Suppose that the (inverse) market demand for COVID Vaccine is given by P=400−2Q. Where Q is total industry output. [NOTE: Show all the details and steps of your calculation to answer following questions] a) Assume Pfizer is the only producer in the market with a constant marginal cost of production equal to $40. Calculate the profit maximizing price/quantity for Pfizer facing the entire market. Moderna announces that they have found another formulation for COVID Vaccine. Now, there are two equally powerful firms in the same market. Assume, each firm has the same constant marginal cost of production equal to $40 and they are competing in quantities. That is, they each choose production levels simultaneously. b) Calculate the best response function for each firm (i.e. each firm's profit maximizing choice of quantity given the other firm's production levels) c) Calculate the Cournot equilibrium for this industry. Calculate each firm's profits. d) Now, suppose that the two firms decide to form a cartel. Calculate the cartel output for each firm. e) Now calculate the cartel cheating response if either firm decides to cheat and break the cartel agreement.