Question 3. Apple and Samsung. (25 marks) Consider the price competition between Apple and Samsung in the U.S. market for smartphones. Assume that the demand for iPhones is determined by the following equation: Q4(PA, PS) = 5000 - 3PA + 2PS where PA is Apple's price for an iPhone, and P" is Samsung's price for a Galaxy. The demand for Samsung Galaxy phones is Q5(PA, ps) = 5000 - 3P5 + 2PA. Each firm has a constant marginal cost of $1000: MCA = MCS = 1000. (a) (4 marks) Determine the optimal pricing strategy for each firm. (b) (2 marks) Calculate the equilibrium profits for each firm. Next consider the following two scenarios independently. Scenario I. Tariff. Suppose the U.S. imposes a tariff on imports of Chinese goods, which increases the marginal cost of the iPhone by $100. On the other hand, we assume that the tariff has no impacts on Samsung Galaxy. (c) (5 marks) Redo (a) and (b). (d) (3 marks) Based on your answers in (a)-(c), discuss how the tariff affects (i) the prices of smartphones, (ii) the market share of each firm, and (iii) the profits of each firm. Scenario II. Research and Development. Suppose now each firm can make an investment in R&D to enhance its product features and differentiate the product from its rival. Denote by /4 the amount of money Apple spends on R&D, and Is the amount of money Samsung spends on R&D. For simplicity, assume IA and Is admit the following two values: $0 and $500,000. Given (14, IS), the demand for iPhones is determined by the following equation: Q4(PA, PS, 14, IS) = 5000 + - 3PA + 2PS 500 and the demand for Samsung Galaxy phones is Q5(PA, p5, 14, Is) = 5000 + IS - 14 - 3p5 + 2PA. 500 Consider the following two-stage game. In the first stage, Apple and Samsung simultaneously choose R&D spending /4 and I', respectively. In the second stage, after observing each other's investment in R&D in the first stage, Apple and Samsung simultaneously choose prices PA and PS, respectively. (e) (8 marks) Find the subgame perfect Nash equilibrium of this two-stage game. (f) (3 marks) Based on your answer in (e), discuss whether the R&D race on product differen- tiation leads to the Prisoner's dilemma between Apple and Samsung