Consider a monopoly whose: Inverse Demand curve is P = 90 - 0.5Q. The Total Cost function is TC = 20 + 2Q + 2Q2. The Marginal Cost equation is MC = 2 + 4Q.

Based on this information, answer the following questions: (i) Obtain the equation of the MR curve for the monopolist. (ii) Calculate the monopolist's profit maximising price and quantity, and show your working. (iii) Calculate the monopoly's market power and explain your work. (iv) By using the information in the question, draw appropriate curves on a diagram to show the monopoly's (a) profit maximising level of output and price, (b) the level of producer surplus and (c) the level of deadweight loss. (v) Calculate the value of producer surplus at the profit maximising price and quantity, and show your working. (vi) Calculate the size of the deadweight loss at the profit maximising price and quantity, and show your working. (vii) If this monopolist was perfectly price discriminating, then what area in your diagram for part (iv) would show the producer surplus? Explain your answer