Problem:
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 declines 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.
1) Calculate the arc cross-price elasticity of demand for B.B. Lean's deluxe garment bag.
2) B.B. Lean's deluxe garment bag sales recovered from 4800 units to 6000 units following a price reduction of $130 per unit. Calculate B.B. Lean's arc price elasticity of demand for this product.
3) Assuming the same are price elasticity of demand calculated in part B, determine the future price reduction necessary for B.B. Lean to fully recover lost sales (i.e., regain a volume of 10000 units).