micro-fall2007-3

micro-fall2007-3 - Markets Taxes Detour A.2 Elasticity...

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Markets Taxes Detour A.2: Elasticity De&nition The elasticity of a variable measures the percentage change of its value as a result of an increase of the value of another variable by 1 % . Elasticity : = Δ y y Δ x x = Δ y Δ x & x y , where Δ x , respectively Δ y denote the change of x , respectively y . Ani Guerdjikova ECON 313 Fall 2007 35 / 59

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Markets Taxes Example Elasticity of demand Suppose that the elasticity of demand for gas is & 0 , 3. Then, a 5 % increase of gas price leads to a 1 , 5 % decrease of demand for gas: Δ y y = & 0 , 3 Δ x x = = & 0 , 3 ± 0 , 05 = = & 0 , 015 Ani Guerdjikova ECON 313 Fall 2007 36 / 59
Markets Taxes The elasticity of a function f ( x ) = y is given as: Elasticity : = f ( x 0 ) & f ( x ) f ( x ) x 0 & x x = f ( x 0 ) & f ( x ) x 0 & x ± x f ( x ) If f is di/erentiable at x , df ( x ) dx : = lim x 0 ! x f ( x 0 ) & f ( x ) x 0 & x , the elasticity of f at point x can be written as: Elasticity : = df ( x ) dx ± x f ( x ) Ani Guerdjikova ECON 313 Fall 2007 37 ± 59

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Markets Price Adjustment 1. Tatonnement Price adjustment process: p t + 1 > p t if D ( p t ) > S ( p t ) p t + 1 = p t if D ( p t ) = S ( p t ) p t + 1 < p t if D ( p t ) < S ( p t ) .
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micro-fall2007-3 - Markets Taxes Detour A.2 Elasticity...

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