Question: The Lone Star Transportation Company hauls coal and manufactured goods. The demand curve for its services by the coal producers is

P_C = 495 – 5Q_C

where P_C is the price (in dollars) per ton-mile of coal hauled and Q_C is the number of ton-miles of coal hauled (in thousands). The demand curve for its services by the producers of manufactured goods is

P_M = 750 – 10Q_M

where P_M is the price (in dollars) per ton-mile of manufactured goods hauled and Q_M is the number of ton-miles of manufactured goods hauled (in thousands). The firm’s total cost function is

TC = 410 + 8(Q_C + Q_M)

where TC is total cost (in thousands of dollars).

a. What price should the firm charge to haul coal?

b. What price should the firm charge to haul manufactured goods?

c. If a regulatory agency were to require the firm to charge the same price to haul both coal and manufactured goods, would this reduce the firm’s profits? If so, by how much?