Problem 3: [30 pts] Consider the dynamic monopoly model studied in class. Suppose instead that Hal, Hilbert, Lauric, and Laurel's valuations changed to the following: The above table means that Hal and Hilbert obtain a total of 1200+xp1 utils for purchasing the printer in period 1 at a price of p1, 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 xp2. Part a: [10 pts/. Suppose that x=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 x=1000. Repeat part a. Part c: / 10 pts/ Finally suppose that x=500. Repeat part a. Part d: I 10 pts Extra Credit/ Compare the profits to the seller in SPNE computed in part a and part c. Does it necessarily bencfit the seller when x is higher? Explain why your finding makes scnse intuitively. Problem 3: [30 pts] Consider the dynamic monopoly model studied in class. Suppose instead that Hal, Hilbert, Lauric, and Laurel's valuations changed to the following: The above table means that Hal and Hilbert obtain a total of 1200+xp1 utils for purchasing the printer in period 1 at a price of p1, 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 xp2. Part a: [10 pts/. Suppose that x=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 x=1000. Repeat part a. Part c: / 10 pts/ Finally suppose that x=500. Repeat part a. Part d: I 10 pts Extra Credit/ Compare the profits to the seller in SPNE computed in part a and part c. Does it necessarily bencfit the seller when x is higher? Explain why your finding makes scnse intuitively