The Plymouth Software Company has the following demand curve with MC = $10 and P = 100 Q with MR = 100 2Q. The company has option of charging monopolist price or perfect competitor price. Here it is assumed that monopoly demand curve is identical with market demand curve of perfectly competitive market (i.e., they share the same demand curve):

a. Compute profit maximizing price and output under perfectly competitive market and under monopoly. And compare the difference between them in terms of P and Q and discuss reason for the difference.

b. Compute consumer surplus under perfect competition and monopoly.

c. Is there any additional downside of monopolist vis - vis pure competition from a society's point of view in terms of Pareto's efficiency? Hint: reexamine consumer surplus discussed in (b). 

d. Many amusement parks charge entrance fee and separate fees for each ride. In view of the above discussion, what do you think is the reason for it? Hint: consider consumer surplus.

e. What is the advantage for duopoly (two oligopoly firms) with equal size sharing the identical demand to behave as one monopolist and split the profit afterward rather than behave as two different firms under oligopoly? Under duopoly, each duopoly each firm would be able sell 30 units each. Present your arguments clearly with quantitative support for your answer. 

f. Suppose that the two firms under the above duopoly have now two different demand curves, not one identical market demand curve; one is more elastic than the other. Would it be still advantageous for them to behave as one monopolist or not? Why or why not? You do not need quantitative support in answering this question.