Uniform Pricing Monopolist

Suppose a uniform pricing monopolist’s price equation is P(Q) = 100 – 2Q; the uniform pricing monopolist’s marginal revenue is MR(Q) = 100 – 4Q; the uniform pricing monopolist’s total cost is C(Q) = 2Q2 + 12Q + 50; and the uniform pricing monopolist’s marginal cost is MC(Q) = 4Q + 12.

a. Solve for the profit-maximizing (or loss minimizing) quantity (Q*).

b. Solve for the profit-maximizing (or loss minimizing) price (P*). 

c. Should the uniform pricing monopolist produce Q*? Explain why using one of the four key questions and solutions.

d. Does the uniform pricing monopolist make a profit? Explain why using one of the four key questions and solutions.

e. How much profit (or loss) does the uniform pricing monopolist make?