Firms maximize profit by choosing the output where marginal revenue equals marginal cost. Consider a monopolist whose inverse demand is P = 20 - Q, TC = 1.5Q² and MC = 3Q.

a. What quantity maximizes this firm's profit? Write down the firm's marginal revenue, set it equal to marginal cost and solve for Q. This is the firm's profit-maximizing output.

b. What price does the profit-maximizing firm charge? Evaluate the firm's inverse demand function at the profit-maximizing output. When Q^maxequals the profit-maximzing output, the profit-maxizing price is given by P^max = 20 - Q^max.