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In a preseason sale, the catalog retailer offered a discounted "early bird" price of $70 on Birkenstock sandals and noted a moderate increase in weekly sales from 275 to 305 pairs per week. This $5 discount from the regular price of $75 represents a modest 6.7 percent mark-down. Using the arc price elasticity formula, the implied arc price elasticity of demand on Birkenstock sandals is

E = Q2 - Q1 X P2 + P1 P P2 - P1 Q2 + Q1 = 305 - 275 X $70 + $75 = $70 - $75 X 305 + 275 = -1.5

In the absence of additional evidence, this arc price elasticity of demand EP = -1.5 is the best available estimate of the current point price elasticity of demand. Using Equation 12.9, the $75 regular catalog price reflects an optimal markup on cost of 200 percent because

Optimal Markup _ -1

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