economics/cost&inversedemand

(20 points) The market inverse demand curve is P(y) = 10 23/, and a monopolist's cost curve is y2 + 2. (a) (b) What output level y maximizes the monopolist's revenue? What output level y maximizes the monopolist's prot? Identify which of the two output levels is lower, and explain why using economic intuition. Suppose a second rm with cost curve y2 + 2 is considering entering the market. If after entry, the rms would compete a la Cournot, what would be the Cournot- Nash equilibrium output levels yl and y2 of rms 1 and 2? What would be the equilibrium prots for each rm? Will rm 2 choose to enter the market? Suppose that if rm 2 enters, both rms collude, choosing output levels that maxi- mize total prots and then split the prots equally between them. What would be the prots to each rm? Will rm 2 choose to enter the market in this case