Suppose that the demand for bentonite is given by Q = 40 - 0.5P, where Q is in tons of bentonite per day and P is the price per ton. Bentonite is produced by a monopolist at a constant marginal and average total cost of $10 per ton.
a. Derive the inverse demand and marginal revenue curves faced by the monopolist.
b. Equate marginal cost and marginal revenue to determine the profit-maximizing level of output.
c. Find the profit-maximizing price by plugging the ideal quantity back into the demand curve.
d. How would your answer change if marginal cost were instead given by MC = 20 + Q?