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08-27-08 - Econ 302 Intermediate Microeconomic Theory...

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Econ 302: Intermediate Microeconomic Theory Andres Elberg University of Illinois at Urbana-Champaign August 27, 2008 Andres Elberg (University of Illinois at Urbana-Champaign) Lecture 2: Consumer Theory: Preferences August 27, 2008 1 / 29
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Part 1. Consumer Theory Andres Elberg (University of Illinois at Urbana-Champaign) Lecture 2: Consumer Theory: Preferences August 27, 2008 2 / 29
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Overview Consumer theory aims at explaining how a rational agent decides to allocate her income across di/erent goods. The basic idea is that the consumer compares di/erent bundles of goods and chooses the most preferred one(s) among those that are feasible (i.e. a/ordable given her income and market prices) We° ll proceed in three steps to develop the theory: 1 We will characterize the constraint faced by the consumer (the budget constraint) 2 We will describe the way the consumer chooses between di/erent commodity bundles (consumer preferences) 3 We will ±nd the optimal consumption bundle (choice) Andres Elberg (University of Illinois at Urbana-Champaign) Lecture 2: Consumer Theory: Preferences August 27, 2008 3 / 29
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The Consumption Set There are L commodities available to the consumer. We denote by x l the quantity of good l = 1 , ..., L purchased by the consumer. The object of choice is a consumption bundle denoted by the vector ( x 1 , x 2 , ..., x L ) De±nition The consumption set, X, is the set of all possible consumption bundles the consumer can conceive X = f ( x 1 , x 2 , ..., x L ) j x 1 ° 0 , x 2 ° 0 , ..., x L ° 0 g Andres Elberg (University of Illinois at Urbana-Champaign) Lecture 2: Consumer Theory: Preferences August 27, 2008 4 / 29
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Prices Denote commodity prices by p 1 , p 2 , ..., p L We assume the consumer is a price taker, so prices are given Prices do not depend on how much the consumer chooses buy of each good Thus total expenditure on a consumption bundle is given by: p 1 x 1 + p 2 x 2 + ... + p L x L Andres Elberg (University of Illinois at Urbana-Champaign) Lecture 2: Consumer Theory: Preferences August 27, 2008 5 / 29
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Consumer°s Budget Set The consumer is endowed with an income of m . A consumption bundle is a/ordable at prices p 1 , p 2 , ..., p L if p 1 x 1 + p 2 x 2 + ... + p L x L ± m De±nition The consumer°s budget set is de±ned as B ( p 1 , ..., p L , m ) = f ( x 1 , x 2 , ..., x L ) 2 X j p 1 x 1 + p 2 x 2 + ... + p L x L ± m g That is, the consumer°s budget set includes all a/ordable consumption bundles. Andres Elberg (University of Illinois at Urbana-Champaign) Lecture 2: Consumer Theory: Preferences August 27, 2008 6 / 29
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Consumer°s Budget Line The consumer°s budget line is the upper boundary of the budget set. i.e. set of just a/ordable bundles p 1 x 1 + p 2 x 2 + ...
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