Consider a monopolistic market with inverse demand P(q) = 500-2q. Suppose the monopolists cost function is c(q)=5q2+2g+20. a) What is the profit maximizing quantity qM and price pM? b) Depict the market graphically. Be sure to depict demand, marginal cost, average total cost, and the firm's profit (figure does not need to be to scale). c) How could the government set a price ceiling to improve social welfare?