Problem

Supply-Chain Design

Muslin Office Furniture manufactures a popular line of filing cabinets and has a very strong competitive position in its market. The company sells its product to a number of wholesale distributors, who in turn sellto retail customers. In this environment, the company faces a demand curve of the following form:

Q₁ = 20 0.6P₁

where P₁ denotes its selling price and Q₁ denotes the volume (in thousands) sold at that price. Muslin also experiences increasing marginal costs of the 0.8Q₁. Increasing marginal costs occur because quality losses and congestion on the shop floor volume rises.

One of Muslins distributors is a subsidiary known New England Supply. They represent Muslins exclusive distributor in the Northeast, and the parent comply allows them to operate as an independent entity, focused on distribution. They buy filing cabinets from Muslin and sell them to retail customers in Northeast. In that market, New England Supply faces its own demand curve:

Q₂ = 10 0.2P₂

where P₂ denotes the retail selling price and Q₂ denotes the volume (in thousands) sold in the Northeast at that price. New England Supply incurs its own operating costs, in addition to the cost of purchasing the product from Muslin, so that its marginal cost function takes the form P₁ + 0AQ₂.

a. Suppose Muslin Office Furniture and New England Supply each analyze their own pricing strategies separately. That is, Muslin finds its profit-maximizing price. Then New England Supply, whose cost is influenced by Muslins price, maximizes its own profits. What is each firms optimal price, and how much profit is earned between the two companies?

b. Suppose instead the two firms make coordinated decisions. In other words, they choose a pair of prices, one wholesale and one retail, aimed at maximizing the total profit between the two firms. What is each firms optimal price in this coordinated environment? How much profit is earned between the two companies?