Problem 4: [30 pts] Consider the problem of Dell and its production of computers. In order sell its computers, Dell must buy an Intel chip for each computer that it sells. However, Intel sole supplier of these chips and so exercises market power over Dell in its supply decision. To model this scenario, we study the following dynamic game. The game begins with Int setting a price py E [0, 100]. Then after observing this price, Dell decides on a price pp > [ Given these prices, the demand for Dell computers by consumers is determined by: 306 QD(PD) = 100 - PD. Since each computer that Dell sells must contain an Intel chip, it must purchase QD(pp) units of chips from Intel at the chosen price of py. Suppose there are no further costs of production. Thus, the utility (profit) functions of the firms are: UI(PI, PD) = PI(100 - PD), up(PI, PD) = (PD - PI) (100 - PD). Part a: /10 pts/ Solve for the NE of the proper subgame after Intel decided on a price of py E [0, 100] for its chips. Part b: /10 pts/ Solve for the subgame perfect Nash equilibria of this game. What is the chosen strategy profile? What is the actual price that Dell chooses in equilibrium? Part c: /10 pts/ Suppose hypothetically that Dell and Intel decided to merge so that all Intel chips can be produced without cost to Dell. Let's call this giant monopoly Delltel. Suppose that Delltel is a monopolist with demand given by: Q = 100 - p. As a result, if the monopolist chooses a price p 2 0, then it would obtain profit of: (100 - p)p. What price would the monopolist choose? Compare this to the solution from Part b? Which scenario would the consumers prefer? Discuss the intuition