Problem 2. Suppose there are two emergency hospitals in Townville, State ER and University ER. Overall demand (patients) for ER visits in Townville is P = 120 262 per day, Where Q = qs + qu. Marginal cost at the State ER is ca = 84 per patient. University has access to better equipment so their marginal cost is Cu 2 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 prot function for State ER as a function of their quantity of patients (qs) and the choice of University's quantity of patients (qu). 2. Solve for State's optimal strategy in the Stackelberg game. 3. Write down the prot function for University ER as a function of their quantity of patients (qu) only. 4. Solve for University's optimal strategy. 5. Solve for both hospitals quantity of patients served, the equilibrium price, and prot for both rms when the SPNE is played. 6. What is total surplus (Consumer surplus+Prot)? 7. Suppose after State makes their choice of quantity of patients, University is able to react and easily expand or contract their service. What is the outcome of this model and Why is it different from above? (No need to solve the model, just intuitively explain what will happen and Why)