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ComparativeStatics

ComparativeStatics - Comparative Statics A L TEX le...

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Comparative Statics L A T E X file: ComparativeStatics-nb-all — Daniel A. Graham <[email protected]>, June 22, 2005 Comparative-statics 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 Cobb-Douglas 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 == 0 , 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 comparative-static 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 [ Simplify [ % ]] In: - ( (a * m) / ( (a + b) * px
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