ECON100A_7 - Demand 1 Elasticity Measuring response to a...

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 1/4/2008 1 Comparative Statics of  Demand
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 1/4/2008 2 Elasticity Measuring response to a change Could look at slope: Also could look at responses to percent changes Percent changes make more sense A a one dollar change in the price of a Lexus is very different from a 1 dollar change in the price of a banana!! Elasticity captures notion of price sensitivity 1 1 p x 1 2 1 1 ) , , ( p I p p x = ) , , ( ) , , ( % % 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 = = = = =
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 1/4/2008 3 Exercise F(x)=mx is a function with constant slope Show that F(x)=Ax α is a function with constant elasticity ) ( ) ( ), ( x F x dx x dF E x X F =
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 1/4/2008 4 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 = = = = =
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 1/4/2008 5 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 spending down 1% if I’m spending all my income on good 1. 1 1 1 1 x p p x
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 1/4/2008 6 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 7 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
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 1/4/2008 8 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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