Question: (a) If a firm sells Q tons of a product, the price P received per ton is P = 1000 - 1/3Q. The price it has to pay per ton is P = 800 + 1/5Q. In addition, it has transportation costs of 100 per ton. Express the firm's profit as a function of Q, the number of tons sold, and find the profit-maximizing quantity.
(b) Suppose the government imposes a tax on the firm's product of 10 per ton. Find the new expression for the firm's profits πˆ and the new profit-maximizing quantity.