Suppose there is an incumbent monopolist in a market. A potential entrant is deciding whether to ‘enter’ or ‘not enter’ the market. If the potential entrant chooses ‘enter’, then the incumbent can...

Suppose there is an incumbent monopolist in a market. A potential entrant is deciding whether to ‘enter’ or ‘not enter’ the market. If the potential entrant chooses ‘enter’, then the incumbent can choose to either ‘lobby’ or ‘not lobby’ the government to impose a tax on the potential entrant. If the incumbent chooses to ‘lobby’, this imposes a cost on it of $20, but as a result, the government passes a law that places a tax of $60 on the potential entrant. If the potential entrant chooses to not enter the market, it makes zero profit and the incumbent firm makes a monopoly profit equal to $100. If the potential entrant enters the market, it earns a duopoly profit of $50, minus any tax, and the incumbent earns a duopoly profit of $50, minus any lobbying costs. a Use a game tree to represent this game. b What is the subgame perfect Nash equilibrium of this game?