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2010Exercise2-1

2010Exercise2-1 - Econ 200 Homework Exercises 1 Elasticity...

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Econ 200 Homework Exercises 1. Elasticity For any function ( ) y f x = , the elasticity of this function is ( , ) x dy y dx y x ε = . (a) Show that ln ( ) ln ( , ) d y x dx d x dx y x ε = . (Thus if you graph ln y against ln x , the slope of the graph is the elasticity.) (b) Show also that if ( ) y f x = and ( ) z g x = , where ( ) 0 g x , ln ( ) ( , ) ln ( ) d y x dx y z d z x dx ε = . (Thus if you graph ln y against ln z , the slope of the graph is the elasticity.) Hence or otherwise prove the following. (i) ( , ) ( , ) y x y x α β ε ε = (ii) 1 1 ( , ) ( , ) , ) ( y x y x x y ε ε ε = = − (iii) 1 1 ( , ) ( , ) y x y x ε ε = (iv) 1 2 1 2 ( , ) ( , ) ( , ) y y x y x y x ε ε ε = + (v) 1 2 1 2 ( / , ) ( , ) ( , ) y y x y x y x ε ε ε = (vi) 2 1 1 2 1 ( , ) ( , ) y y p y y p ε ε = 2. Elasticity of Substitution
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