1. The market inverse demand curve isP(y) = 102y, and a monopolist's

cost curve isy2+ 2.

1. (a)What output levelymaximizes the monopolist's revenue? What output levelymaximizes the monopolist's profit? Identify which of the two output levels is lower, and explain why using economic intuition.
2. (b)Suppose a second firm with cost curvey2+ 2 is considering entering the market. If after entry, the firms would compete a la Cournot, what would be the Cournot- Nash equilibrium output levelsy1andy2of firms 1 and 2? What would be the equilibrium profits for each firm? Will firm 2 choose to enter the market?
3. (c)Suppose that if firm 2 enters, both firms collude, choosing output levels that maxi- mize total profits and then split the profits equally between them. What would be the profits to each firm? Will firm 2 choose to enter the market in this case?