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:

MC_O =  $350 + $0.00005Q_O (Olympia).

MC_Y =  $150 + $0.0002Q_Y (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 price necessary 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.