2 Problem 2 Firm 1 and firm 2 compete with each other by setting thecorieach firm, its demand depends on its own procend the price of its opponent The demand function can be written as q = 20- p+pi. The marginal cost is constant at $4 for both firms. There is no fixed cost. Firm 1 and firm 2 set their prices every year. In each year, there is probability this market dies and their relationship ends. Assume no discounting. Answer the following questions. 1. Suppose= 0 (this is a one-shot simutaneous game), compute the equilibrium prices, quan- tities and profits for both firms. Answer: Firm 1 solves the maximization problem: max 74 = (20- p1 + ,p2) (p1 - 4) PI FOC(p1): - (p1 - 4) + (20 p1 + >p2) = 0 = p1 = 12 + p2 Since the game is symmetric, we pavep2. Then we can solve that= p = 16. The quantities are = op = 12. The profits are = Te = 144