Consider two firms, Firm A and Firm B, who compete as duopolists. Each firm produces an identical product. The total inverse demand curve for the industry is = 250 − ( + ). Firm A has a total cost curve ( ) = 100 + 2 . Firm B has a total cost curve ( ) = 100 + 2. a. Suppose for now, only Firm A exists ( = 0). What is the Monopoly equilibrium quantity and price? What is Firm A's profit? b. Find the Nash Cournot equilibrium price and output level. What are the firms' profits? c. Find the equilibrium price and output level in the market if firm A acts as a Stackelberg leader. What are the firms' profits? d. Suppose that the two firms are able to form a cartel. Derive the output each firm will produce, the market price, and the total profit under the cartel solution. e. Compare the Cournot, Stackelberg, and Cartel outcomes to the monopoly outcome you calculated in part a.

The owners of backstreets italian restaurant are considering starting a delivery service forpizza and their other italian dishes in the small college town where they are located. theycan purchase a used delivery van and have it painted with their name and logo for $21,500.they can hire part-time drivers who will work in the evenings from 5 p.m. to 10 p.m. for$8 per hour. the drivers are mostly college students who study at the restaurant when theyare not making deliveries. during the day, there are so few deliveries that the regular employeescan handle them. the owners estimate that the van will last 5 years (365 days per year)before it has to be replaced and that each delivery will cost about $1.35 in gas and othermaintenance costs (including tires, oil, scheduled service, they also estimate that onaverage each delivery order will cost $15 for direct labor and ingredients to prepare andpackage, and will generate $34 in revenue.a. how many delivery orders must backstreets make each month in order for the service to break even? b. the owners believe that if they have approximately the break-even number of deliveries during the week, they will at least double that number on fridays, saturdays, and sundays. if that’s the case, how much profit will they make, at a minimum, from their delivery service each month (4 weeks per month)?