Question is below:

II. Consider a monopolyr with the marginal cost :1: and the inverse demand function F = o inc. {1} Conrm that the production maximizing the monopolf's prot is {(H b 1):: ox)' = II] a I'.' (111' x = E and the price at that time is p = T" {2} Find the price at which the consumer surplus is maximized in the range in which the rm does not shut down its operation. Find the production at that time. {3} Illustlate the three changes of regions due to the price a change from EH1} to (112] corresponding to ia] the social surplus . increase, {b} the consumer surplus increase, and is} the firm '1'\" 2 prot decreases, on the graph on the right. ' C o r: 2!: {4} Suppose that the price is determined by a contest with the Tullocl: contest function between a consumer group and the monopoly. where the price of EH2} is realized if the consumer group wins and the price of 011} is realized if the monopoly; wins. Find the sum of the resources input by the {31:}2 41:: consumer group and the monopoly; in equilibrium (Hint: Introduce a constant A7 = }. Does the social surplus increase due to this rent-seeking contest? (Hint: check the sign of "the area of owns] x the percentage of the consumer group's win - the resource sum\")