented by utility func- tion u ( x 1 ;x 2 ) = v ( x 1 ) + x 2 ; where v ( x 1 ) > 0 is any increasing, concave function. For example, the utility function u ( x 1 ;x 2 ) = p x 1 + x 2 represents quasi-linear preferences. (The pref-
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This note was uploaded on 04/07/2012 for the course ECON 3010 at Cornell University (Engineering School).

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Lecture 8 handout - Utility Functions and Choice - 1 Four...

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