Problem 4. The city of Philadelphia would like to start allowing electric scooter companies to operate in town. There are two potential bidders for a contract to operate scooters: Scoot-Away Inc. (SA) and Electric-Slide Co. (ES). The (inverse) demand for scooters is known to all and is stable over time: P = 156 - Q (Note that this implies SA and ES scooters are perfect substitutes.) For both SA and ES, the (monthly) cost of putting a scooter on the road is zero MC = 0. In addition, each firm pays a (monthly) fixed cost F to keep their operation going. The fixed cost is the same for SA and ES and commonly known between them. The city does not know F. The price is that which clears the market. The mayor tasks the city's department of transportation to design the contracting. Officials decide that in their application for a permit SA and ES must set out how many scooters they will put on the road each month. To avoid potential collusion, (monthly) quantities stated on the application are final. However, officials are unsure whether they want to award contracts (1) simultaneously or (2) sequentially. If they decide to contract in sequence, the city will choose the leader by a public lottery. 1. Write down each firm's profit (objective) function. Do firms choose their price or their quantity? 2. Suppose the city believes that F =$100. What is the (monthly) consumer surplus in the scooter market if contracts were awarded simultaneously