2010_lecture_4

2010_lecture_4 - Economics 101Lecture 4 The Basic Model of...

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Economics 101—Lecture 4 The Basic Model of Consumer Choice II George J. Mailath January 25, 2011
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In our last episode 1 We introduced preferences ± over consumption bundles x X , where X is the consumption set. Typically X = R n + . 2 A utility function U : X R represents ± if x ² ± x ²² ⇐⇒ U ( x ² ) U ( x ²² ) . 3 Monotone preferences are characterized by their indifference curves (where an indifference curve is a locus of bundles over which the consumer is indifferent). For a fixed bundle x ² , the indifference curve through x ² is the set ± ( x ² ) ≡ { x ²² X : x ²² ± x ² } .
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In our last episode, cont. Preferences are convex if the better than sets are convex, which requires diminishing MRS (i.e., the indifference curves are convex).
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In our last episode, cont. Preferences are convex if the better than sets are convex, which requires diminishing MRS (i.e., the indifference curves are convex). The MRS ( marginal rate of substitution ) of good i in terms of good j is the (negative of the) slope of the indifference curve (in the ij direction): MRS ij = U i U j = U / x i U / x j .
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Example: Cobb Douglas U ( x 1 , x 2 ) = x α 1 x β 2 , for some α , β > 0.
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Example: perfect complements U ( x 1 , x 2 ) = min { α x 1 , β x 2 } , for some α , β > 0.
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Example: Perfect substitutes U ( x 1 , x 2 ) = α x 1 + β x 2 , for some α , β > 0.
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Utility Maximization Suppose consumer’s preferences are represented by a utility function U defined over consumption bundles x R n + .
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This note was uploaded on 03/02/2011 for the course ECON 101 taught by Professor Dannicatambay during the Spring '08 term at UPenn.

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2010_lecture_4 - Economics 101Lecture 4 The Basic Model of...

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