2. An incumbent rm has a monopoly in the market for a particular good. Demand for the industry's product is described by the inverse demand curve P : 10 Q if Q g 10, where P is the price of the good and Q is total output. The incumbent rm has a constant unit cost of 2 (i.e., total cost 2Q of producing Q units of output). A new firm is considering competing with the incumbent. The new rm can also produce the good at a constant unit cost of 2. However, the new firm would have to incur a xed cost of 1 to enter the industry. (a) 0)) Suppose the firms compete according to the following timeline. First, the new rm decides whether or not to incur the fixed cost of 1 and enter the market. If the new rm does not enter, the incumbent rm maintains its monopoly. If the new rm does enter, the rms compete in Stackelberg fashion, with the incumbent choosing its level of output first, and the new firm choosing second. Firms' payoffs are their prots, with the new rm's xed cost included in [i.e., subtracted from) its prot if it enters. Find the subgame perfect equilibrium of this game, and the subgame perfect equilibrium outcome. When stating the equilibrium, remember to account for the incumbent's action in the subgame in which the new rm does not enter. Now consider the same interaction with one change in the timeline: the incumbent moves rst and chooses its level of output before the new rm decides to enter or not. The new rm then either stays out, or enters and chooses its output. Find the subgame perfect equilibrium of this game. Hint: it will be important to write the new rm's prot when it enters as a function of the incumbent's choice of output. To do so, substitute the expression relating the incumbent's output to the new rm's output that is derived by requiring the new rm to use a best response in the last stage of the game