where Y and X are two different products. The arc cross-price elasticity relationship is constructed in the same manner as was previously described for price elasticity:
E = Percentage Change in Quantity of Y PX Percentage Change in Price of X
= (Qy2 - Qy1)/[(Qy2 + Qy1)/2] (Px2 - Px1)/[(Px2 + Px1)/2] = AQy x PX2 + PX1 APx Qy2 + Qy1
The cross-price elasticity for substitutes is always positive; the price of one good and the demand for the other always move in the same direction. Cross-price elasticity is negative for complements; price and quantity move in opposite directions for complementary goods and services. Finally, cross-price elasticity is zero, or nearly zero, for unrelated goods in which variations in the price of one good have no effect on demand for the second.
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