Suppose Comcast $($C$)$ and Verizon $($V$)$ have a constant $\backslash (\backslash$mathrm$\{$MC$\}=\backslash$mathrm$\{$AC$\}=\backslash$$ $20\backslash )$ per customer connected to their internet network. The market $($inverse$)$ demand curve for basic internet service is given by:

$\backslash [$

$\backslash$begin$\{$array$\}\{$l$\}$

$\backslash$mathrm$\{$P$\}=80-2\backslash$mathrm$\{$Q$\}\backslash \backslash$

$\backslash$mathrm$\{$Q$\}=\backslash$mathrm$\{$q$\}\_\{\backslash$mathrm$\{$c$\}\}+\backslash$mathrm$\{$q$\}\_\{\backslash$mathrm$\{$v$\}\}$

$\backslash$end$\{$array$\}$

$\backslash ]$

A$)$ Find the Cournot$-$Nash equilibrium output, price and profit for each firm

B$)$ Find the output, price, and profit for each firm if the two were to collude

C$)$ Suppose now Comcast is a Stackelberg leader. Find each firm's output, price, and profit

D$)$ Find the output, price, and profit for each firm if they were to compete on price instead of quantity.