Please help answer questions 3-8. Thank you!

For example, pharmaceutical companies that hold patents on several pharmaceutical drugs sell their products at prices with relatively high markups. After a very large and risky cost for research and development to discover the new drug, the drug company must also pay the high costs of clinical trials as it progresses through the Food & Drug Administration (FDA) approval process which may take several years. If the FDA approves its drug (failed clinical trials may prevent FDA approval), then the firm will be allowed to sell its new drug on the market. The firm will earn monopoly profits on its product for the remaining years of the life of its patent, until generic drug companies (i.e. its competitors) may entire the market after the patent expires. Suppose a pharmaceutical company has invested $520 million to discover a new drug (Drug X) that alleviates all symptoms of the COVID-19 virus. It is awarded a patent on December 1, 2020. The companies spend an additional $420 million on extensive clinical trials to gain FDA approval on December 1, 2024. Suppose the annual demand for the new drug is given by P(Q) = 400 - 0.04Q where Q is the number of units of the drug (in thousands) and P is the price of the drug (in dollars). Assume that the firm faces a constant marginal cost and average total cost of production equal to $40 per unit. Answer the following questions: 1. At what date will the patent expire? 2. How many years will the firm be able to sell drug X at monopoly prices? Recall that drug companies must gain FDA approval before they may sell their product. 3. Derive the monopoly profit-maximizing output level the firm will produce annually? What is the profit-maximizing price? Include all units for full points. 4. Draw a graph to identify the monopoly equilibrium price and output level for a given year. Label the horizontal axis as "Quantity (in thousands)" and the vertical axis as "Price (in dollars)." You must include all relevant curves and label them appropriately. 5. Calculate the total profit earned annually by the firm. 6. Label and shade the total annual profit in your graph drawn in part (4) in blue. 7. Calculate the total profit earned over the lifetime of the patent. (For simplicity, ignore the present discounted value.) 8. Does the firm ever recoup the cost of its investments? How much does the firm earn in profit minus its investments during the lifetime of its patent? Part II A debate within economics is the conflict between antitrust principles (which are designed to protect and promote competition among firms) and