3.12 Suppose that an incumbent can commit to producing a large quantity of output before the potential entrant decides whether to enter. The incumbent chooses whether to commit to produce a small quantity, qi, or a large quantity. The rival then decides whether to enter. If the incumbent commits to the small output level and if the rival does not enter, the rival makes $0 and the incumbent makes $900. If it does enter, the rival makes $125 and the incumbent earns $450. If the incumbent commits to producing the large quantity, and the potential entrant stays out of the market, the potential entrant makes $0 and the incumbent makes $800. If the rival enters, the best the entrant can make is $0, the same amount it would earn if it didn’t enter, but the incumbent earns only $400. Show the game tree. What is the subgame perfect Nash equilibrium? (Hint: See Solved Problem 14.3.)