2010Exercise2-1

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

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Econ 200 Homework Exercises 1. Elasticity For any function () y fx = , the elasticity of this function is (,) x dy y dx yx ε = . (a) Show that ln ( ) ln d y x dx d x dx = . (Thus if you graph ln y against ln x , the slope of the graph is the elasticity.) (b) Show also that if ( ) = and ( ) zg x = , where ( ) 0 gx , ln ( ) ln ( ) d y x dx yz d zx dx = . (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 αβ = (ii) 11 (, ) ( ,) ,) ( y x xy εε == (iii) ( = (iv) 12 1 2 (, )( , , ) yy x y x =+ (v) 1 2 ( / ,) y yx =− (vi) 21 1 ) (,) yy p p = 2. Elasticity of Substitution
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Suppose 11 2 2 arg { | ( ) } c x x Min p x p x U x U =+ . This is known as the consumer’s “compensated demand” since, as the price vector changes, the consumer’s income is adjusted so that utility is constant. (a) Use the above results to show that 21 12 (,) (,) cc x px p x p σ εε == , HINT: define / p pp = . This elasticity of the consumption ratio with respect to the price ratio is called the elasticity of substitution.
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2010Exercise2-1 - Econ 200 Homework Exercises 1. Elasticity...

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