# Cross-Price and Advertising Elasticity

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Cross-Price Elasticity.

B.B. Lean is a catalog retailer of a wide variety of sporting goods and recreational products. Although the market response to the company's spring catalog was generally good, sales of B.B. Lean's $140 deluxe garment bag declined from 10,000 to 4,800 units. During this period, a competitor offered a whopping $52 off their regular $137 price on deluxe garment bags.

A. Calculate the arc cross-price elasticity of demand for B.B. Lean's deluxe garment bag.

B. B.B. Lean's deluxe garment bag sales recovered from 4,800 units to 6,000 units following a price reduction to $130 per unit. Calculate B.B. Lean's arc price elasticity of demand for this product.

C. Assuming the same arc price elasticity of demand calculated in part B, determine the further price reduction necessary for B.B. Lean to fully recover lost sales (i.e., regain a volume of 10,000 units).

Advertising Elasticity.

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 $3250 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% of all purchases and monthly sales rose to 15,000 units.

A. Calculate the arc price elasticity implied by the initial response to the Enchantment price increase.

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

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

D. Why might the true arc advertising elasticity differ from that calculated in part C?

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This solution finds the elasticity of demand: cross price and advertising elasticity in easy to follow, step by step calculations.

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The cross-price elasticity of demand = percentage change in quantity demanded (B.B. Lean) / percentage change in price (competitor).

The percentage change in quantity demanded = (4,800 - 10,000) / [(4,800 + 10,000) / 2] = -0.7027 = 70.27%.

The percentage change in price = (85 - 137) / [(85 + 137) / 2] = -0.4685 = -46.85%

The cross-price elasticity of demand = -0.7027 / -0.4685 = 1.50.

The price elasticity of demand = percentage change in quantity demanded / percentage change in price.

The percentage change in quantity demanded = (6,000 - 4,800) / [(6,000 + 4,800) / 2] = 0.2222 = 22.22%

The percentage change in price = (130 - 140) / [(130 + ...

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