calculation of arc elasticity
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5. Ez Auto Wash recently decided to raise its regular price on wash and wax cycles from $5 to $7 following increases in the costs of equipment and materials. Unfortunately, sales dropped sharply from 6,000 to 2,000 per month. In an effort to gain lost sales, EZ ran a coupon promotion featuring $4 off the new regular price. Coupon printing and distribution costs totaled $100, and caused only modest increase in the typical advertising budget of $1650 per month. The promotion was judged a success as it proved highly popular with consumers. In the period of expiration, coupons were used on 25% of all purchases and monthly sales rose to 3,600 washes.
A. Calculate the arc elasticity implied by the initial response to EZ's price increase.
B. Calculate the effective price reduction resulting from the coupon promotion.
C. In light of this price reduction, and assuming no change in the price elasticity of demand, calculate EZ's arc advertising elasticity.
D. Why might the true arc advertising elasticity differ from that calculated in part C?
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Solution Summary
calculation of arc elasticity and effective price reduction based on coupon promotion
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The arc elasticity concept is appropriate when considering the effect large changes in independent variable. The arc elasticity is an average elasticity over a range along a given function. When we use arc elasticities we do not need to worry about which point is the starting point and which point is the ending point.
For the arc elasticity calculation you use this equation:
deltaQ/deltaP *(P2+P1)/(Q2+Q1)
Demand fell from 6,000 to 2,000, or 4000. The price increased from 5 to 7 dollars, or 2. Thus we ...
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