Part B

Consider a monopoly that faces market demand $\backslash (\backslash$mathrm$\{$P$\}=80-2\backslash$mathrm$\{$Q$\}\backslash )$ and has a total cost function $\backslash (\backslash$mathrm$\{$TC$\}=\backslash )\backslash (3$ Q$^\{2\}\backslash ).$

$($i$)$ What are the profit maximizing price and output level of this monopoly? Show all the steps of calculation.

$($ii$)$ Based on your answers in $($i$),$ what is the profit amount for this monopoly? Show all the steps of calculation.

$($iii$)$ What are the price and output level that maximize social surplus? Show all the steps of calculation.