Question: (a) By selling x tons of one commodity the firm gets a price per ton given by p(x). By selling y tons of another commodity the price per ton is q(y). The cost of producing and selling x tons of the first commodity and y tons of the second is given by C(x, y). Write down the firm's profit function and find necessary conditions for x∗ > 0 and y∗ > 0 to solve the problem. Give economic interpretations of the necessary conditions.
(b) Suppose that the firm's production activity causes so much pollution that the authorities limit its output to no more than m tons of total output. Write down the necessary conditions for x^ > 0 and y^ > 0 to solve the problem.