# Cross-price elasticity | Economics homework help

1.) 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 reductionto \$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).

2. ) Supply Curve Determination. Olympia Natural Resources, Inc., and Yakima Lumber, Ltd., supply cut logs (raw lumber) to lumber and paper mills located in the Cascades Mountain region in the state of Washington. Each company has a different marginal cost of production depending on its own cost of landowner access, labor and other cutting costs, the distance cut logs must be shipped, and so on. The marginal cost of producing one unit of output, measured as one thousand board feet of lumber (where one board foot is one square foot of lumber, one inch thick), is:
MCO = \$350 + \$0.00005QO (Olympia).
MCY = \$150 + \$0.0002QY (Yakima).

The wholesale market for cut logs is vigorously price competitive, and neither firm is able to charge a premium for its products. Thus, P = MR in this market.

A. Determine the supply curve for each firm. Express price as a function of
quantity and quantity as a function of price. (Hint: Set P = MR = MC to find each firm=s supply curve.)

B. Calculate the quantity supplied by each firm at prices of \$325, \$350, and \$375. What is the minimum pricenecessary for each individual firm to supply output?

C. Assuming these two firms make up the entire industry in the local area, determine the industry supply curve when P < \$350.

D. Determine the industry supply curve when P > \$350. To check your answer, calculate quantity at an industry price of \$375 and compare your result with part B.

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