Enchantment Cosmetics, Inc., offers a line of cosmetic and perfume products marketed through leading department stores. Product manager Erica Kane recently raised the suggested retail price on a popular line of mascara products from $9 to $12 following increases in the costs of labor and materials. Unfortunately, sales dropped sharply from 16,200 to 9,000 units per month. In an effort to regain lost sales, Enchantment ran a coupon promotion featuring $5 off the new regular price. Coupon printing and distribution costs totaled $500 per month and represented a substantial increase over the typical advertising budget of $3,250 per month. Despite these added costs, the promotion was judged to be a success, as it proved to be highly popular with consumers. In the period prior to expiration, coupons were used on 40 percent of all purchases and monthly sales rose to 15,000 units.

1. Calculate and interpret the arc price elasticity implied by the initial response to the Enchantment price increase.

2. Calculate the effective price reduction resulting from the coupon promotion.

3. In light of the price reduction associated with the coupon promotion and assuming no change in the price elasticity of demand, calculate and interpret Enchantment’s arc advertising elasticity.

4. Why might true arc advertising elasticity differ from that calculated in item 3?

C. To calculate the arc advertising elasticity, the effect of the $2 price cut implicit in the coupon promotion must first be reflected. With just a price cut, the quantity
Demanded would rise to 13,000, because:
EP= (Q-Q1)/(P2-P1) x (P2-P1)/(Q+Q1)

-2 =(Q-9000)/($10-$12) x ($10-$12)/(Q+9000)

-2 = (-11(Q-9000))/█((Q+9000)@)
-2(Q* + 9,000) = -11(Q* - 9,000)
-2Q* - 18,000 = -11Q* + 99,000
9Q* = 117,000
Q* = 13,000

Then, the arc advertising elasticity can be calculated as:
EA =