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lecture06_slides

lecture06_slides - Econ 121 Intermediate Microeconomics...

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Econ 121. Intermediate Microeconomics. Eduardo Faingold Yale University Lecture 6
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Outline of the course I. Introduction II. Individual choice III. Competitive markets IV. Market failure
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Outline of the course I. Introduction II. Individual choice ± Budget constraint (Ch. 2) ± Preferences (Ch. 3) ± Utility (Ch. 4) ± Consumer problem (Ch. 5) ± Revealed preference (Ch. 7) ± Slutsky equation (Ch. 8) ± Endowment income effect ± Intertemporal choice III. Competitive markets IV. Market failure
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Slutsky equation Recall that x ² 1 .p 1 ; p 2 ; m/ designates the demand for good 1 under prices p 1 , p 2 and income m . Define the compensated demand for good 1 given prices p 1 , p 2 and a bundle x as follows: x s 1 .p 1 ; p 2 ; x/ D x ² 1 .p 1 ; p 2 ; p 1 x 1 C p 2 x 2 /; i.e. x s 1 .p 1 ; p 2 ; x/ is the optimal consumption bundle given the budget line that has slope NUL p 1 =p 2 and passes through bundle x . This means that when the price of good 1 changes from p 1 to p 0 1 , the consumer’s income is adjusted by m D .p 0 1 NUL p 1 /x 1 :
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Slutsky equation Fix p and m and write x ² D x ² .p 1 ; p 2 ; m/ . By the revealed preference argument we saw in the previous lecture, p 0 1 > p 1 H) x s 1 .p 0 1 ; p 2 ; x ² / NUL x s 1 .p 1 ; p 2 ; x ² / < 0: Thus, x s 1 .p 0 1 ; p 2 ; x ² / NUL x s 1 .p 1 ; p 2 ; x ² / p 0 1 NUL p 1 < 0 for all p 0 1 ¤ p 1 ; and therefore, @x s 1 @p 1 .p 1 ; p 2 ; x ² / < 0: That is, the substitution effect is always negative.
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Slutsky equation Let us calculate @x s 1 [email protected] 1 using the definition x s 1 .p 1 ; p 2 ; x ² / D x ² 1 .p 1 ; p 2 ; p 1 x ² 1 C p 2 x ² 2 /: By the chain rule of calculus, @x s 1 @p 1 .p 1 ; p 2 ; x ² / D @x ² 1 @p 1 .p 1 ; p 2 ; p 1 x ² 1 C p 2 x ² 2 / C @x ² 1
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