204_summer_2009_lecture_3

204_summer_2009_lecture_3 - University of Toronto...

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University of Toronto Department of Economics ECO 204 Summer 2009 Sayed Ajaz Hussain Lecture 3 1 Ajaz Hussain. Department of Economics
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Last Time Scientific modeling in Economics Consumption set Representing preferences , , ~ Rational preferences Convex preferences Monotone preferences Felicity surfaces Utility function Ajaz Hussain. Department of Economics 2 f ~ f
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Today Some interesting utility functions Graphing indifference curves Marginal rate of substitution Interpretation and application Monotonic transformations Non convex preferences Modeling some preferences Utility maximization problem (UMP) Optimal choice Sensitivity analysis 3 Ajaz Hussain. Department of Economics
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Some Utility Functions Linear utility function: U = α Q 1 + β Q 2 Cobb Douglas utility function: U = Q 1 α Q 2 β Complements utility function: U = min( α Q 1 , β Q 2 ) Quasi Linear utility function: U = Q 1 + f(Q 2 ) CES utility function: U = [ ρ Q 1 + ρ Q 2 ] 1/ ρ See HW 2 whether these represent rational, convex, monotone preferences Ajaz Hussain. Department of Economics 4
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Utility Functions: Discussion Graphing indifference curves Marginal rate of substitution (MRS) Goods 1 vs. 2: likes and dislikes Advertising Segmentation Monotonic transformations Log transformation Non convex preferences Modeling some preferences Ajaz Hussain. Department of Economics 5
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Graphing Indifference Curves Recall felicity plots from lecture 2 Contours correspond to felicity ‐‐ utility – level “indifference curves” To graph these: Pick an arbitrary utility U Obtain equation with: Q 2 as “y” variable Q 1 as “x” variable Plot in two dimensions Ajaz Hussain. Department of Economics 6
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