The City of Berkeley is currently considering alternative ways of providing cable service to its citizens. Based on an econometric analysis of several recently awarded cable franchises in other cities, economists have determined that the total cost, $T C$, and inverse demand curves for a cable company in Berkeley would be:
$$
\begin{gathered}
T C=2 Q-0.1 Q^2+0.005 Q^3 \text { and } \\
P=20-0.5 Q,
\end{gathered}
$$
where output, $Q$, is measured in thousands and $P$ is the monthly basic tier price.
a. Given this information, what are the equations for the total and marginal revenue curves, and what do these curves look like on a graph?
b. City Councilor A believes the city should own and operate a cable system for the purpose of making as much profit as possible. The profit would be used to lower the city government's deficit. If Councilor A gets her way, what will be the price and output of cable and by how much will the cityowned system be able to reduce the city's deficit?
c. Councilor B believes the city should produce as much cable service as possible without losing money (i.e., the city should provide cable to its citizens on a nonprofit basis). If Councilor B gets his way, what output and price will result?
d. Councilor $\mathrm{C}$ believes that the private sector should provide cable to the city but that the single, private firm that gets the city's franchise should pay 10 percent of its total revenue back to the city in the form of an annual franchise fee. If Councilor $\mathrm{C}$ gets her way and the franchise is awarded to the firm promising to pay the largest franchise fee, what price and output will result? What will be the size of the annual franchise fee?