7_UtilityFunctions_ToPost

7_UtilityFunctions_ToPost - LesterFreamon ECON 410...

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“We’re building something here…and all the pieces matter.”  – Lester Freamon ECON 410 Utility Functions
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2 Class 7 - Utility Functions (Cont.) What: Peer Tutoring in all subjects Where: 2nd floor of Dey Hall When: 6-9pm Tues and Weds nights Notes: There is no tutoring the weeks of Fall and Thanksgiving Breaks, and tutoring ends on November 30th.
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3 Class 7 - Utility Functions (Cont.) Marginal Rate of Substitution Define the Marginal Rate of S ubstitution between Good 1 and Good 2 ( ) as: 1. The maximum amount of Good 2 the individual would be willing to give up to get one more unit of Good 1. 2. The minimum amount of Good 2 the individual would need to receive to give up one unit of Good 1. 3. (The negative of) the derivative of the indifference curve, x2=f(x1). , MRS x x 1 2
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4 Class 7 - Utility Functions (Cont.) Good 2 Good 1 I 1 A note on derivatives…
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5 Class 7 - Utility Functions (Cont.) Marginal Rate of Substitution Define the Marginal Rate of S ubstitution between Good 1 and Good 2 ( ) as: 1. The maximum amount of Good 2 the individual would be willing to give up to get one more unit of Good 1. 2. The minimum amount of Good 2 the individual would need to receive to give up one unit of Good 1. 3. (The negative of) the derivative of the indifference curve, x2=f(x1). , MRS x x 1 2
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6 Class 7 - Utility Functions (Cont.)
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7 Class 7 - Utility Functions (Cont.) Utility Function A utility function exists if and only if preferences are rational.
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Group-Clicker Question (1 pt): Pat’s preferences over dating are such that Pat always wants to date an individual Pat isn’t currently dating. For instance, if Pat is dating J ordan, Pat prefers to date anyone other than J ordan (Pat’s not the best at commitment). Does a utility representation exist representing these preferences? 1. Yes 2. No 3. More information is needed.
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9 Class 7 - Utility Functions (Cont.) Continuous Utility Function A continuous utility function exists if and only if preferences are rational and continuous .
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10 Class 7 - Utility Functions (Cont.) Increasing Utility Function An increasing utility function exists if and only if preferences are rational and monotonic .
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11 Class 7 - Utility Functions (Cont.) Complete Preferences x x x x Transitive Preferences x x x x Monotonic Preferences x x Continuous Preferences x x Utility Function Properties: N/A N/A Increasin g Continuou s Increasing, Continuous
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Group-Clicker Question (1 pt): Assume an individual’s preferences are such that they do not like HW. Thus, the less HW, the happier they are. Also, we happen to notice that their preferences are continuous. As always, if we are not given an explicit violation of completeness, we may assume preferences are complete. What kind of Utility function exists? 1. Continuous and Increasing 2. Continuous 3.
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