Problem 3: Mathematical Monopoly! [12 Points] "(ainios aj (vloganoM :S malday!) Suppose that a firm acts as a local monopolist that sells tobacco. The monopolist faces a local demand given by: QD = 100 - 4p This firm also has a cost structure given by: MC = habramad 00.23 The firm has zero fixed costs. 9. What is the profit-maximizing quantity for this monopolist to produce? Show your work. [2 points] Now suppose that the government steps in to regulate this monopolist, and imposes a price ceiling of $15 for this monopolist. 10. Draw a figure here that includes the demand curve, marginal cost (MC), marginal revenue (MR), and original choice of production (answer to part 1). As always, keep quantity on the x-axis and price on the y-axis. Label all intercepts. [2 points] 11. At what quantity will this new regulated monopolist choose to produce? Show your work. [2 point] 12. What happens to both profits and consumer surplus in this case? If they change, by how much? Show your work. [HINT: To do this, you will need to calculate the old CS & PS under the unregulated monopoly, and then the new CS & PS with the price ceiling. ] [6 points]