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Unformatted text preview: Comparative Statics L A T E X file: ComparativeStaticsnball Daniel A. Graham <daniel.graham@duke.edu>, June 22, 2005 Comparativestatics involves the determination of the effect of changes in the value of an exogenous variables on the value of an endogenous variable , e.g., the effect of a change in price of x on the quantity demanded of x. Explicit Solution If we have enough information we can solve for the comparative static effects explicitly. If, for example, we started with the CobbDouglas utility function util = a Log [x] + b Log y ; In: we could derive the demand function for x via the substitution method by solving the budget constraint for y, budget = Solve px x + py y == m,y In: (( y m px x py )) Out: substituting the result into the utility function, util = util/.budget [[ 1 ]] In: a Log [x] + b Log " m px x py # Out: differentiating with respect to x, firstorder = D [ util , x] In: a x b px m px x Out: setting the result equal to zero and solving for x sol = Solve [ firstorder == ,x] In: (( x am (a + b) px )) Out: We could then differentiate the demand function obtained in this way with respect to px to obtain the comparativestatic effect of a change in px upon the quantity demanded of x: D [x /.sol [[ 1 ]], px ] In: am (a + b) px 2 Out: InputForm...
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This document was uploaded on 10/20/2011.
 Spring '09
 Physics

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