. As long as no firm has cheated, play according to the agreement to optimize joint profits and split the proceeds . If either firm has cheated in any earlier period , play the static Nash equilibrium in every period from now on. 1. If both firms follow the proposed strategy, what is the present discounted value of each firm's profits? 2. If one firm decides it will cheat on the agreement and violate the strategy, what is the highest profit that firm can achieve? 3. Based on your previous answers in this question , is the proposed strategy an equilibrium? Why or why not? 4. What is the lowest discount factor, . that the firms could have for the proposed strategy to be an equilibrium? Problem 6 (This problem is NOT to be handed in ). Suppose there are two emer gency hospitals in Townville, State ER and University ER. Overall demand (patients) for ER visits in Townville is ? = 120 - 20 per day, where @ = q, + 4. . Marginal cost at the State ER is c. = 84 per patient. University has access to better equipment so their marginal cost is C. = 70. Suppose University ER is the Stackelberg leader and is able to choose their quantity before State ER . State ER then responds to the choice by University. 1. Write down the profit function for State ER as a function of their quantity of patients (q.) and the choice of University's quantity of patients (.). 2. Solve for State's optimal strategy in the Stackelberg game. 3. Write down the profit function for University ER as a function of their quantity of patients (9.) only. 4. Solve for university's optimal strategy