Zagna is a pharmaceutical company that holds a patent on a new drug; thus, it is a monopolist. The demand for its drug by is given by
Q = 180 - 2P
where P is the price per dose (in dollars) and Q is the number of doses demanded each month (in millions). The total cost of providing this drug is Total Cost = 20 + Q2, while the marginal cost is given by MC = 2Q. If the monopolist is unregulated, what price will it charge per dose? Calculate Zagna's profit at this price and Total Welfare to Society. Now, suppose that the government thinks that Zagna is charging too high a price and institutes a price cap at $10 below what Zagna is charging (that is, $10 below the profit maximizing price). How much output would the firm produce at this price? What would Profit and Total Welfare to Society be in this case? What if the price cap is set $15 below the profit-maximizing price?