Lecture_2_January 28

Lecture_2_January 28 - Logistics LOGISTICS Read this week...

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January 28, 2010 1 L OGISTICS Logistics Read this week Chapter -1 (mathematical refresher) Chapter 0 (introduction to representative-agent framework) Chapter 1 (consumer theory) Read for next week Chapter 2 (static consumption-leisure framework) Practice Problem Set 1 Posted on web Reviews consumer theory Discuss in recitations this week Recitations begin tomorrow All course material posted on course website on www.elms.edu
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R EVIEW OF C ONSUMER T HEORY (C ONTINUED ) J ANUARY 28, 2010
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January 28, 2010 3 U TILITY F UNCTIONS Review of Consumer Theory Describe how much “happiness” or “satisfaction” an individual experiences from “consuming” goods – the benefit of consumption Marginal Utility The extra total utility resulting from consumption of a small/incremental extra unit of a good Mathematically, the (partial) slope of utility with respect to that good One-good case: u ( c ), with du / dc > 0 and d 2 u / dc 2 < 0 Recall interpretation: strictly increasing at a strictly decreasing rate Diminishing marginal utility Two-good case: u ( c 1 , c 2 ), with u i ( c 1 , c 2 ) > 0 and u ii ( c 1 , c 2 ) < 0 for each of i = 1,2 Utility strictly increasing in each good individually (partial) Diminishing marginal utility in each good individually Readily extendable to N -good case: u ( c 1 , c 2 , c 3 , c 4 ,…, c N ) Alternative notation: du / dc OR u ’( c ) OR u c ( c ) OR u 1 ( c )
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January 28, 2010 4 U TILITY F UNCTIONS Review of Consumer Theory One-good case c u(c) Slope (marginal utility) asymptotes to (but never reaches…) zero Example: u ( c ) = ln c or u ( c ) = sqrt( c )
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January 28, 2010 5 U TILITY F UNCTIONS Review of Consumer Theory One-good case Two-good case c u(c) Slope (marginal utility) asymptotes to (but never reaches…) zero Example: u ( c ) = ln c or u ( c ) = sqrt( c ) Example: u ( c 1 , c 2 ) = ln c 1 + ln c 2 or u ( c 1 , c 2 ) = sqrt( c 1 ) + sqrt( c 2 )
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January 28, 2010 6 U TILITY F UNCTIONS Review of Consumer Theory One-good case Two-good case c u(c) Slope (marginal utility) asymptotes to (but never reaches…) zero Example: u ( c ) = ln c or u ( c ) = sqrt( c ) Example: u ( c 1 , c 2 ) = ln c 1 + ln c 2 or u ( c 1 , c 2 ) = sqrt( c 1 ) + sqrt( c 2 ) c 1 u(c 1 ,c 2 ) Viewed in good-by- good space
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January 28, 2010 7 U TILITY F UNCTIONS Review of Consumer Theory One-good case Two-good case c u(c) Slope (marginal utility) asymptotes to (but never reaches…) zero Example: u ( c ) = ln c or u ( c ) = sqrt( c ) Example: u ( c 1 , c 2 ) = ln c 1 + ln c 2 or u ( c 1 , c 2 ) = sqrt( c 1 ) + sqrt( c 2 ) c 1 u(c 1 ,c 2 ) c 2 u(c 1 ,c 2 ) Viewed in good-by- good space
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January 28, 2010 8 U TILITY F UNCTIONS Review of Consumer Theory Alternative views Emphasizing the contours Indifference Curve: the set of all consumption bundles that deliver a particular level of utility/happiness
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January 28, 2010 9 U TILITY F UNCTIONS Review of Consumer Theory Alternative views Emphasizing the contours Indifference Curve: the set of all consumption bundles that deliver a particular level of utility/happiness Viewing only the contours
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January 28, 2010 10 U TILITY F UNCTIONS Review of Consumer Theory
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