Problem 2. Consider the market for a covid19 vaccine. Suppose the marginal cost of producing the vaccines follows P = 10 + 505. and that the IP owner is willing to sell the vaccine at marginal cost. Demand follows P = 20 500. Here, 0 represents vaccines, measured in 100 million doses. As always, these numbers are made up with the goal of making the problem solving easy for you. Assume: (A1) that demand fully reflect the private marginal benefit of using the vaccine, and (A2) that the use of vaccines generates an external benefit of $10 per 0, due to the decreased risk of spreading disease to others. That is, each unit consumed generates $10 of value to people other than the consumer. 6) Find the equilibrium 0 if the government paid consumers $10 to consume vaccinations in order to help consumers internalize the positive extemalities they generate by using the vaccine. HINT: This will change demand. Everyone should be willing to face a $10 higher price, since the government will give them a $10 rebate. f) Consider the possibility that consumers' valuation of the vaccine is too high (relative to being fully informed) because they don't fully appreciate the risk of side effects. How would that case relate to the Theorem of the Second Best? (Two sentences)