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E100LectureNotes7

# E100LectureNotes7 - Comparative Statics of Demand 1...

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1/4/2008 1 Comparative Statics of  Demand

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1/4/2008 2 Elasticity Elasticity expresses the % change in consumption in response to a %change in price Convenient way to think about price sensitivity ) , , ( ) , , ( % % 2 1 1 1 1 2 1 1 1 1 1 1 1 1 , 1 1 1 1 1 1 1 1 1 1 I p p x p p I p p x x p p x p x E p x p x p p x x p x = = = = =
1/4/2008 3 Elasticity as a function Elasticity differs at different points on a demand curve. X 1 P 1

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1/4/2008 4 Example 1 What is elasticity of demand for x 1 (p 1 , p 2 , I ) = I /p 1 ? A. 1 B. 0 C -1 D. It depends Intuition : price up 1% means ___________ ___ if I’m spending all my income on good 1. 1 1 1 1 x p p x
1/4/2008 5 Example 2 x 1 =a-bp 1 E x1,p1 = = -bp 1 /(a-bp 1 ) X 1 small, p 1 large→ E x1,p1 large (in abs value) , 1 1 1 1 x p p x X 1 P 1

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1/4/2008 6 Notes Elasticity rigorously defined captures responses to very small %changes in price. (Recall calculus). Captures “local” elasticity at given prices and income We simplified when we defined elasticity as % change in x 1 in response to an increase of “1%” in p 1 . This was for intuition Also, elasticity goes both ways: It characterizes local responses to increases or decreases in p 1 ) , , ( ) , , ( 2 1 1 1 1 2 1 1 I p p x p p I p p x
1/4/2008 7 Some Definitions Own-price Elasticity: Relatively Elastic: Unit Elastic: Relatively Inelastic: Perfectly Inelastic: Cross-price Elasticity: 1 1 , p x E 1 1 1 , p x E 1 1 1 , = p x E 1 1 1 , p x E 0 1 1 , = p x E 1 2 2 1 , , or p x p x E E

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1/4/2008 8 Question 1 The price of Honda Accords just went up. What will probably happen to demand for Toyota Camrys? A. Rise B. Fall C. Stay the same
1/4/2008 9 Substitutes p 1 X 1 X 2 I/p 1 I/p 2 In other words, p 1 ↑→x 2 p 2 ↑→x 1 Tend not to combine these goods Note: Do not confuse with “perfect” substitutes 0 , 0 1 2 2 1 , , p x p x E E p 1 ↑→x 2

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E100LectureNotes7 - Comparative Statics of Demand 1...

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