Consider the following simple model. Suppose that the research and development cost of a new vaccine is equal to $15. A company X is considering investing in developing this vaccine.

The demand for the final product is given by P=10-Q, where P is the price of one vaccine dose and Q is the quantity demanded. The marginal cost of producing one dose of vaccine is constant (i.e. it does not depend on the output level) and is equal to $2. Let's assume for simplicity that the vaccine production process does not involve any fixed cost. This implies that the average total cost is also constant and equal to $2.

(a) Suppose that after developing a vaccine, company X can apply for patent which will prevent other firms from manufacturing and selling this product. Effectively, company X becomes the monopolist producer of the vaccine it has developed. What price will it charge for a vaccine dose? How many doses of vaccine will it produce? Hint: the marginal revenue curve of a monopolist in this market is MR=10-2Q. How much profit will it make? Given these outcomes, does it have an incentive to develop this vaccine in the first place? Demonstrate your answer on a GRAPH, carefully labelling all relevant variables and concepts. Overall do you think the patent is a good way to incentivise the development of a vaccine? Can you think of any possible drawbacks of this arrangement?

(b) Suppose that after company X develops a vaccine, other companies can freely use this idea to enter the market and produce and sell this vaccine. What will be the resulting market structure? What will be the equilibrium price and quantity? How much profit will each firm make? Does company X has an incentive to develop the vaccine on the first place? Demonstrate your answer on a GRAPH, carefully labelling all relevant variables and concepts. Overall, do you think allowing imitation is a good way to incentivise the development of a vaccine? What are the possible drawbacks of this arrangement?