The City of Oakland is considering alternative ways of providing cable TV service to its residents. Based on an econometric analysis of several recently awarded cable franchises in other cities, economists have determined that the total cost, TC, and demand curves for a cable company in Oakland would be:
TC=2Q-0.1Q2+0.005Q3
P=20-0.5Q

Q is measured in terms of thousands of customers, and P is a basic monthly price.
a. Given the above information, what are the equations for the total revenue (TR) curve and the marginal revenue curve? Draw a graph for each one. TR=PQ. Note on Blackboard: the marginal revenue curve has the same intercept and double the slope of the demand curve. 
b. A first city council member believes that the city should operate the franchise and try to maximize profit. What would be the values for P and Q? You can get an approximate answer by drawing a diagram, or an exact answer by using calculus (the derivative of TC with respect to Q equals MC).
c. A second city council member argues that the city should provide as much cable service as possible without losing money. Use a diagram for total revenue and total cost to find the values of P and Q where profit becomes zero, and where Q is as high as it can be without losses being incurred.
d. A third city council member believes that the private sector should provide the service, but the private company that gets the franchise should pay 10 percent of its total revenue back to the city as an annual franchise fee. If the franchise would be given to the company promising to pay the largest franchise fee, what P and Q would occur? What will be the size of the annual franchise fee?