Currently, There Is an Incumbent Monopoly in the Market

Essay

Currently, there is an incumbent monopoly in the market. Next year, a potential entrant may enter. The incumbent needs to make a decision on whether or not it should spend $50 to lobby the government into passing legislation which places a lump- sum tax of $100 on the potential entrant if it enters. If the potential entrant stays out of the market it makes zero profit and the incumbent firm makes a monopoly profit, Profit_m>0, minus expenditures on lobbying if any ($50 or $0). If the potential entrant enters the market, it gets duopoly profit, Profit_d=$200, minus the tax if any, and the incumbent gets duopoly profit minus the lobbying costs if any.
a)Show the game in extensive form. What strategies will be played?
b)Suppose the tax on the potential entrant is $210 instead of $100. Repeat part A. How large must Profit_m be for the monopolist to want to lobby?