Consider the dynamic monopoly model studied in class. Suppose instead that Hal, Hilbert, Laurie, and Laurel's valuations changed to the following: Hal, Hilbert Laurie, Lauren Period 1 1200 400 Period 2 2 200 Total 1200 + r 600 The above table means that Hal and Hilbert obtain a total of 1200+2-pi utils for purchasing the printer in period 1 at a price of p, because they are able to enjoy the printer for both periods. On the other hand, if Hal and Hilbert were to buy the printer in period 2 at a price of p2, then they only obtain a total utility of 2-p2. Part a: (10 pts). Suppose that z = 200, then is there a SPNE in which Hal and Hilbert purchase in period 1 and Lauric and Lauren both purchase in period 2? Explain why or why not. In either case, describe a SPNE of this game. Part b: (10 pts/ Now suppose that z = 1000. Repeat part a. Part c: [10 pts/ Finally suppose that a = 500. Repeat part a. Part d: +10 pts Extra Credit] Compare the profits to the seller in SPNE computed in part a and part c. Does it necessarily benefit the seller when r is higher? Explain why your finding makes sense intuitively.