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When referring propensity, we are talking about the first derivative---- dY/dX , while elasticity has the form (dY/Y)/(dX/X). To see why we need to use the second nasty formula, try d(PQ)= Q*dP+P*dQ. To check if d(PQ) >0 holds, we can check instead the PdQ/(QdP)'s relation with -1.
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